ANALYSIS OF A STRATEGY TO FORECAST SCHOOL DISTRICT
FISCAL HEALTH IN TEXAS
by
WILLIAM H. MAURER, B.S. in Ed., M.Ed.
A DISSERTATION
IN
EDUCATION
Submitted to the Graduate Faculty of Texas Tech University in
Partial Fulfillment of the Requirements for
the Degree of
DOCTOR OF EDUCATION
Approved
Accepted
August, 1988
ACKNOWLEDGMENTS
I wish to recognize and thank Dr. William Sparkman who
encouraged me to enter doctoral studies. Without his
guidance and support, I would not have been able to complete
this project. Appreciation is extended to members of the
dissertation committee. Dr. David Welton, Dr. John Champlin,
Dr. Thomas Irons and Dr. Paula Lawrence. Special thanks
also are extended to Penny Taulman, who typed this manu
script, and to Robert Leung, who offered his skills in
computer programming.
Special appreciation goes to my wife, Patricia
Alexander Maurer, and our daughter, Sarah Elizabeth Maurer,
for their faithful love, support, patience and under
standing. During the two years of research and writing,
they made many sacrifices that enabled me to complete my
studies.
11
TABLE OF CONTENTS
ACKNOWLEDGMENTS ii
LIST OF TABLES V
LIST OF FIGURES viii
CHAPTER
I INTRODUCTION 1
Statement of the Problem 1 Delimitations 3 Limitations 4
Justification for the Study 4 Assumptions 6 Definition of Terms 6 Procedures 8 Organization of the Research Report 10
II REVIEW OF RELEVANT RESEARCH AND LITERATURE 11
Planning the School Budget 11 Fiscal Strain 13 Forecasting Techniques 15 Studies of School District Fiscal Health ... 18 Identification of Variables 24 Summary 30
III PROCEDURES AND PRESENTATION OF THE DATA , 32
Source of the Data 32 Sorting the Data and Identifying the Variables 33 Statistical Procedures 36 Analysis of the Data 61
IV PRESENTATION AND ANALYSIS OF DATA 66
Discussion of Research Questions 67
111
V SUMMARY, MAJOR FINDINGS, CONCLUSIONS AND RECOMMENDATIONS 80
Summary 80 The Problem of the Study 81 Procedures 81
Major Findings 82 Conclusions 91 Recommendations 92
REFERENCES 94
APPENDICES
A TABLE A.l CORRELATION MATRIX 1980-1981 INDEPENDENT VARIABLES 1981-1982 DEPENDENT VARIABLE ALL SCHOOL DISTRICTS 97
B TABLE B.l CORRELATION MATRIX 1981-1982 INDEPENDENT VARIABLES 1982-1983 DEPENDENT VARIABLE ALL SCHOOL DISTRICTS 104
C TABLE C.l CORRELATION MATRIX 1982-1983 INDEPENDENT VARIABLES 1983-1984 DEPENDENT VARIABLE ALL SCHOOL DISTRICTS H I
IV
LIST OF TABLES
2.1 VARIABLES 26
3.1 NUMBER OF SCHOOL DISTRICTS INCLUDED IN THE STUDY 34
3.2 MEAN AND STANDARD DEVIATION, 1980-1981 INDEPENDENT VARIABLES, 1981-1982, DEPENDENT VARIABLE, ALL SCHOOL DISTRICTS, N=979 37
3.3 MEAN AND STANDARD DEVIATION, 1981-1982 INDEPEDENT VARIABLES, 1982-1983 DEPENDENT VARIABLE, ALL SCHOOL DISTRICTS, N=979 39
3.4 MEAN AND STANDARD DEVIATION, 1982-1983 INDEPENDENT VARIABLES, 1983-1984 DEPENDENT VARIABLE, ALL SCHOOL DISTRICTS, N=978 41
3.5 MULTIPLE REGRESSION SUMMARY TABLE 1980-1981 INDEPENDENT VARIABLE 1981-1982 DEPENDENT VARIABLE, ALL SCHOOL DISTRICTS 45
3.6 MULTIPLE REGRESSION SUMMARY TABLE 1980-1981 INDEPENDENT VARIABLE 1981-1982 DEPENDENT VARIABLE, FIRST QUARTILE 46
3.7 MULTIPLE REGRESSION SUMMARY TABLE 1980-1981 INDEPENDENT VARIABLE 1981-1982 DEPENDENT VARIABLE, SECOND QUARTILE 47
3.8 MULTIPLE REGRESSION SUMMARY TABLE 1980-1981 INDEPENDENT VARIABLE 1981-1982 DEPENDENT VARIABLE, THIRD QUARTILE 48
3.9 MULTIPLE REGRESSION SUMMARY TABLE 1980-1981 INDEPENDENT VARIABLE 1981-1982 DEPENDENT VARIABLE, FOURTH QUARTILE 49
3.10 MULTIPLE REGRESSION SUMMARY TABLE 1981-1982 INDEPENDENT VARIABLE 1982-1983 DEPENDENT VARIABLE, ALL SCHOOL DISTRICTS 50
V
3.11 MULTIPLE REGRESSION SUMMARY TABLE 1981-1982 INDEPENDENT VARIABLE 1982-1983 DEPENDENT VARIABLE, FIRST QUARTILE 51
3.12 MULTIPLE REGRESSION SUMMARY TABLE 1981-1982 INDEPENDENT VARIABLE 1982-1983 DEPENDENT VARIABLE, SECOND QUARTILE 52
3.13 MULTIPLE REGRESSION SUMMARY TABLE 1981-1982 INDEPENDENT VARIABLE 1982-1983 DEPENDENT VARIABLE, THIRD QUARTILE 53
3.14 MULTIPLE REGRESSION SUMMARY TABLE 1981-1982 INDEPENDENT VARIABLE 1982-1983 DEPENDENT VARIABLE, FOURTH QUARTILE 54
3.15 MULTIPLE REGRESSION SUMMARY TABLE 1982-1983 INDEPENDENT VARIABLE 1983-1984 DEPENDENT VARIABLE, ALL SCHOOL DISTRICTS 55
3.16 MULTIPLE REGRESSION SUMMARY TABLE 1982-1983 INDEPENDENT VARIABLE 1983-1984 DEPENDENT VARIABLE, FIRST QUARTILE 56
3.17 MULTIPLE REGRESSION SUMMARY TABLE 1982-1983 INDEPENDENT VARIABLE 1983-1984 DEPENDENT VARIABLE, SECOND QUARTILE 57
3.18 MULTIPLE REGRESSION SUMMARY TABLE 1982-1983 INDEPENDENT VARIABLE 1983-1984 DEPENDENT VARIABLE, THIRD QUARTILE 58
3.19 MULTIPLE REGRESSION SUMMARY TABLE 1982-1983 INDEPENDENT VARIABLE 1983-1984 DEPENDENT VARIABLE, FOURTH QUARTILE 59
3.20 TOTAL R^ VALUES 63
3.21 INDEPENDENT VARIABLES WITH RSQ CHANGE GREATER THAN OR EQUAL TO .01 64
VI
3.22 MEANS AND STANDARD DEVIATIONS OF CASH BALANCE 65
5.1 INDEPENDENT VARIABLES WITH R^ CHANGE GREATER THAN OR EQUAL TO .05 85
5.2 FREQUENCIES OF INDEPENDENT VARIABLES WITH R^ CHANGE GREATER THAN OR EQUAL TO .05 THAT OCCURRED IN MORE THAN ONE MODEL 89
A.l CORRELATION MATRIX 1980-1981 INDEPENDENT VARIABLES 1981-1982 DEPENDENT VARIABLE ALL SCHOOL DISTRICTS 98
B.l CORRELATION MATRIX 1981-1982 INDEPENDENT VARIABLES 1982-1983 DEPENDENT VARIABLE ALL SCHOOL DISTRICTS 105
C.l CORRELATION MATRIX 1982-1983 INDEPENDENT VARIABLES 1983-1984 DEPENDENT VARIABLE ALL SCHOOL DISTRICTS 112
Vll
LIST OF FIGURES
4.1 FREQUENCIES OF VARIABLES THAT ARE INCLUDED IN THE MODELS 70
4.2 VARIABLES INCLUDED IN THE MODELS FOR ALL SCHOOL DISTRICTS, FIRST QUARTILE AND FOURTH QUARTILE 75
Vlll
CHAPTER I
INTRODUCTION
Statement of the Problem
Legal mandates, constrained public funds, and increased
public demands for efficient management of our schools
require that planning be an integral component of the school
budgeting process. Forecasting school district fiscal
health is an essential part of the planning process. In the
final analysis, the school budget is "the translation of
educational needs into a financial plan..." (Candoli et al.,
1984, p. 127).
Fiscal health may be defined in terms of absolute
fiscal health or relative fiscal health (Smith, 1985) .
Texas identifies a school district as being fiscally healthy
if its ending fund balance is $0.00 or more. A deficit fund
balance is illegal according to state law (Texas Education
Code, 23.45b, 1978). However, authorities in education
finance advocate that a district should maintain a balance
or reserve equal to one to three months of expenditures
(Gaylord, 1983; Roland, 1986; Walker, 1986). If a budget
does not reflect fiscal health, the school district will be
less likely to meet the needs of its students. Likewise, it
can be assumed that a school district with a higher level of
fiscal health or higher cash balance, is more able to meet
1
the needs of its students than a school district with a
lower level of fiscal health or lower cash balance. Whether
it does or not is another question.
A part of budget planning and control is the local
education agency's assurance that revenues are equal to or
greater than expenditures because the legal mandate in Texas
requires that school districts -operate on a cash basis.
Decision makers at the local level prepare school district
budgets and bear the greatest responsibility for the alloca
tion of limited financial resources. Research efforts that
can provide assistance to local districts in forecasting
budget needs have been limited. A direct causal relation
ship has not been established between certain local school
district characteristics and the fiscal health of school
districts.
This study attempted to answer a number of questions.
First, is school district fiscal health predictable?
Second, what fiscal indicators, subject to the control of
local decision makers, can be used to forecast school
district fiscal health? Third, do different indicators have
predictive significance for school districts with a higher
level of fiscal health than for those school districts with
a lower level of fiscal health? Finally, does the
methodology employed in this study provide a viable strategy
for differentiating levels of school district fiscal health?
This study included 66 specific variables, deemed as
independent, from the area of local revenue, local
expenditures by function, and local tax data, which are
found on the Texas Education Agency Official Budget for
Texas Public Schools. Stepwise multiple regression was used
as the primary statistical procedure to obtain predictive
values (Nie et al., 1975; Hull and Nie, 1981). The
independent variables were regressed against ending fund
balance, the dependent variable.
Delimitations
1. The population consisted of all public school
districts in the State of Texas, excluding state-operated
schools and school districts serving fewer than twelve
grades.
2. Data were derived from summary reports submitted
on the Texas Education Agency Official Budget for Texas
Public Schools.
3. Data were included for the years 1980-1981,
1981-1982, 1982-1983, 1983-1984, prior to the reforms of
1984. Computerized data were unavailable from Texas Educa
tion Agency for the 1984-1985 and 1985-1986 school years.
4. Only indicators that are subject to control by
local decision makers were examined.
5. Quantitative measures were used as opposed to
qualitative measures.
Limitations
1. The number of school districts varied during the
years selected for the study because of the consolidation or
creation of school districts.
2. Texas Education Agency revised the budget docu
ments during the years selected for this study; therefore,
specific budget items vary from year to year.
3. While some independent variables were identified
on the basis of justifications provided by the literature or
authorities in the field, some a priori decisions were made
concerning other variables that were included in the study.
4. This correlational study, while both descriptive
and inferential, cannot demonstrate cause and effect.
5. This study did not examine economic conditions
such as employment, sales and property values.
6. This study did not examine qualitative measures of
fiscal health.
7. Results of this study cannot be generalized to
other states because data were confined to Texas.
Justification for the Study
Costerison (1984) identified major causes of fiscal
stress on school budgets. These include declining enroll
ment, voter resistance to tax increases, inflation, declin
ing state and federal aid, and employee demands. In a
period of fiscal retrenchment, school budget officers need
to make decisions which will protect the fiscal health of
their organizations. Traditional research on fiscal health
has focused on demographic variables and factors relating to
state funding formulas (Lee, 1983). The value of such
research to local budget officers is limited because it
reports on factors beyond their control. There is, conse
quently, a real need for research which gives the local
school administrator predictive control over local school
district fiscal health (Hentshcke and Yagielski, 1982a).
In Texas the fiscal burden on local school districts is
increasing (Jordan, 1985) . From 1973-74 to 1983-84 average
per pupil expenditures, not adjusted for inflation, have
increased from $910.00 to $2,960.00. Local contribution to
the total school budget increased from 41.5 percent to 46.4
percent during that same time period. This shift means that
local school administrators must assume a more proactive
responsibility for efficient use of available resources.
They can no longer depend on money from state and federal
sources to bridge the gap between mandates for new programs
and their costs. This study attempted to identify specific
indicators that local school administrators can control to
improve fiscal health.
Wegenke and Smith (1983) have identified characteris
tics of useful fiscal data. They suggest that fiscal data
must be translatable into understandable language in order
to be useful. In addition, useful data are described as
being credible throughout the term of the budget, timely and
subject to change.
This study seeks to increase the usefulness of budget
data available to local school administrators because
it defines that data in terms of its credibility or lack of
credibility to produce timely change.
Assumptions
1. Standardized data and other data provided to the
Texas Education Agency are accurate.
2. Fiscal data selected as independent variables can
be used as indicators of fiscal health.
3. Fiscal health can be influenced or controlled by
local school district administrators.
4. Fiscal health can be quantitatively defined as
cash balance.
5. School district decision making is more accurately
described as consumer behavior rather than producer behav
ior.
Definition of Terms
Budget is a plan of financial operation embodying an
estimate of proposed expenditures for a given period or
purpose and the proposed means of financing them.
Expenditures are total charges incurred for current
expense, capital outlay and debt service.
7
Fiscal data include quantitative information such as
local property taxes, total instructional payroll costs,
supplies and materials, tuition and fees that are taken from
the official school budgets.
Fiscal health, for purposes of this study, is defined
as the total fund balance that is indicated on the official
budget. School districts with higher fund balances are
fiscally healthier than school districts with lower fund
balances.
Fiscal indicators are budget items listed on the Texas
Education Agency Official Budget for Texas Public Schools
that can be controlled by local school district administra
tors .
Fiscal strain, as used in this study, is synonymous
with fiscal stress, conditions under which school district
decision makers are forced to purchase fewer or less desir
able inputs than in the past due to declining revenues,
increasing costs or a combination of both.
Function classification as applied to expenditures
refers to an activity or service aimed at accomplishing a
certain purpose or end; for example, instruction, instruc
tional administration, plant maintenance and operation.
Local revenue includes revenue generated from real and
personal property taxes, services to other local education
agencies, tuition and fees from patrons, within state
8
transfers, co-curricular enterprises and other local
sources.
Object classication as applied to expenditures refers
to an article or service received; for example, payroll
costs, purchased and contracted services, materials and
supplies.
Refined average daily attendance is the aggregate days
attendance of eligible students divided by the number of
days that school is in session. It is equal to the gross
average daily attendance less ineligible average daily
attendance.
Tax is a compulsory charge levied by a governmental
unit for the purpose of financing services performed for the
common benefit.
Procedures
This study was conducted using the following proce
dures:
1. Phase one of the study consisted of two tasks to
determine the feasibility of the project. Previous research
was examined in a review of the relevant school finance and
school budget literature. Texas Education Agency was con
tacted to determine that data were available.
2. Phase two of the study consisted of sorting the
data to extract independent and dependent variables and the
school districts that were included. Independent variables
consisted of budget data selected from tax information,
expenditures by function and local revenues. The dependent
variable was ending fund balance. Data files had to be
constructed in order to prepare the data for running the
stepwise multiple regression program. Independent and
dependent variables for all school districts in the State of
Texas that offered grades kindergarten through twelve were
identified. For each school district selected data from the
official budget report were divided by the refined average
daily attendance of the school district as means of provid
ing standard units for comparison. School districts were
ranked according to end of year fund balance divided by
refined average daily attendance and sorted into quartiles.
3. In phase three of the study, data for the whole
population and for quartiles were subjected to stepwise
multiple regression: 1980-1981 independent variables were
regressed against fiscal health in 1981-1982; 1981-1982
independent variables were regressed against fiscal health
in 1982-1983; 1982-1983 independent variables were regressed
against fiscal health in 1983-1984. Longitudinal data were
used because budget decisions to determine tax rates,
expenditures and revenues are made in the year preceding the
actual implementation of the budget. The major purpose of
this study was to analyze a strategy used to forecast school
district fiscal health.
10
4. Phase four of the study consisted of analyzing and
summarizing the data for presentation and analysis. Results
of multiple regressions were compared across quartiles and
across years.
Organization of the Research Report
This research is reported in five chapters. Chapter I,
the introduction, includes the statement of the problem,
delimitations, limitations, justification for the study,
assumptions, definition of terms, procedures and organiza
tion of the research report. Chapter II presents a review
of relevant literature and research. Chapter III consists
of the procedures and presentation of the data. Chapter IV
contains the findings and analysis of the data. Chapter V
presents a summary, major findings, conclusions and
recommendations.
CHAPTER II
REVIEW OF RELEVANT RESEARCH AND LITERATURE
This chapter presents a review of the literature
related to forecasting school district fiscal health. It
presents a brief discussion of managing and planning the
school budget, and discusses fiscal strain and its causes.
It identifies forecasting techniques and the consumer
approach to school district decision making and presents
summaries of pertinent research that focuses on forecasting
school district fiscal health. A summary concludes Chapter
II.
Planning the School Budget
In times of economic turbulence, public schools as well
as the private business sector have been subjected to finan
cial hardship. School district decision makers face the
dilemma of reconciling a decline in revenues while maintain
ing or even expanding programs. The public calls on school
district administrators to reduce costs while demanding that
the school improve the basic skills of pupils, expand pro
grams and provide more opportunities for special student
populations (Chabotar, 1987) . The problem is exacerbated as
staffs request higher salaries and more benefits (Hartman
and Rivenburg, 1985) , and by state and federal mandates to
implement new programs without providing additional funds to
11
12
cover the costs of expanding the school program. Inflation
takes its toll on budgets even when there is no demand for
growth and expansion. In its national annual survey, the
National School Boards Association reported that in 1981,
1982 and 1983 the greatest concern of school board members
was lack of funding (Smith, 1985).
The budget is the fiscal plan that reflects the educa
tional needs of the school district (Candoli, et al., 1984).
It operationalizes philosophies, priorities and strategies
and is the strongest measure of the priorities of local
education agencies (Hartman and Rivenburg, 1985). All
accepted definitions of budgeting include planning as a
component part, in addition to receiving funds, spending
funds and evaluating results (Burrup and Brimley, 1982).
Decisions at the local level are subject to the idiosyn
crasies of the school district such as local politics,
economic and social conditions, beliefs, attitudes and
priorities of the decision makers. However, the budget does
provide a common basis for making comparisons, and is the
strongest measure of comparison since it closely corresponds
with operations of the school district (Hartman and
Rivenburg, 1985). In states such as Texas, which mandate a
uniform format for reporting the school district budget,
these comparisons have the potential for predictive
applications.
13
Forecasting while focusing on immediate fiscal concerns
is an important part of the fiscal planning process (Wegenke
and Smith, 1983). Prudent decisions affecting the budget
consider past, present and projected trends. This process
requires that a school district establish financial review
and analysis procedures. Wegenke and Smith also specify
that fiscal data be understandable, credible, timely and
part of the overall financial picture making it subject to
change in the future. Because a budget defines fiscal
limits, local decision makers must manipulate those limits
to maximize their levels of consumption.
Fiscal Strain
The fiscal health of a school district can range from a
negative budget balance, which is illegal in Texas, to a
high budget balance. Dickmeyer (19 79) defined fiscal health
as the "ability to pay bills" (p. 161) . A school district
that is considered to be fiscally unhealthy can be described
as experiencing fiscal strain or fiscal stress. It is
difficult to define fiscal strain operationally since it is
a matter of degree; a relative term. Hentschke and
Yagielski (1982a) defined fiscal strain as the condition
that forces decision makers to purchase inputs that are less
desirable than the inputs that are currently being
purchased; that is, the combination of resources for next
year are less preferred. Zerchykov, et al. (1982) defined
14
fiscal strain as organizational shrinkage. Fiscal strain
reduces the discretion of school boards. Costerison (1984)
reported that the State of Indiana defines fiscal strain as
the condition under which a school district cannot carry out
its educational duty without emergency aid; and, that
Pennsylvania defines fiscal strain using various indicators
that range from inability to meet payroll to default on bond
payments.
It is important that planners be cognizant of causes of
fiscal strain because decisions should be based on qualita
tive as well as quantitative considerations. Lee (1983)
specified four major causes of fiscal strain. They included
decline in public confidence, unemployment, fewer voters
with school age children and declining enrollments.
Hentschke and Yagielski (1982a) added increasing prices of
inputs and changes in the input mix. Inflation, decreasing
state and federal revenues, increasing state and federal
mandates for new programs were added to the list by Hartman
and Rivenburg (1985) . Costerison (1984) expanded the list
of major causes to include 31 specific causes of fiscal
strain. Exogenous factors are listed above; however, the
local school district decision maker must exercise caution
not to introduce internal causes of fiscal strain such as
overspending, failing to adjust the tax rate, failing to
project student enrollment and staffing requirements.
15
Forecasting Techniques
Chabotar (1987) identified forecasting as a critical
issue, but cautioned that forecasting should be used as one
input in the decision making process along with economic and
political factors. He confirmed, along with the studies of
Lee (1983), Smith (1985) and Ward (1985), that forecasting
can be used effectively by school district decision makers
to make fiscal decisions and that there is a great need for
linking the annual budget to long-term fiscal plans.
Chabotar identified four forecasting techniques. The
first is subjective judgment, which is not a quantitative
procedure. It is based upon the expertise and experience of
the forecaster. One example is the Delphi panel. Causal
models constitute a second forecasting technique. These
types of forecasts are based upon relationships between
revenue, expenditures and independent variables selected by
the forecaster. Examples of this type are ratio methods,
multiple correlation, regression and path analytic models.
Extrapolation is the third technique. This type of forecast
predicts the future based upon revenues and expenditures
continuing at the same rate. It depends upon using stable
data such as birth rates, economic conditions and policies.
This technique assumes the existence of a particular trend
and that the trend will continue through the years of the
forecast. Chabotar included normative approaches as a
fourth technique although he contended that they really are
16
not forecasts. Instead they are descriptions of scenarios
in terms of what should be. Predictions may or may not
reflect historical trends. Normative approaches may use
statistical relationships and extrapolations for background
information. Gaylord (1983) provided caveats to
forecasting: forecasting is a conservative approach since
it cannot predict sudden and unanticipated deviations from
historical trends; it is not causal; and it requires
consistent and precise data.
School district decision making is more accurately
described as consumer rather than producer behavior because
budget decisions are a function of the interactions between
preferences and budget constraints (Hentschke and Yagielski,
1982b). These authors described three characteristics of
decision making that justify this conclusion. First, the
behavior of local decision makers reveals preferences in
dealing with theoretically unlimited wants and budget
constraints. The budget reflects what was given up in some
items in order to gain other items; that is, the consid
eration of opportunity costs. Second, the principle of
diminishing marginal utility is applicable. The satis
faction gained from the first unit of a good or service is
greater than the satisfaction that is derived from addi
tional units. Third, the consumer model suggests causes and
descriptions of fiscal strain: increasing, maintaining or
decreasing levels of consumption. Hentschke and Yagielski
17
(1982a) also indicated that the consumer model assumptions
are more theorectically valid and empirically descriptive
than the assumptions of the producer model which assumes an
agreed upon definition of quality and a constant level of
the quality of the output of schooling. The consumer model
allows a situation to be described as fiscal strain even
when there is an increase in the total budget. Thomas
(1980) supported the application of the consumer approach.
He stated that the producer approach is inadequate because
it is based on the factory model which oversimplifies the
decision making behavior. It fails to recognize and con
sider the "multiplicity of decision makers, the diversity of
goals, the complex nature of educational inputs and intri
cate relationships ... between resources and outcomes" (p.
252) . It is very difficult to determine the utility of
inputs. Alternatives are not comprehensive nor of equal
financial magnitude or consequence (Hentschke and Yagielski,
1982b).
The literature and research cited above provide justi
fication for choosing multiple linear regression and corre
lation as a strategy for forecasting school district fiscal
health. Chabotar (1987) indicated that using regression and
correlation statistics to create a causal model is the best
forecasting technique. Its credibility is based on the use
of hard data and the statistical power of the procedures.
Ward (1985) used multiple regression to create a causal
18
model using bond ratings. Ward's model exhibited 85%
accuracy in predicting presence or absence of fiscal strain.
Studies of School District Fiscal Health
Murphy (1980) tried to determine if financial, demo
graphic, economic, electoral or environmental variables
could be identified that would characterize school districts
in Ohio that were financially troubled or that were experi
encing fiscal strain. He identified financially troubled
districts as those that were forced to close between 1976
and 1978, and districts that received emergency loans from
the state. All other school districts were considered to be
fiscally healthy. The study used analysis of variance to
differentiate variables that distinguished the two groups of
school districts. Murphy concluded that:
1. Financially troubled districts are primarily classified as central city and rural.
2. Over-staffing is not a factor contributing to the fiscal problems of financially troubled districts.
3. Financially troubled districts are concentrated in the northern and southern sections of the state.
4. Financially troubled districts are spread over more geographical space. This difference was not translated into significantly higher per pupil transportation expenses.
5. Financially troubled districts are characterized by high proportions of special cost students.
6. Financially troubled districts cannot be characterized as declining enrollment districts.
19
7. Financially troubled districts can be characterized as low fiscal capacity districts in terms of having lower median family income. There was not a significant difference when fiscal capacity was defined in ... equalized assessed valuation per pupil.
8. Financially troubled districts had a significantly lower equalized millage rate. Unequalized and debt millages were not significantly different between financially troubled and non-troubled districts.
9. Financially troubled districts are low revenue districts. Almost all the difference is in locally raised revenue.
10. Financially troubled districts are characterized as high health and interest expense districts and as low instruction, general control, and plant maintenance expense districts.
11. Financially troubled districts appear to pass fewer requests for millage.
(Murphy, 1980, pp. 177-184)
The variables in Murphy's study that met the criteria
of being subject to change or under the control of local
decision makers are particularly relevant to the current
study. Murphy concluded that the level of staffing was not
a factor that contributed to fiscal strain. However,
personnel costs were significant because they constituted
the largest portion of a school district's expenditures due
to the labor intensive nature of schooling. Murphy also
noted that locally raised revenue accounted for most of the
difference between financially troubled and non-troubled
districts. Financially troubled school districts were
characterized by high health and interest expenses while
20
expenditures for instruction, general control and plant
maintenance were low.
Berny attempted to identify the variables that could be
used to discriminate between financially troubled and
non-troubled rural school districts using a causal-
comparative research method. Multiple discriminant analysis
was conducted to determine the relative influence of six
fiscal and demographic variables: geographical size,
special cost children, fiscal capacity, tax effort, total
general revenue and excess staff. Financially troubled
school districts were those districts that closed and those
districts that applied for preclosing audits. Berny
concluded that:
1. There was no discernible statistical difference between the rural districts defined as financially troubled and non-troubled for any of the years studied on any of the variables tested.
2. None of the selected variables possessed a higher discriminating capacity than any of the others.
3. When examined from a nonlinear point of view, there was no interactive or cumulative effect of the selected variables that exceeded the effect of any one alone.
(Berny, 1982, p. 480)
It is significant that the variables investigated in
Berny's study did not discriminate troubled from non-
troubled rural school districts. It appears that the
variables were not relevant to the question studied.
However, his results contradicted certain conclusions of
21
Murphy (1980) who used a larger sample that included rural,
urban and suburban districts. Murphy found that financially
troubled districts were characterized by large geographic
area, high proportions of special cost students, low fiscal
capacity, low tax effort and low revenue. Berny agreed with
Murphy (1980) that staffing levels did not discriminate
levels of fiscal health.
Lee (1983) attempted to predict fiscally distressed
school districts using ratio analysis. School districts
that received emergency state loans in 1981 were identified
as experiencing fiscal distress; 36 of the 615 school
districts in Ohio were eliminated from the study because of
problems with data. Lee analyzed financial and staffing
ratios using multiple discrimination analysis and correla
tion. He used the qualitative dependent variable of dis
tressed or not distressed. Five ratios, which displayed
predictive significance, were used in the fiscal distress
predictive model included the following:
1. True Day's Cash Ratio = (12/31/80 Cash Balance-Encumbrances) / (1980 Current Expenditures/365 days)
2. True Ending Cash Balance Ratio (12/31/80 Cash Balance-Encumbrances) / (1980 Total Operating Funds)
3. Salaries/Operating Ratio = 1980 Salaries & Wages / 1980 Total Operating Funds
4. Salaries-Fringes/Operating Ratio = 1980 Salaries & Wages + Fringe Benefits / 1980 Total Operating Funds
22
5. Investment Earnings Ratio = 1980 Investment Earnings / 19 80 Total Operating Funds
Lee concluded that:
1. Financial ratios have the ability to forecast fiscal distress as early as one year in advance. ... historical data were able to forecast over 90 percent of the districts that eventually experience financial problems.
2. Liquidity ratios demonstrated strength in forecasting financial problems in school districts. Unlike private business enterprise ... education ... is more sensitive to cash balance fluctuations.
3. Elementary/secondary institutions are labor intensive. In this study, the percent of operating funds spent for salaries, wages and fringe benefits proved to be potent indicators of impending fiscal doom.
4. Although not the primary cog in the fiscal distress model, the Investment Earnings ratio enhances the accuracy of the model.
5. ... expenditures and revenues per pupil have little or no value in forecasting fiscal distress. These conclusions do not recommend the banishment of per pupil expenditure data, but caution their use in respect to fiscal health.
6. There were no relationships found between elevated staffing levels and fiscal distress.
7. Trend ratios, measuring changes between the beginning and ending fiscal periods of 1980 did not demonstrate any predictive significance in the Fiscal Distress model.
8. The borrowing or loan repayment ratios were not found to have any predictive relationships with fiscal distress.
(Lee, 1983, pp. 261-262)
Authorities in school finance have labelled Lee's study
a milestone in predictive research (Lee, 1983). Conclusions
23
4, 5, 6 and 8 are of interest since they discuss variables
used in this study. Lee's study was the impetus for Smith's
work.
Smith (1985) based his forecasting study on Lee's
research. Smith redefined fiscal health, the dependent
variable, in quantitative terms, defined the variables using
raw data, examined more areas and analyzed a time frame of
three years rather than one year. His population consisted
of all 616 school districts in Ohio. Independent variables
included specific indicators in the categories of liquidity,
salaries and capital projects funds. Smith concluded that:
1. ... school district fiscal health lends itself to considerable predictability.
2. ... predictability improves with shorter prognostic periods.
3. ... predictive models, as developed in this study, are highly temporal — that is, they are unique to each fiscal period.
4. ... the consistent nature gf the findings, particularly the pattern of R values and the rankings ... demonstrate the general validity for the approach taken by this study.
5. ... a relatively few indicators, when considered together with all the indicators examined, contribute to the predictability of school district fiscal health. The five most important, in descending order, are: (1) personnel costs; (2) local receipts; (3) liquidity; (4) purchased services; and (5) investment earnings.
6. ... some of the indicators examined are weak predictors of school district fiscal health, when considered together with the other variables examined. They are, in descending order of importance: (1) material, supply and textbook expenditures; (2) capital outlay expenditures; (3)
24
voted and effective millage; and (4) capital project fund indicators.
7. ... indicators maintain their relative importance irrespective of the prognostic period.
(Smith, 1985, pp. 139-140)
This study builds upon Smith's work. Raw data were
used as independent variables; levels of fiscal health have
been identified in order to make comparisons within each
year and across years. The techniques were applied to the
present study of school district budgets in Texas using a
function/object type of budget format.
Identification of Variables
The selection of independent variables was based
primarily upon criteria established by Smith (1985) which
require that:
1. Its numerical value must be capable of being changed by local decision makers.
2. Its potential usefulness (in making forecasts) is indicated by relevant literature; and
3. The data used to compute it must be readily available and accurate.
(Smith, 1985, p. 84)
In addition to Smith's criteria, fiscal indicators were
selected as independent variables because the best projec
tions are based upon the lowest level of detail; that is,
the most specific information that is available, not lump
sums (Chabotar, 1987). Also, these independent variables
25
are used consistently throughout the state, are relatively
easy for all school districts to provide, and are compre
hensible and usable in terms of budget decisions ("Is Your
Budget in Tune?", 1981).
Research studies cited above validate the variables
that were selected for this study. Those studies were
conducted in other states; therefore, the variables do not
have exactly the same labels as those that are used in the
Texas budget format. Some of the variables used by Murphy
(1980) were tax rate, locally-raised revenue, health
expense, plant maintenance and personnel costs. Berny
(1982) included fiscal capacity and tax effort. Lee (1983)
constructed ratios using cash balance and expenditures.
Smith (1985) included personnel costs, local receipts,
material, supply and textbook expenditures and local
receipts.
Table 2.1 lists and defines the independent variables
and indicates the years in which they are found in the
budgets. A total of 66 variables was identified and used in
this study. Texas Education Agency revised the budget
reporting form during the years included in this study;
therefore, the same fiscal indicators are not found in each
year, although the budget format remained the same. The
major revisions that affected this study were made after
1981-1982, when tax data categories for maintenance taxes
and debt service taxes were combined into totals for the
fiscal years 1982-1983 and 1983-1984.
26
Fiscal Year
1980- 1981- 1982-1981 1982 1983
X X
Maintenance Taxes
1983-1984
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
Table 2.1
VARIABLES
Variable Identification and Explanation
VI Balance of funds
Vll Assessed valuation
V12 Tax rate/$100
V13 Gross taxes assessed
V14 Discounts and adjustments
V15 Net taxes assessed
Vl6 Estimated uncollectible current taxes
V17 Net taxes collectible on current year's levy
V18 Total current year deferred revenue (...to be collected in subsequent years)
VI9 Current year tax revenue
V20 Prior years tax revenue
V21 Penalties, interest and other tax revenue
Debt Service Taxes
X
X
X
X
X
X
X
X
X
V22 Assessed valuation
V23 Tax rate/$100
V24 Gross taxes assessed
V25 Discounts and adjustments
X X
X X
X X
27
TABLE 2.1 (continued)
^ ^ V26 Net taxes assessed
^ ^ V27 Estimated uncollectible current taxes
X V28 Net taxes collectible on current year's levy
V29 Total current year deferred revenue (...to be collected in subsequent years)
V30 Current year tax revenue
V31 Prior years tax revenue
^ ^ V32 Penalties, interest and other tax revenue
Total Tax Data (Maintenance Plus Debt Service)
X V33 Total appraised value per tax roll
X V34 Total appraised value for school tax purposes
X V35 Calculated tax levy
X V36 Additional tax levy generated due to bond rate charged against exempted homestead property
X V37 Tax levy loss due to tax freeze
X V38 Other adjustments, and discounts
X V39 Net taxes assessed
Expenditures by Function
X X X V50 Instruction
X V51 Instructional computing
X X X V52 Instructional administration
28
TABLE 2.1 (continued)
X X X V53 Instructional resources and
media services
X X X V54 School administration
X X X V55 Instructional research and development
X X X V56 Curriculum and personnel development
X X X V57 Communications and dissemination
X X X V58 Guidance and counseling services
X X X V59 Attendance and social work services
X X X V60 Health services
X X X V61 Pupil transportation -regular
X X X V62 Pupil transportation -
exceptional children
X X X V63 C o - c u r r i c u l a r a c t i v i t i e s
X X X V64 Food s e r v i c e s
X X X V65 G e n e r a l a d m i n i s t r a t i o n
X X X V66 Debt s e r v i c e
X X X V67 P l a n t m a i n t e n a n c e and o p e r a t i o n
X X X V68 Facilities acquisition and
construction
X X X V69 Management (Data Processing)
X X X V70 Computer processing X X V71 Development (Data Processing)
29
TABLE 2 . 1 ( c o n t i n u e d )
X X X V72 I n t e r f a c i n g ( T e c h n i c a l
a s s i s t a n c e )
X X X V73 Community s e r v i c e s
Revenue from L o c a l and I n t e r m e d i a t e S o u r c e s
X X X V80 L o c a l m a i n t e n a n c e t a x
X X X V81 Debt s e r v i c e t a x
X X X V82 L o c a l r e v e n u e from s e r v i c e s t o o t h e r LEA's and ESC's
X X X V83 T u i t i o n and f e e s from p a t r o n s
X X X V84 T r a n s f e r s from w i t h i n t h e s t a t e
X V85 Transportation fees from patrons
X X
X X
X X
X X
X X
X V86 Enterprise funds
X V87 Other revenue from local sources
X V88 Revenue from intermediate sources
X V89 Non-revenue receipts (proceeds from bonds, loans, lease/purchases, etc.)
X V90 Revenues from outside the state
X V91 Transfers in
30
Consequently, the number of variables examined each year of
this study is less than 66. Variables were assigned numbers
arbitrarily; VI is the fund balance; Vll through V39 are tax
data; V50 through V73 are expenditures by function; and V80
through V91 are revenues.
Summary
Chapter II discussed the recent evolution of a rela
tively new area of school finance. The importance of con
tinuous planning was emphasized because the school budget
reflects educational needs and priorities and can be used as
a measure of comparison among school districts. Causes of
fiscal stress were identified along with forecasting techni
ques in order to facilitate the budget planning process. It
was discussed that school district budget planners take a
consumer approach to decision making. Studies by Murphy
(1980), Berny (1982), Lee (1983) and Smith (1985) indicated
that multiple regression and correlation techniques were
appropriate statistical procedures to use in this study.
These studies also identified criteria to use in selecting
variables. Tax data, expenditures by function, and revenue
subject to the control of local decision makers were
selected as variables for this study and divided by refined
average daily attendance to provide common units of
comparison. The methodology was selected based upon the
31
studies cited in this chapter and because of the structure
of the budget that is mandated by Texas.
CHAPTER III
PROCEDURES AND PRESENTATION OF THE DATA
The purpose of this study was to analyze a strategy for
forecasting school district fiscal health in Texas. Cash
balance was selected as the quantitative measure of school
district fiscal health, the dependent variable, and the
fiscal indicators of tax data, expenditures by function and
revenues divided by refined average daily attendance were
the independent variables. The goal of this study was to
determine if the relationships between the dependent vari
ables and the independent variables could be used to predict
fiscal health.
The purpose of this chapter is to describe the research
procedures. Phases of the study are outlined; the popula
tion is defined; statistical strategies are identified; and
data are presented.
Source of the Data
In phase one, fiscal data for the official budgets were
obtained from Texas Education Agency Division of Policy
Analysis. Master computer files included all fiscal data
that were submitted by each school district to the Texas
Education Agency, district names and identification numbers,
32
33
and refined average daily attendance for all school dis
tricts and Education Service Centers in the state.
Fiscal data were taken from the Texas Education Agency
Official Budget for Texas Public Schools for the fiscal
years 1980-1981, 1981-1982, 1982-1983 and 1983-1984.
Sorting the Data and Identifying the Variables
Phase two of the study consisted of sorting the data.
Variables were identified and data files were constructed.
Texas Education Agency provided dumps of their fiscal files
which included extraneous data that had to be eliminated.
The population for this study consisted of all school
districts in the State of Texas that offered programs for
grades kindergarten through twelve. Deleted from the study
were school districts that did not offer those grades and
Education Service Centers which were identified according to
information in the Texas Education Agency School Directory
for the years included in the study. As shown in Table 3.1,
the total number of school districts included in the study,
the N of cases, varies from year to year because school
districts were either consolidated or created. Differences
in the N of cases did not affect the results of the multiple
regressions because this study examined budget characteris
tics in general and not the fiscal performance nor budgets
of individual school districts.
34
TABLE 3.1
NUMBER OF SCHOOL DISTRICTS INCLUDED IN THE STUDY
1980- 1981- 1982- 1983-Quartile 1981 1982 1983 1984
1 245 245 245 245 2 245 245 245 245 3 245 245 244 245 4 244 244 244 245 Total N 979 979 978 979
35
A number of data files were set up in order to process
the data and to provide a means of checking the process.
The data files include the following information: names of
all school districts and their refined average daily
attendance listed by county-district identification number;
all school districts with all budget items included in the
study listed in order of county-district identification
number; all school districts ranked according to fund
balance divided by refined average daily attendance
(dependent variable); all school districts with all budget
items selected for this study divided by refined average
daily attendance and ranked according to fund balance
divided by refined average daily attendance; and, all school
districts with all dependent and independent variables
listed in order by county-district identification numbers.
Budget categories selected for use in this study were
divided by the refined average daily attendance. This
provided a common means of comparison. School districts
were ranked according to the dependent variable and the data
for each year were divided into quartiles so that compari
sons could be made among four levels of fiscal health within
each year and across years.
Statistical Procedures
Phase three of the study consisted of statistical
analysis of the data. The data files were organized to
36
facilitate the use of stepwise multiple regression. Statis
tical Package for the Social Sciences (Nie et al. 1975;
Hull and Nie, 1981) was employed using the facilities of the
Texas Tech University Academic Computing Services.
The first step in the statistical analysis of the data
was to generate descriptive statistics that were examined to
determine whether multiple regression procedures were appro
priate. The mean and standard deviation of dependent and
independent variables for all school districts, displayed in
Tables 3.2, 3.3 and 3.4 were generated along with
correlation matrices for all variables for all school
districts, which are located in Appendix A, Appendix B and
Appendix C. These statistics provide a preliminary
understanding of the data that were selected for the study.
Pearson product-moment correlations were calculated for all
possible pairs of dependent and independent variables.
Because no controls were made for the influence of other
variables, these are called zero-order correlations (Nie et
al. 1975).
TABLE 3.2
MEAN AND STANDARD DEVIATION, 1980-1981 INDEPENDENT VARIABLES, 1981-1982 DEPENDENT VARIABLES,
ALL SCHOOL DISTRICTS N = 979
37
VARIABLE
VI Vll V12 V13 V14 V15 V16 V18 V19 V20 V21 V22 V23 V24 V25 V26 V27 V29 V30 V31 V32 V50 V52 V53 V54 V55 V56 V57 V58 V59 V60 V61 V62 V63 V64 V65 V66 V67 V68 V69 V70
MEAN
518.715 125976.959
2.414 1001.284 10.644 990.640 19.520 971.120 945.612 16.676 3.944
126339.420 0.328
151.860 1.574
150.285 3.028
147.257 142.781 3.125 0.796
1289.235 23.664 35.742 105.178 1.008 0.096 0.207 34.499 1.723 13.970 124.580 3.194 49.469 18.224 266.287 161.739 290.020 248.929 0.264 0.321
STD. DEV.
752.814 237334.284
3.481 1051.052 27.935
1037.147 39.186
1024.908 1010.951 23.642 8.435
237286.628 0.528
173.009 5.667
170.845 4.919
169.306 166.265 4.726 3.678
460.413 42.810 28.115 59.733 11.934 4.146 1.389 39.134 5.424 32.569 98.852 14.240 48.369 44.175 214.863 171.176 271.208 797.294 4.763 3.254
38
TABLE 3 . 2 ( c o n t i n u e d )
VARIABLE MEAN STD. DEV,
V71 0.000 0.000 V72 0.017 0.483 V73 5.868 61.708 V80 966.233 1016.473 V81 146.702 167.781 V82 2.894 20.743 V83 2.846 6.106 V85 0.372 1.657 V86 3.168 18.179 V87 43.558 155.899 V88 18.898 63.339 V84 3.481 15.371 V90 0.158 4.831 V89 52.585 445.019
39
TABLE 3 . 3
MEAN AND STANDARD DEVIATION, 1 9 8 1 - 1 9 8 2 INDEPENDENT VARIABLES,
1 9 8 2 - 1 9 8 3 DEPENDENT VARIABLES, ALL SCHOOL DISTRICTS
N = 979
VARIABLE MEAN
VI Vll V12 V13 V14 V15 V16 V17 V18 V19 V20 V21 V22 V23 V24 V25 V26 V27 V28 V29 V30 V31 V32 V50 V52 V53 V54 V55 V56 V57 V58 V59 V60 V61 V62 V63 V64 V65 V66 V67 V68
628.047 236004.075
16.487 1142.359 11.274
1131.085 19.428
1111.656 30.751
1080.905 16.551 4.249
236601.623 2.362
176.065 1.822
174.243 3.172
171.071 5.698
165.372 3.481 6.734
1450.647 26.342 41.454 124.465 0.775 1.661 0.329 38.559 1.786 15.534 138.904 3.702 58.869 21.893 296.041 191.928 333.330 274.286
STD. DEV.
965.273 711478.493
23.440 1166.779
29.309 1151.273
30.269 1138.290
40.473 1128.079
28.973 8.432
711423.671 4.145
208.300 5.844
205.482 5.678
203.067 8.768
199.138 5.742 1.294
565.893 40.668 33.503 71.732 11.129
9.760 0.067
40.547 5.081
36.743 106.878
12.396 56.439 49.158
228.559 216.809 257.858 930.963
40
TABLE 3 . 3 ( c o n t i n u e d )
VARIABLE MEAN STD. DEV.
45.566 2.887 1.125 0.513
54.897 1133.702
200.718 29.569
7.014 61.279 22.423
122.032 72.118
9.748 547.921
V69 V70 V71 V72 V73 V80 V81 V82 V83 V84 V86 V87 V88 V90 V89
1.849 0.438 0.053 0.032 5.721
1103.705 169.587 4.325 3.487 5.224 4.526 51.357 20.795 0.454 67.128
41
TABLE 3.4
MEAN AND STANDARD DEVIATION, 1982-1983 INDEPENDENT VARIABLES, 1983-1984 DEPENDENT VARIABLES,
ALL SCHOOL DISTRICTS N = 978
VARIABLE MEAN STD. DEV.
VI V50 V51 V52 V53 V54 V55 V56 V57 V58 V59 V60 V61 V62 V63 V64 V65 V66 V67 V68 V69 V70 V71 V72 V73 V80 V81 V82 V83 V84 V86 V87 V88 V90 V91 V89 V33 V34 V12 V23
669.925 1591.870
2.833 29.128 45.652 139.761 0.714 2.084 0.445 42.288 2.029 16.956 145.628 4.331 96.985 181.620 307.741 207.628 355.756 310.063 0.184 0.938 0.361 0.022 5.647
1217.141 192.205 4.667 4.485 8.123
110.843 77.056 19.986 0.394 4.199 72.743
346473.771 291496.260
14.172 1.940
865.890 534.814
12.442 44.986 33.839 75.090 11.048
8.504 2.491
42.888 5.663
39.731 108.363
13.204 71.469 71.827
217.773 262.320 243.840 907.272
2.298 4.579
10.209 0.285
52.334 1207.168
246.312 23.245
8.850 35.570 88.024
145.264 71.780
7.671 32.156
446.868 948656.139 936934.602
21.130 3.541
42
TABLE 3 . 4 ( c o n t i n u e d )
VARIABLE MEAN STD. DEV.
1345.724 7.250
29.171 45.310
1323.975
V35 V36 V37 V38 V39
1466.868 1.169 18.537 16.835
1432.980
43
In the final phase of statistical analysis, data were
subjected to stepwise multiple regression which yielded
prediction equations (Cornett and Beckner, 1975; Kerlinger,
1973; Kim and Kohout, 1975) based on correlation. Multiple
linear regression was selected because this multivariate
procedure can be used to analyze effects of more than one
independent variable on a dependent variable. It is the
most useful and flexible method because any number of
continuous or categorical variables can be analyzed; and it
is appropriate for non-experimental variables to examine
within-group variance (Kerlinger, 1973).
The stepwise regression program examined each variable
that was selected for analysis. The computer entered one
variable at a time in single steps beginning with the
variable that explained the greatest amount of variance with
the dependent variable and continuing in descending order of
importance. Three options were used to determine which
variables were included in the regression equation generated
by the program (Nie, et al. 1975). The first option
permits the programmer to select or limit the number of
variables that may be included in the predictor list. The
second option is the determination of the minimum value of
the F ratio that the programmer will accept for variables to
be included in the equation. F ratios were computed for
independent variables not yet included. The F ratio was the
value that would be obtained if the variable were included
44
on the next step. The tolerance of an independent variable
was the third option. Tolerance is the proportion of the
variance of that variable not explained by the variables
already included.
The values of the options selected for this study
exceeded the default values. All variables were included in
the analysis. The F value was set at .05; the default value
is .01. The tolerance index was set at .20; the default
value is .001. More conservative default values were
selected to make the data more manageable and to include in
the equation those variables that had greater explanatory
power.
A total of 15 stepwise regressions was conducted.
Independent variables for 1980-1981 were regressed against
the dependent variable for 1981-1982; independent variables
for 1981-1982 were regressed against the dependent variables
for 1982-1983; independent variables for 1982-1983 were
regressed against the dependent variable for 1983-1984. The
regression program yielded a number of statistics that
described the relationship between fiscal indicators, the
independent variables and cash balance, the dependent
variable.
Summary Tables 3.5 through 3.19 display values of
2 2 multiple R, R , R change, simple R and B, the regression
2 coefficient, for independent variables with R change
greater than or equal to .01. Multiple R, the multiple
45
CQ t-H ' ^ o^
• «—1
CN m KD
• rH
O a\ ^
• i n
o en r^
• 1
vo cr> vo
• o
«
IT) •
ro
W 1 ^ ffi < E-t
W h^ ffi < E-i
>H K
en w t ^ CQ < H ff;
H
< H W
< <: « EH S > < U s p w
s o H W W w «
o w K
w h^ fi^ M EH t ^ D S
EH
2 H Q 2; H CM H D IS H
i H 00 cr» i - i 1
o 00 <T> i H
> M «
EH EH
S W W M Q P IS H t- CU O K O Q ffi
U CN CO 00 cr. f j rH t^ 1 <
T-H 00 CT\ rH
W tJ CU s H W
w o 2 <: re u a w «
w p rt: D O W
tf
2: o H EH
<:
a is H
W
w OQ <
>
H
H EH
D
H
OQ
H Pi < >
CN
ro rH
ro o
ro CM o
cy> 00 o ro
00 ro t-H
• O
KD 00 O
• O
00 CM O
• o
rH CM o
• o
CM rH O
« o
00 ro r H
IT) CM CM
ro i n CM
"^ r-CM
r^ 00 CM
CM
ro ro o in
CN in
ro in
o in
00 r-t >
V^ 00 >
o CM >
* * T-i >
in
in
46
PQ cri CM ro
• o 1
r^ i n 00
• CM 1
O ^ CM
• rH
^ V£) :< •
o 1
cr» o> 00
• i n r-\
^ 00 I ^
• i-{
Pi
V£> •
ro
W 1^ PQ < EH
W t-q W m H <: h i H EH PQ 1-5
< P3 >^ H <C Pi p; H < < «
s > < S > H D EH •q W IS EH H
H IS EH 2 : P W « O IS Q < H H ^ ; D w cu w a W W P< W D W EH p; IS Q W O H « W CM H Pi rH 00 fa
00 <T\ W cr> tH i-:i «-! 1 eu 1 -H H O 00 EH 00 CTi ^q cr. rH D H
s
H Hi PU S H W
H U S < K U
a w Pi
H Pi < P
a w Pi
Pi
IS
o M ^ < o a H
2 : H
W W i-:i CQ < H p; < >
w hi (h M tH ^J D S
W t-q PQ < M Pi < >
r-CM CM
• o 1
VD V£) rH
• O 1
r>-r-o
• o
o 00 o
• o 1
o CO T-i
• o 1
VD CM O
• o 1
in o
ro CM o
rH O
o
o rsi o
o o o
o o o
^ r-o
00 00 o
<y\ o rH
<y\ rH T-^
V£> i n r-t
r^ CM CN
• o
ro t^ CM
• o
00 a\ CN
• o
o ro ro
• o
i n * * ro
• o
i n a\ ro
• o
^ o 00
• in CM
>
CN T-\
CM >
O y£> >
m CM >
i n CN >
-p (n
§
PQ CM 00
in
o I
CM in 00
CM
r •
ro
W hi PQ < ir^
W t^ W CQ W <; hi H EH CQ t^
< PQ X M <: Pi Pi H < rt: Pi s > <; w S > h P EH H W S EH EH
H IS P: IS Q H <: O IS Q P M w IS a Ui CU K CO fa CU Q fa O fa 2 Pi s p o O H U fa CM fa Pi rH 00 W
00 a \ fa <r> rH ^^ H 1 PH I H H O 00 EH 00 O^ t-1 C5 H P H
Pi
fa 1-1
H W
fa
u o w Pi
fa Pi < p o w Pi
ro CM
o I
00
o 00 o
ro o
00 x-\
o •
o
ro 1-i
o •
o
** r-i
o •
o
ro T-^
o •
o
o r-{ O
• o
00 r H O
• o
(N ro o
• o
VD 'sr O
• o
o i n o
• o
o r o
• o
IS
o H EH <: p a fa IS H
W fa t-1 CQ < H Pi < >
Pi
fa Hi P4 H E H hi
P
s
fa hi PQ < H
Pi
>
ro in rH CM
CM VD CM
ro >
O 00 VD CN 00 rH > > >
in crv o •
in ro CM
8
48
PQ
169
• o
468
• o 1
398
• o 1
702
• o
Pi
00 •
ro
fa hi PQ < b^
fa hi PQ
w fa
< hi fa EH
>H Pi (rf s s p w IS
PQ hi < PQ H < Pi H <: Pi > <
> fa ^ hQ IS EH H fa IS EH P fa Pi
o IS p <: H W W fa Pi o fa Pi
fa t ^ PH H EH h:i P S
fa IS P cu fa a fa P4 P fa P IS P Pi H H
CM ffi r H 00 EH 00 CTi CJ\ y-^ H 1
1 H O 00 00 a\ (T» T-i rH
fa hQ P4
s H W
fa o IS < K u o w Pi
fa Pi < p a w Pi
«
IS o H EH < P a fa
2; H
W fa hQ PQ < H PS < >
fa ^A Cu H EH hi P s
fa hi CQ < H Pi < >
1—1
in i H
• o
'^r o^ o
• o 1
00 CM 1-i
• o 1
T-i
in o
• o
CM CM O
CM O O
o o o
CN CN O
r-^ o
00 in o
o r^ o
r-{ in rH
• O
r^ rH CM
• O
CM ^ CN
• O
'5J< \D CM
• O
•«* \D r-i
•
430
o ro in K£> i n > >
00
>
49
CQ VD r-i o
• CM
a\ VD ro
• o
00 00 VD
• o
^ in in
• ^
CM CN CTi
•
-36
Pi
C3> •
ro
fa hi OQ < iri
fa hQ W PQ fa < h:i fa EH PQ h^
< CQ >< H <C Pi Pi H < < ^ S > < fa § > 1-1 P EH W IS EH
H EH
fa IS Pi IS P fa O Z P H fa 2 W CU fa CO fa PU fa P fa Pi IS p U H fa CM Pi TH 00
00 <y> fa 0^ rH ^A H 1 P< 1 H H O 00 EH 00 a\ nq cr. rH P -H S
< P O
E EH Pi P O fa
fa hQ CU S H in
fa o IS < ffi u a en Pi
fa « < p a w p;
Pi
z o H EH < P a fa
fa hi OA H EH h l p S
cn fa 1-3 CQ < H Pi < >
fa hi CQ < H Pi < >
VD 00 ro
VD o ro
in in CM
vo a\ «H
VD o rH
CN r^ ^ r-i o o
rH O O
o^ ^ rH
. o
cr> in CN
• o
rH O ro
. o
a\ rH ro
• o
r-i ro ro
• o
vo 00 ro
cr> o in
<j\ ^ in
in VD in
vo r-in
o t-\
00
V87
V20
V65
V16
V12
(Cons
50
CQ r -" r ro
• o
H 00 VO
• o
CM ^ ro
• CM
t ^ in r~
• o
'^ ro ro
• ro 1
CM ro VD
• T-i
ro
fa hi PQ < E H
fa 1-1 cn CQ fa < h^ ^ OQ
< >H H Pi Pi < <
>
IS fa p IS
p cn
IS O H fa cn P4 cn fa fa p Pi IS o H fa Pi CN
00
fa cr> i^ H
fa 1 ^ OQ < H
Pi
>
IS fa P IS fa P4 fa p
Cl4 H EH hi P
s
I T-i 00 cr>
cn EH O H Pi EH cn
hi o o ffi u
ro cn 00
I CN 00
hi
<
Pi
fa hQ
s H cn
fa
<
u a cn Pi
fa Pi < p a cn
Pi
Pi
IS
o H EH < P
a fa
^ H
cn fa hQ CQ < H Pi < >
fa hi Oi H EH h^ P S
fa (-1 CQ < H Pi < >
o o
ro 00 ro
vo
ro
CM vo ro
o CM
VD rH
O
o vo 1-i
• o
rH "* r-i
• O
r-in o
• o
rH rH O
• O
ro T-\
o •
o
CM r H O
• o
o vo
CN O ro
in ro ro
00 ro
o
o o ' d '
• o
cr» '^ in
• o
G^ cr> in
• o
a\ o vo
• o
o CM VO
• o
00 ro vo
• o
ro ^ 00
• in
in T-i
>
<Ti 00 >
r-00 >
in VD >
rr VD >
r>> CM >
g u
51
CQ ro rsi ro
• o
^ 00 ^
• o 1
CM i n ro
• o 1
00 ro ^
t
o
CM ^ ro
• ^
i n VD CM
• o 1
Pi
rH T-i
• ro
fa hi CQ < b^
fa hQ cn OQ fa < h i fa EH PQ h i
< PQ >H H < P^ Pi H << •< Pi S > < fa S > hi P EH H cn 3 EH EH
fa IS p; IS P fa < O IS P P H fa IS a cn p< fa cn fa Pn EH
fa p fa cn Pi IS P Pi O H H fa ro fa Pi CM 00
00 a\ fa CTi rH h i H 1 CU I CM H rH 00 EH 00 0^ h i C^ rH P H
s
fa hi Oi
s H cn
fa o s < ffi u a cn Pi
fa « < p a cn
Pi
Pi
IS o H EH < P a fa
IS H
cn fa (-1 CQ < H Pi < >
fa h l PH H EH hi P s
fa hQ CQ < H Pi < >
'cr * * T~<
• o
rH [ ^
o • o
1
CM " 5 ^
T-i •
O 1
CTt i n o
• o
00 VD o
• o
ro 00 o
• o 1
o (N O
CM o
ro T-i
o o
T-i
o o
o o
o rH
o o
o CN o
00 ^ o
T-i VD O
i n r-o
CN CN i-H
CM ro T-i
^ ^ x-i
9
O
<y> rH CM
• O
r--«* CN
• O
i n r-" CM
• o
o> * * ro
• o
ro vo ro
• o
i n ro vo
• 00 VD
§
00 o VD >
' ^ VD >
i n i n >
r CM >
CM VD >
-P CO G 0 U
52
PQ
.164
o
.726
CN
862
o
191
CN
118
o 1
340
o
501
rH
111
o 1
368
r-i
.916
CM 1
CM rH
t
ro
fa hi CQ < iri
fa hQ PQ
cn fa
< h i fa bi
>H Pi
P cn
PQ yA < PQ H < p; H < Pi > <: fa
> h i ^ H IS EH EH fa IS Pi
IS P fa <
o H cn cn fa « O fa P:
fa hQ P4 H ^ hQ p
s
IS P P fa S O PH fa fa PH P P fa IS 2 P O H U
ro fa CN 00 cn 0 0 <T> OS T-i rH 1
1 CN rH 00 CO CJ O^ T-i rH
IS
o H < P
o fa IS H
cn fa hQ OQ < H
Pi
>
fa hQ P4
H
cn
fa O IS < ffi u a cn Pi
fa Pi < p a cn
Pi
p;
fa h i P4 H EH hi P
fa h i CQ < H Pi < >
CM in
o CM o
T-i
o
VD
o
o o 00
o
00 CM VD O
ro
o cr> o
o I
o I
o I
ro
o
VD T-i
o
o
ro T-i
o
o
o T-i
o o
rH
o
o
o rH
o
o
T-i
o
o
in T-i
o
o
o
o
ro CM o
o ^ o
ro i n o
' 5 * '
VD O
^ r-o
r-00 o
r--cr> o
T-i
rH rH
I ^ CM rH
00 VD T-i
CN in T-i
o o CM
o ro CM
ro in CM
ro CM
in CN
CN rH ro o
ro ro
in ro
i n ro 00
• o CN
CM T-i
r^ CM i n ro > >
IT) >
vo 00 >
ro vo >
i n CM >
vo vo >
a\ CN >
r-CM >
§
53
PQ vo o ^
• o 1
<y\ in ^
• o 1
00 ro o • o 1
^ T-i
o • o
Pi
ro rH
• ro
fa hQ PQ < iri
fa 1-1 cn OQ fa < hQ fa EH CQ hQ
< CQ >i i-i f^ Pi tf H < <: Pi s > < s > w P EH hQ cn IS EH H
fa IS EH IS P fa Pi O IS P < H fa S P cn cu fa a cn fa P4 fa p fa p Pi IS p Pi O H H fa ro « Pi CM 00 EH
00 cr. fa Cr» rH 1-1 H 1 C^ 1 CM H rH 00 EH CO a> hQ <y> rH P H S
fa hi P4
s H cn
fa O S < ffi u o cn Pi
fa Pi < p a cn Pi
IS
o H < P a fa
Pi
fa hQ pu H EH hi P
cn fa hi CQ < H Pi < >
fa 1 ^ CQ < H Pi < >
00 VD CM
• O
^ 04 rH
• o 1
i n r^ rH
• o
CM o CM
• o
CN
o CM T-i
o o
o rH O
o
rH O
o
CM r-o
* * 00 o
* * <T\ o
00 o rH
CO VD CN
O
CM o ro
CM
ro
in in
CTi
CM
§
ro »H >
VD CO >
'^r (N >
O i n >
4J cn g p U
54
PQ
.850
o
.486
CM
.158
o 1
.549
00 1
423
ro
196
o 1
143
r^ ^
878
ro
070
vo 1
449
o 1
Pi
'sr T-i
. ro
fa hi PQ < EH
fa hi cn PQ fa < hQ fa EH CQ hQ
< PQ >i ^-^ < Pi Pi H < < Pi s > < w S > hQ P EH H cn IS EH EH
fa S Pi IS P fa < o 2: p P H fa IS O cn pu fa cn fa P ffi fa P fa EH « 21 p Pi O H P fa ro O Pi <N 00 fa
00 as fa CJ rH hQ «H 1 PH I CM H rH 00 EH 00 <r» ^q a* rH P H S
fa hQ Cm S H
cn
fa o z < K u a cn Pi
fa Pi < P a cn
Pi
Pi
IS o H ^ < P a fa
2: H
cn fa hi CQ < H Pi < >
fa hQ CU H b^ 1-1 P s
fa t J ffl < H p; < >
.503
o
.327
o
209
o 056
o 1
114
o
072
o
118
o
206
o
.129
o
.115
o
ro in CM
o o
ro
o TH
o o
o o
rH
o o
TH
o
o
ro rH
o
o
ro rH O
o o o
ro in CN
ro CN ro
vo vo ro
ro 00 ro
in as ro
as o 'd '
ro CM ^
VD ro »*
o in ' ^
T-i
vo ' ^
ro o in o
00 vo in
• o
in o vo
• o
as rH VO
• o
00 CN VO
• o
as ro vo
• o
o in VD
• o
o vo VD
• o
o r~> VD
• O
as r^ VD
• o
CM VU (M
•
063
§
as 00 >
,-i vo >
o VD >
CO rH >
CO vo >
r-CM >
o CO >
' ^ vo >
r-vo >
4J CO C u u
55
OQ ro 00 in • o
as 1-i CO • o
in
ro
fa hi CQ < E H
fa hi cn OQ fa <
P cn
o H
1 ^ CQ <
>H H Pi Pi < <
>
iri
fa P IS fa
cn cu cn fa
fa hQ CQ < cn H b^ Pi u
fa Pi
p IS
O H fa p; ro
00 fa as hQ tH PH I H CM EH CO hi as P H S
< >
EH IS fa P ^ fa Oi fa ffi P U
cn
CO as
H Pi iri cn H p hQ O o
I ro 00 as
hi hQ <
Pi
fa hi P4
s H cn
fa o IS < u
a cn Pi
fa p; < p o cn
Pi
Pi
r-rH in • o
ro vo CM • o
r vo CM • o
00 rH o • o
VD CM
VD 00 CN
IS o H B^ < P a fa IS H
cn fa hi OQ < H Pi < >
fa t - 1 Oi H ^ ( P s
fa hi CQ <: H Pi < >
r-
.51
o
as ro >
in ro in
ro vo a\
• in
CO >
CO
g
56
OQ VO VD ro • o
^ rH rH • o 1
CN VD ro •
rH 1
r cr> rf • o 'sr
ro as ro • o
fO CO VD • o 1
00 ro o • o 1
Pi
fa hQ
s H cn
ro vo ro as
vo o
ro o
'vt* o a\ o
o I
o I
o I
o I
vo
ro
fa O IS < U
a cn Pi
vo CM o • o
r-rH O •
O
o I-I o • o
rH rH O • o
CM rH o • o
rH T-i
o • o
o rH O • o
fa hi OQ < ti
fa Pi < P a cn Pi
vo CM O
^ •cy O
"^ in o
in vo o
r-r-o
as 00 o
as as o
IS
o H < P
a fa
Pi
fa hQ
H
P
ro VD rH
• o
as o CM
CM ro CM
vo i n CN
as
rsi
00 a\ CM
i n rH
ro o
vo
00
CN
2: H
cn fa hQ CQ < H Pi < >
fa
OQ < H
Pi
>
00 i n >
VD CM
g g 5 00 ro >
CM T-i >
00 >
-P CO
57
OQ rH * * CM
• O
rH T-i rH
• o
VD CM O
• o 1
ro
fa hi OQ <
fa hi cn OQ fa < hi
OQ <
>H H p; Pi <
s p cn
IS
o
>
iri IS fa P IS
H fa cn Oi cn fa fa p
fa hQ OQ < H Pi < fa > hi
IS H
Pi o fa Pi ro
CO fa as h:i H P4 I H CN EH 00
Pi < p a p 2: o u
^ fa 00 cn
T-i I
ro 00 as
EH
fa P IS fa Oi fa p
hi p
cr>
2 O H EH < P a fa
Pi
fa hi
PH
H
cn
fa o
u a cn Pi
fa Pi < p a cn
Pi
Pi
fa 1 ^ p^ H
hQ P S
cn fa (^ OQ <: H Pi < >
fa hi 03 < H Pi < >
cr> o
o a\ o o
vo rH O o
ro T-i
o o
o o
VD CN O
as ro o
<T> ro rH
CM VD
as ro
ro
CM o as
• ro CM
g
CN ' ^ in >
in ro >
4-> CO
c P U
58
PQ CM 00 CO • o
^ r vo • CM 1
ro vo CO • o 1
ro o .H •
O
ro '* ro • o
r-r CM • o 1
Pi
CO
ro
fa hQ PQ <
fa h i cn CQ fa
hQ CQ <
X H
Pi Pi
> p cn
IS o
IS fa p
fa cn P cn fa fa P Pi ^ o H fa Pi ro
00 fa as hQ H PLI I H CM EH 00 h i as P H
fa h : | OQ < H Pi < >
p
fa hi
EH IS EH fa (^
< P
fa O Oi fa p p Pi
H
00 EH as T-i I
ro 00 as
cn
fa O IS <
u
a cn Pi
fa Pi < p a cn
fa t ^ CU s
'r in 1-i
• o
ro rH 1-H
O 1
'r a\ o
t o 1
^ in T-i
• o
** as o • o
ro ^ o • o 1
Pi
IS o H ^ < P a fa s H
cn fa hi CQ < H Pi < >
fa hi 0* H EH ^A P S
fa iJ CQ < H Pi < >
ro CN o CN
o
ro rH O O
rH O
O
CM rH
o
o
o T-i
o o
ro rsi o
in ^ o
00 in o
vo r o
CO CO o
a\ as o
'r in T-i
• o
CM T-i CM •
O
CM ^ CN •
O
r>-r CN • o
CO as CN • o
in rH ro • o
o CN 'a* •
542
ro as in >
o vo >
r vo >
CN in >
4-» CO
§
59
OQ r-T-i
r •
o
CO CO r •
rH
O ro ro •
1
in CM o • ro 1
T-i
in o •
VD ro
as in in •
^
CM o a\
9
O
Pi
<T> T-i
• ro
fa hi 01 < ^
fa hQ cn PQ fa <; hQ fa EH m hi
< CQ >H H < Pi Pi H < < Pi S > < fa S > hQ P EH H cn IS EH EH
fa IS Pi IS p fa <: O IS P P H fa 2; O cn cu fa cn fa a. ffi fa P fa EH Pi IS p p; O H P fa ^ o Pi ro CO fa
CO as fa Cr> rH hQ H 1 PH I CO H CN CO EH CO o^ hi O^ rH P rH S
fa 1^ cu S H cn
fa o IS < ffi
u o cn Pi
fa p; < p a cn
Pi
Pi
IS
o H EH < P
a fa
s H
cn fa tJ CQ < H Pi < >
fa hi PH H EH tJ P
s
fa hQ CQ < H Pi < >
in r-ro
r-Oi CM
CM T-i O
r vo rH
VO VO rH
ro as CM
vo ro ro
o r 00 ro rH o o
rH
o
o
ro rH O o
ro rH O o
o
o
o r-r- vo
CTv o T-i CM
o
CN CN
ro CN
ro vo CM
in r ro •
o
T-i CN 'r •
O
ro ^ ^ •
o
as in •^ • o
ro r-'^ •
o
r 00 ** • o
ro TH in • o
r--CN o •
061
in ro >
00 >
o ro o^ ro in vo vo VD in vo > > > > >
-P CO
c 8
60
correlation coefficient, indicates the correlation between
the dependent variable and the weighted sum of the indepen
dent variables. 2
R , the coefficient of determination, indicates the
amount of variability in the dependent variable that can be
explained by an independent variable; that is, the strength
of the relationship (Nie et al. 1975) . This statistic is
the square of the multiple correlation coefficient. Cause 2
and effect relationships cannot be determined from R . 2
The amount of change in R , RSQ Change, indicates the 2
amount of change in R at each successive step. This sta
tistic was used to determine at what step the addition of
independent variables did not add significantly to the
amount of variance that was already explained by variables
already included in the regression equation.
Simple R, the zero-order correlation coefficient, is
included in the summary tables for convenience. This sta
tistic indicates the strength and direction of the rela
tionship between variables.
B is the partial regression coefficient. It represents
the expected change in the dependent variable for each
change of one unit in an independent variable when the other
variables in the equation are held constant (Nie et al.
1975). Combined effects of variables are additive.
Finally, the constant is provided. This statistic is
the Y intercept. The F ratio and beta values are not
61
included in the summary tables because the stepwise regres
sion program excluded independent variables that did not
meet or exceed the value of the specified F ratio and the
variables are presented in descending order of their beta
values.
Analysis of the Data
Phase four of the study consisted of analyzing the data
generated by the stepwise multiple regression program. The
data were analyzed to answer the research questions. First,
is school district fiscal health predictable? Second, what
fiscal indicators, subject to the control of local decision
makers, can be used to forecast school district fiscal
health? Third, do different indicators have predictive
significance for school districts with a higher level of
fiscal health than for those school districts with a lower
level of fiscal health? Finally, does the methodology
employed in this study provide a viable strategy for differ
entiating levels of school district fiscal health?
The data in the summary tables includes all independent
variables that met the criteria chosen for the F ratio and
tolerance options. The researcher decided to further reduce
the number of variables by limiting the models to those
2 variables that displayed a change m R greater than or
equal to .01; that is, those variables that accounted for
one percent or more of the variance in the dependent
62 2
variable. The R value for each model is displayed in Table
2 3.20. R values were examined to compare the amount of
variability in the dependent variables that were attributed
2 to each model. The R values for all 15 regression runs are
displayed in Table 3.20.
Table 3.21 identifies those variables, the values of
2 the change in R for each, and the budget category of each
variable. Although 15 multiple regressions were run, dis
cussions and further analysis will focus on the data that
were obtained for all school districts, the first quartile
2 and the fourth quartile. The R values of the models for
2 the extremes were higher than the R values for the second
and third quartiles except for the models derived from the
1981-1982 independent variables.
Table 3.22 displays the means and standard deviations
of cash balance for models that include all school dis
tricts; first quartile and fourth quartile. It appears that
the low values of R^, from Table 3.20, for the first quar
tile correspond with the low cash balance as displayed in
Table 3.22. Higher cash balances were found for the fourth
quartile and for all school districts. The means of cash
balance for all school districts for all years included in
the study displayed the greatest variability according to
the values of the standard deviations.
TABLE 3.20
TOTAL R VALUES
63
Independent Variables
Dependent Variables
All School Districts
First Quartile
Second Quartile
Third Quartile
Fourth Quartile
1980-1981 1981-1982 1982-1983
1-1982
.285
.128
.070
.070
.331
1982-1983
.394
.095
.134
.108
.461
1983-198
.286
.099
.050
.099
.249
64
CN
ro
fa h i
fa O IS <
u •-< o
a . cn a o iri
in ^ H < 12 P a cn fa fa h i PQ < H IS Pi <
p; o
>
EH
fa P IS fa Pi P o fa p IS
in
Pi fa EH
< fa
ro CO a\
I
CM 00 as
-P
CM 00 as
I
I-H 00 as
O Cn cn C Pi fO
U
Q) r-i X! fO
•H 5H
>
u o
3 -P OQ fO
U
0)
O C cn to p; i i :
u 0)
rH
•H u to >
CO CTt
I
o 00 as
4J O
cn IT> ^3 (U 13 4J OQ fO
U
(U
a C cn to Pi ^
u
<u
to • H
SH
to >
(U o cn cn
T l CU
OQ to
* u
r^ 00 VD rH CM O
VD r^ O rH CM rH O CM rH rH iH rH rH rH O O O O O O O
o r^ 00 'r ro ro rH ^ ro rH rH rH rH rH rH O O O O O O
as r-ro 00 > >
CO vo CM 00 CM r^ in in in r- ro rH 00 > > > > > > >
i n P>- o ro ON ro i n ro CO vo vo vo i n vo > > > > > > >
in Pi W f a f a f a E H E H P i E H p i W f a f a f a W
O rH r^ rH r o CM VD - ^ i n rH rH rH 1-1 r H O O O O
O r-- ro '^ rH O CN CM rH rH rH rH
o o o o o o
in o^ r^ in 'ST r-TH 00 00 vo vo CM > > > > > >
CO o ' ^ i n r^ CN i n vo vo i n rvi VD > > > > > >
E H p i P i f a f a E H fafafafaEHfa
CO VD CO rH CM ro 00 CM CM rH rH O O O O
TH ro ^ o O o m c>i T-i c^ T-i T-i o o o o o o
00 i ^ o 'S" i n rH CO CN rH VD > > > > >
^ CN rH o ro i n VD rH CM vo CM CN > > > > > >
EH Pi EH EH fa fa EH EH W E-I EH
r o o r o r ^ r ^ « ! * ^ r o r o ^ - ^ i n t ^ ' ^ r r H - r H r H r H r H r H r H C N O O O O O O O O O
o ^ r ^ r H O o o o o r ^ o ^ ^ ^ C O O O V O V D r H V D C M O O V O V D > > > > > > > > > >
piPifafaEHfaEHpifafa
CTi O CM r - CN «;}' rH « * rH rH T H rH O O O
r^ o i n VO CM CO CM vo rH rH > > > > >
Pi EH fa EH EH
Q)
>
Pi
Pi
o • H 4J U
c 4H
Q) }H :3 4-> • H TJ C G)
X fa
fa
to
to
r-i 0 0
j : :
o
CO j j
u •H U -P to
•H cn p
Q) rH •H
+J -p cn u u to
•H 13
fa a
rH x: -H •p -p }H U 3 to O J3 fa a
X to EH
Ii
in
65
00
as T-i
I ro 00 cr>
U
to 4J
O
to +J TJ to
cn p
to
s
r-ro ' ^
• i n 00 00
CM as CM
• O VD
O i n vo
• CM ^ CM
i n CM a\
• as vo vo
r-vo as
• T-i
o t -H
i n a\ as
• CN CM r-
CM CM
• ro fa hi
cn IS o H in < H > fa fa U P IS
< Pi ^ < OQ
p
< cn EH <
cn u p fa IS o < cn
I fa
ro CO cr> rH I
CM 00 as
CM CO
as rH I
rH CO
cn
•73 }H
u
O •H
to +J TJ to
to 4J cn p
to Q)
o •H
to -P Ti 10 to 4J cn p
ro
CN
vo VD
as
CO
CN
in
in VD
in in
in ro
• in
CM
o in
r-"sr o
• CO CM VO
CM rsi o
• ro as
as o vo
• CM in VD
VD
in
d to Q) S
t-i 0 0 XJ u cn t-\
t-i
i n rH r^
• 00 rH
in
cn 4J U
•H VH 4-> cn
•H < p
•P cn u
•H fa
^ vo VD
• r-r~-
Q) rH •H •P U to :3 o
o o as
9
VD
13
2
Q) rH
45 -H JJ 4J U U p to 0 J3 fa O
CHAPTER IV
PRESENTATION AND ANALYSIS OF DATA
The purpose of this chapter is to investigate the
research questions that were presented in Chapter I. The
questions are addressed separately using stepwise multiple
regression as the primary statistical method in order to
examine the relationships between the independent variables
of tax data, expenditures by function, and local revenues,
and the dependent variable, cash balance. For purposes of
reporting and analyzing the statistical results, several
groups of school districts were used. The first group
included all school districts in Texas (N for 1980-1981 and
1981-1982 was 979; N for 1982-1983 was 978). Next the
districts were divided into quartiles on the basis of fiscal
health as measured by cash balance divided by refined
average daily attendance. Because there appeared to be
little differences in the two middle quartiles, the decision
was made to focus the analysis on the first quartile (N=245)
and the fourth quartile (N=244), which represented the
extremes. In addition, a three-year time period was used to
provide a longitudinal analysis of the results.
66
67
Discussion of Research Questions
1. Is fiscal health predictable?
This question was investigated by subjecting the
variables to stepwise multiple regression. Independent
variables for 1980-1981 were regressed against the dependent
variable for 1981-1982; 1981-1982 independent variables were
regressed against the dependent variable for 1982-1983;
1982-1983 independent variables were regressed against the
dependent variable for 1983-1984. For all models, variables
were restricted to those that contributed one percent or
more to the variability of the dependent variable.
2 An examination of the R values for the models for all
school districts and for school districts in the first and
fourth quartiles in Table 3.20 indicates that 9.5 percent to
46.1 percent of the variance in the dependent variable could
be attributed to the independent variables that were
included in the models. For the 1980-1981 models, the
2 values of R were 28.5 percent for all school districts,
12.8 percent for the first quartile, and 33.1 percent for
the fourth quartile. For the 1981-1982 models, the values
of R were 39.4 percent for all school districts, 9.5 per
cent for the first quartile, and 46.1 percent for the fourth 2
quartile. For the 1982-1983 models, the values of R were
28.6 percent for all school districts, 9.9 percent for the
first quartile, and 24.9 percent for the fourth quartile.
68 2
The R values indicate that the models derived in this
study do not have a high level of predictive significance.
Only moderate predictive values were found for all school
districts and for school districts in the fourth quartile. 2
The values of R for the models in the first quartile were
too low to be of value in predicting school district fiscal
health. It appears that there are other intervening factors
beyond the scope of this study that would improve the
ability of regression models to predict school district
fiscal health. Therefore, school district fiscal health
cannot be predicted with accuracy using the methods employed
in this study.
2. What fiscal indicators, subject to the control of
local decision makers, can be used to forecast school
district fiscal health?
Fiscal indicators that are subject to control by local
decision makers were examined, for example, tax rate/$100,
current year tax revenue, adjustments- and discounts,
instructional administration, health services, plant mainte
nance and operation, tuition and fees from patrons, enter
prise funds, non-revenue receipts, and so forth. The
regression program was run using 54 independent variables
for 1980-1981; 55 independent variables were included in
1981-1982; 44 independent variables were analyzed in 1982-
1983. The SPSS stepwise multiple regression program
included all independent variables that were statistically
69
significant at the .05 level in the regression equation.
Because most of the variables accounted for a very small
amount of the variance, the number of variables that were
included in the models was reduced further by identifying
those that exhibited a change in R greater than or equal to
.01; that is, those independent variables that had the
greatest influence in the regression equation. The vari-
ables that displayed R values greater than or equal to .01
and the frequencies with which they appear in the models are
summarized in Figure 4.1.
The number of variables included in the models varies
from two to ten, with five, six or seven variables being
included most often. Most of the variables that exhibited 2
values of R greater than or equal to .01 were expenditures
by function and tax data rather than revenue items. Because
cash balance basically reflects the difference between
expenditures and revenue, with 9 8 percent of local revenue
derived from local tax collections, it appears that school
district decision makers should exercise greatest discretion
in establishing tax rates and adjustments to tax rates along
with how they decide to spend revenues. Cash balance
depends upon tax rates and expenditures as well as revenue.
Even with low revenues, expenditures can be adjusted to
enhance cash balance.
70
Frequency Variable Identification
Maintenance Taxes (1980-1981, 1981-1982)
3 V12 Tax rate/$100
1 V14 Discounts and adjustments
1 V15 Net taxes assessed
1 V16 Estimated uncollectible taxes
2 VI8 Total current year deferred revenue
2 V20 Prior years tax revenue
1 V21 Penalties, interest, and other tax
revenue
Debt Service Taxes (1980-1981, 1981-1982)
1 V23 Tax rate/$100
1 V25 Discounts and adjustments
3 V27 Estimated uncollectible current taxes
Total Tax Data (1982-1983)
1 V35 Calculated tax levy
1 V38 Other adjustments and discounts
1 V39 Net taxes assessed
Expenditures by Function
1 V53 Instructional resources and media
services
1 V54 School administration
1 V55 Instructional research and development
FIGURE 4.1
FREQUENCIES OF VARIABLES THAT ARE INCLUDED IN THE MODELS
71
1 V56 Curriculum and personnel development
2 V58 Guidance and counseling services
4 V60 Health services
1 V61 Pupil transportation-regular
1 V62 Pupil transportation-exceptional
1 V63 Co-curricular activities
4 V64 Food services
4 V65 General administration
1 V67 Plant maintenance and operation
1 V68 Facilities acquisition and construction
1 V69 Management (Data processing)
1 V72 Interfacing (Technical assistance)
Revenue from Local and Intermediate Sources
1 V80 Local maintenance tax
7 V87 Other revenue from local sources
2 V89 Non-revenue receipts (proceeds from bonds, loans, lease/purchases, etc.)
FIGURE 4.1 (continued)
72
According to the data in Figure 4.1, only six
independent variables occur in the different models more
than two times. They are: V12 - maintenance tax rate/$100,
V27—estimated uncollectible current debt services taxes,
(V12 and V27 occur only in 1980-1981 and 1981-1982 because
of revisions in the budget format. Maintenance and debt
service tax data were combined after 1982.), V60—health
services, V64—food services, V65—general administration
and V87—other revenue from local sources.
Tax rate seems to occur frequently because it is the
basic determinant of local tax revenue, the largest source
of local revenue. Regardless of the appraised value per tax
roll and to compensate for uncollectible tax revenues, the
tax rate must be adjusted to meet the local revenue needs of
the school district.
Estimated uncollectible debt service taxes, V27,
occurred in three of the nine models, all of which occurred
using 1981-1982 independent variables. This variable
displayed a negative correlation with cash balance only in
the fourth quartile. School districts can estimate the
amount of taxes that cannot be collected by examining the
history of tax collections and economic conditions, but they
have less control over uncollectible taxes than they do over
other tax items in the budget. Results indicate that this
variable is a significant factor related to fiscal health.
73
Both health services, V60, and food services, V64, are
pupil services that occur in four of nine models. Health
services had a negative correlation in all models where it
occurred except in the fourth quartile in 1982-1983. Food
services displayed negative correlations with cash balance
where it occurred in the first quartiles in 1980-1981 and
1981-1982. Food services may be self-supporting or subsi
dized. Where it appeared in the model for all school
districts and the fourth quartile for 1981-1982, it had a
positive correlation with cash balance. Increasing demands
are placed on schools to provide services related to educa
tion that are not direct instructional services. It appears
that the high costs of providing these services must be met
by the local school districts.
Variable 65, general administration, also occurs in
four models. It had a positive correlation in all models.
This function detail encompasses all activities that include
overall administrative responsibilities, including such
areas as the board of education, superintendent's office,
security, staff accounting, tax administration and computer
services. Costs include salaries, supplies and equipment.
Variable 87, other revenue from local sources, occurs
most frequently appearing in seven of the models. It has a
negative correlation with cash balance only in the model for
the first quartile for 1982-1983. This function includes
earnings from permanent funds and endowments, temporary
74
deposits and investments, net receipts from revolving funds
or clearing accounts, rent, gifts and bequests and any other
revenues from local sources. It appears that school
districts were very enterprising and were able to generate
local revenues from sources other than taxes. This variable 2
ranked first, second or third in its R change in models for
all school districts and for school districts in the fourth
quartile. It contributed the least of all variables that
were included for the first quartile for 1982-1983. The
values of the change in R for V87 range from .010 to .149.
This indicates that local decision makers must continue to
explore alternate sources of revenue.
3. Do different indicators have predictive signifi
cance for school districts with a higher level of fiscal
health than for those school districts with a lower level of
fiscal health?
Figure 4.2 displays the variables that were included in
the models for all school districts, the first quartile and
the fourth quartile. While models within the same year do
not include all the same independent variables, they do have
some variables in common. For 1980-1981, variables 87, 65
and 20 appear in models for all school districts and in the
model for the fourth quartile which have the highest means
of cash balance. Variable 12 appears in the first quartile
and the fourth quartile. Variables 18, 14, 64, 21, 60, 23,
25 and 16 appear only in one model.
75
1980-1981
All School Districts
First Quartile
Fourth Quartile
V18 Total current year deferred revenue V87 Other revenue from local sources V20 Prior years tax revenue V14 Discounts and adjustments V65 General administration
V64 Food services V12 Maintenance tax rate/$100 V21 Penalties, interest and other tax revenue V60 Health services V23 Debt service tax rate/$100 V25 Debt service discounts and adjustments
V87 Other revenue from local sources V20 Maintenance tax prior years tax revenue V65 General administration V16 Estimated uncollectible current maintenance
taxes V12 Maintenance tax rate/$100
1981-1982
All School Districts
First Quartile
Fourth Quartile
V15 Net maintenance taxes assessed V87 Other revenue from local sources V89 Non-revenue receipts (proceeds from bonds,
loans, lease/purchase agreements, etc.) V65 General administration V64 Food services V27 Estimated uncollectible current debt
service taxes
V58 Guidance and counseling services V60 Health services V64 Food services V55 Instructional research and development V27 Estimated uncollectible current debt
service taxes V62 Pupil transportation-exceptional V89 Non-revenue receipts (proceeds from bonds,
loans, lease/purchase agreements, etc.) V87 Other revenue from local sources V61 Pupil transportation-regular
FIGURE 4.2
VARIABLES INCLUDED IN THE MODELS FOR ALL SCHOOL DISTRICTS, FIRST QUARTILE
AND FOURTH QUARTILE
76
total current year V60 Health services V18 Maintenance taxes
deferred revenue V68 Facilities acquisition and construction V27 Estimated uncollectible current debt
service taxes V80 Local maintenance tax V64 Food services V67 Plant maintenance and operation
1982-1983
All V39 School Districts V87
Net taxes assessed (maintenance plus debt service) Other revenue from local sources
First Quartile
V58 Guidance and counseling services V54 School administration V56 Curriculum and personnel development V72 Interfacing (technical assistance) V38 Other adjustments and discounts (mainte
nance plus debt service) V12 Maintenance tax rate/$100 V8 7 Other revenue from local sources
Fourth Quartile
V35 Calculated tax levy (maintenance plus debt service)
V87 Other revenue from local sources V60 Health services V63 Co-curricular activities V69 Management (data processing) V53 Instructional resources and media services V65 General administration
FIGURE 4.2 (continued)
77
In the models for 1981-1982, variables 89 and 87 appear
in all school districts and the fourth quartile. Variable
60 appears in the first quartile and the fourth quartile.
Variables 64 and 27 can be found in all three models for
this year. Variables 15, 65, 58, 55, 62, 61, 18, 68, 80 and
67 appear only once in different models.
The models for 1982-1983 display the least amount of
variables in common. Variable 87 appears in all three
models. The other variables, 39, 58, 54, 56, 72, 38, 12,
35, 60, 63, 69, 53 and 65 appear only once in different
models. Therefore, the models for 1982-1983 provide the
greatest discrimination among different levels of fiscal
health.
The differences between the means of cash balance for
all school districts and the fourth quartile are less than
the differences in the means between the first and fourth
quartiles, and between the first quartile and all school
districts. Therefore, we might expect to find more
similarities in the models for those groups than for groups
that have greater differences in the means of their cash
balances as is the case with variables 87, 65 and 20 in the
models for all school districts and school districts in the
fourth quartile. Variables that appear in more than one
group seem to be more significant in predicting fiscal
health than variables that appear only in one model.
Variable 12, maintenance tax rate/$100, was likely to be a
78
significant variable in all models because it determines the
amount of local tax revenue that a school district could
expect to collect, subject to adjustments and discounts.
The models for the first and fourth quartiles have the
least variables in common. Therefore, research question
number three can be answered in the affirmative. Different
indicators have predictive significance for school districts
with a higher level of fiscal health than for those school
districts with a lower level of fiscal health.
4. Does the methodology employed in this study
provide a viable strategy for differentiating levels of
school district fiscal health?
The statistical methods employed in this study are
accepted standard procedures for predicting and forecasting.
The question of whether the methodology employed in this
study provides a viable strategy for differentiating levels
of school district fiscal health requires an examination of
the variables that were included in the regression models.
If this were a viable strategy, the models in different
years should include the same variables so that the
method/models could be used in any year to predict fiscal
health in the following year.
Referring again to Figure 4.2, we see that variable 87
is the only variable that occurs in the models for all
school districts in all three years. V87, other revenue
79
from local sources, includes earnings from permanent funds
and endowments, earnings from temporary deposits and
investments, net receipts from revolving funds or clearing
accounts, rent, gifts and bequest, and any other
miscellaneous revenue from local sources. As mentioned
above, it appears that school districts are finding ways to
generate local revenue from sources other than taxes.
In the models for school districts in the first
quartile, variables 60 and 64 appear in 1980-1982 and
1981-1982. Variable 12 appears in 1980-1981 and 1982-1983.
Variable 58 appears in the models for 1981-1982 and
1982-1983. For models in the fourth quartile, variable 87
appears in all three years; variable 65 can be found in
1980-1981 and 1982-1983. Differences in the models among
years seem to be due to changes in economic and/or political
conditions. Therefore, the methodology employed in this
study did not provide a strategy for accurately forecasting
levels of school district fiscal health.
CHAPTER V
SUMMARY, MAJOR FINDINGS,
CONCLUSIONS AND RECOMMENDATIONS
The purpose of this chapter is to briefly summarize the
study, present major findings, present conclusions and to
make recommendations using the data that were presented and
analyzed in Chapter IV. Conclusions will be made regarding
the relationships between the independent variables,
specific budget categories and the dependent variable, cash
balance. Each research question as well as the overall
perspective of the study will be addressed.
Summary
Because school district budgets are prepared at the
local level, local decision makers bear the greatest
responsibility for the fiscal health of their school
districts. Educational needs and priorities are translated -1
into fiscal indicators or budget categories. The major .1
purpose of this study was to contribute to school finance
research by examining the relationships between fiscal
indicators and fiscal health so that budget planners could
exercise greater control over the fiscal health of their
school districts.
80
81
The Problem of the Study
The focus of this study was to forecast school district
fiscal health by identifying budget categories that had the
greatest impact on cash balance. A major assumption was
that fiscal security could be improved by increasing cash
balance. The problem was restated in four research
questions.
1. Is school district fiscal health predictable?
2. What fiscal indicators, subject to the control of
local decision makers, can be used to forecast school
district fiscal health?
3. Do different indicators have predictive
significance for school districts with a higher level of
fiscal health than for those school districts with a lower
level of fiscal health?
4. Does the methodology employed in this study
provide a viable strategy for forecasting levels of school
district fiscal health?
Procedures
The research for this study was conducted in four
phases. The purpose of Phase I was to determine the
feasibility of the study by reviewing the relevant school
budget and school finance literature and by contacting the
Texas Education Agency to establish that data were
available. Phase II of the study consisted of sorting the
82
data to isolate the variables and to construct files to run
the stepwise multiple regression program. Phase III
consisted of analysis by running the stepwise multiple
regression program. Results of the computer program were
analyzed and summarized in Phase IV for presentation and
analysis.
Major Findings
To analyze the data, stepwise multiple regression
models were examined for three groups. Fiscal health was
used to divide the school districts into quartiles and an
analysis was conducted for all school districts. Summary
data were analyzed for all school districts and the
extremes, which are the school districts in the first and
fourth quartiles. Findings for each research question will
be addressed separately.
1. Is school district fiscal health predictable?
For the models using the 1980 independent variables,
fiscal health was not predictable for the school districts 2
in the first quartile. The value of R was only .128.
Moderate values of R^, .285 and .331 were obtained for all
school districts and for the fourth quartile, respectively. 2
For 1981-1982 independent variables, R for all school
districts was .394; R^ for the first quartile was .095; and
R2 ^ Q ^ j g fourth quartile was .461, which was the highest
83
value found in the study. Fiscal health for the first
quartile could not be predicted reliably. 2
The lowest R values for the models for all school
districts and for the fourth quartile were found in the
portion of the study that used 1982-1983 independent 2 -)
variables. R for all school districts was .286; R for the
first quartile was .099; R^ for the fourth quartile was
.249.
2
A consistent pattern of R values was found across the
years; that is, the highest values were found in the models
for all school districts and for the models in the fourth 2
quartile. The lowest values of R were displayed by models in the first quartile. It appears that the amount of vari-
2
ance that is explained by the change in R increases as the
amount of cash balance increases. Local decision makers can
control factors to improve fiscal health; that is, to
increase cash balance. However, as reported above, the 2
values of R for models derived from this study indicate
that school district fiscal health cannot be reliably
predicted.
2. What fiscal indicators, subject to the control of
local decision makers, can be used to forecast school
district fiscal health?
In the analysis of the statistical data, models
included only those variables that contributed one percent
or more to the variance in fiscal health. The models did
84
not contain the same variables, which was to be expected for
models in the same group of school districts across years.
The model for the first quartile should have included the
same variables if it were useful to predict fiscal health
across years.
The data also indicated that variables that occur in 2
more than one model do not exhibit the same influence, R
change, upon fiscal health. This is another indication of
the differences among the models for different groups. The 2
same values of R change were not expected- because school
districts were sorted into groups according to cash balance.
One perspective for answering question two is to focus 2
on change in R ; that is, the amount of variability in the
dependent variable, cash balance, that could be attributed
to each of the independent variables. The analysis and 2
discussion focused on independent variables that had R
changes greater than or equal to .01 or only one percent.
Those independent variables comprise the models. It is
useful and more practical to limit the independent variables
2 that displayed a change in R of five percent or more.
Table 5.1 displays those independent variables in descending
order of R^ change. For variables that appear in more than
one model, the largest value of R is provided in the table.
85
TABLE 5.1
INDEPENDENT VARIABLES WITH R^ CHANGE GREATER THAN OR EQUAL TO .05
Variable R^ Change
V39 Net total taxes assessed (1982-1983) .267
V89 Non-revenue receipts .253
V15 Net maintenance taxes assessed .160
(1980-1981, 1981-1982)
V87 Other revenue from local sources .149
V35 Calculated total tax levy (1982-1983) .140 V18 Total current year deferred maintenance .138
revenue (1980-1981, 1981-1982)
V20 Prior years maintenance tax revenue .110 (1980-1981, 1981-1982)
V64 Food services .051
86
Net total taxes assessed obtained the highest value of 2 R change. It accounted for 26.7 percent of the variance in
cash balance for the model that included all school
districts using 1982-1983 independent variables.
Nonrevenue receipts displayed the second highest value 2
of R change by accounting for 25.3 percent of the
variability in cash balance for the model that included
school districts in the fourth quartile for 1981-1982.
Revenue in this category includes proceeds from sales of
bonds, land, buildings, equipment, insurance recovery,
lease-purchases and loans. 2 Net maintenance taxes assessed obtained the R change
value of .160 in the fourth quartile for 1981-1982. This
item reflects adjustments made to gross taxes assessed.
Other revenue from local sources, V87, ranked fourth 2
with an R value of .149. This item includes earnings from
permanent funds, endowments, temporary deposits,
investments, rent, gifts and bequests.
Calculated total tax levy includes taxes levied for
maintenance and debt service, which were not identified
separately in the budget document after 1982. The value of
change in R^ was .140 in the model for school districts in
the fourth quartile for 1982-1983. Total current year deferred maintenance revenue
2 obtained .138 as the value of R change in the model for all
school districts in 1980-1981. Deferred maintenance revenue
87
is revenue that was targeted for day-to-day operations that
is not collected during the current budget year.
Prior years maintenance tax revenue displayed .110 as 2
the R value for the model that included school districts in
the fourth quartile in 1980-1981. This variable includes
maintenance tax revenue assessed in a previous year that is
collectible in the current year.
2
The final independent variable that displayed an R
value equal to or greater than .05 was food services. This
expenditure includes all expenses associated with providing
meals or snacks such as preparing and serving food,
operating kitchens and storage. Costs include
administration and supervision of food services.
Five of the independent variables presented above are
tax data. It appears that, as a group, tax data have the
greatest impact on the variability of cash balance. This
could be expected since tax structure is the driving
mechanism for the largest amount of locally generated
revenues. It also is noteworthy that three of the tax
categories are maintenance which were separated from debt
categories for 1980-1981 and 1981-1982.
Two of the independent variables are revenue data.
Nonrevenue receipts and other revenue from local sources
indicate that school districts need to be entrepreneurs to
enhance fiscal security by generating revenues through
business transactions such as setting up trusts, renting.
88
buying and selling property as the markets make such
transactions advantageous.
Food services is the final independent variable
included in this category. As an enterprise service, it is
another area in which school districts can produce profits.
Another perspective for answering question two is to
examine the frequency with which each variable occurs in the
models identified by this study. Variable 87, other revenue
from local sources, appears in seven of the nine models
prepared in this study, which gives it the highest
frequency. Variable 60, health services, V64, food services
and V65, general administration, each appear four times.
Variable 12, tax rate/$100, and V27, estimated uncollectible
current taxes, both appear three times. Variable 18, total
current year deferred maintenance revenue, V20, prior years
tax revenue, V58, guidance and counseling services, and V89,
nonrevenue receipts, appear two times.
A third strategy for identifying the most important
fiscal indicators is to identify those independent variables 2
that exhibit both the highest values of R change and that
appear with the greatest frequencies in the models. Only
five fiscal indicators meet the combined criteria for
selection in this third group and are listed in Table 5.2.
3. Do different indicators have predictive
significance for school districts with a higher level of
89
TABLE 5.2
FREQUENCIES OF INDEPENDENT VARIABLES WITH R^ CHANGE GREATER THAN OR EQUAL TO .05 THAT
OCCURRED IN MORE THAN ONE MODEL
VARIABLE FREQUENCY R^ CHANGE
V89 Nonrevenue receipts 2 .253
V87 Other revenue from local 7 .149 sources
V18 Total current year deferred 2 .138 maintenance revenue (1980-1981, 1981-1982)
V20 Prior years maintenance tax 2 .110 revenue (1980-1981, 1981-1982)
V64 Food services 4 .051
90
fiscal health than for those school districts with a lower
level of fiscal health?
Different fiscal indicators are included in the models
for the first and fourth quartiles for 1980-1981 independent
variables. For 1981-1982 independent variables, V27,
estimated uncollectible current debt service taxes, and V64,
food services, appear in both the first and fourth quar
tiles. The first and fourth quartiles for 1982-1983 share
only V87, other revenue from local sources. Therefore, it
appears that different fiscal indicators have predictive
significance for school districts with a higher level of
fiscal health than for school districts with a lower level
of fiscal health. This seems to indicate a correspondence
between cash balance and the models that were identified as
2 having higher values of R .
4. Does the methodology employed in this study
provide a viable strategy for forecasting school district
fiscal health?
The data generated by the methodology employed in this
study appear to indicate that this methodology does not
provide a viable strategy for forecasting school district
health. Overall, the values of R change are low. The
models for the same quartiles across years do not include
the same fiscal indicators. A viable strategy would yield
higher R^ values and the fiscal indicators included in
models would be consistent.
91
Conclusions
The perspective of this study focuses on short term
budget decisions. The variables that were analyzed were
budget items planned one year in advance. Studies by Murphy
(1980), Berny (1982), Lee (1983) and Smith (1985) produced
more reliable forecasting models and found stronger rela
tionships between independent variables and dependent
variables by using variables that reflected long term
decisions such as bond ratings and trend ratios that com
pared relationships between indebtedness and total budget,
investment earnings and operating funds, encumbrances and
cash expenditures per day. Their results appear to indicate
that variables reflecting long term budget decisions are
more closely related to cash balance than are the variables
that were used in this study. The results of this study do
not show a strong relationship between the fiscal indicators
that were analyzed and cash balance.
A second indication of the weakness in the strategy to
forecast school district health that was analyzed in this
study is that different variables appeared in the models
across different years. A reliable strategy would use
models that include the same variables. It appears that
other factors affect school district fiscal health more than
those identified in this study. Factors beyond local
control influence local budgets; however, local decision
makers determine local school district budgets; that is, how
92
money is used. It was interesting to note that although
costs of instruction constitute the largest portion of a
school district budget, instructional costs did not have the
strongest influence upon variability of cash balance. This
could be due to mandates that require certain levels of
staffing. A school district has less flexibility in per
sonnel matters than it does in enterprise activities.
Cash balance was used as the dependent variable. A
problem that was recognized at the outset of this study was
that cash balance could not be partitioned into balances
from local, state or federal revenues. Also, cash balance
did not include amounts held in reserve accounts.
Recommendations
While this study did not yield a predictive validity
associated with this strategy for forecasting school dis
trict fiscal health, the goal of determining a viable method
for such predictions remains of significant importance.
Therefore, the following recommendations are proposed:
1. Examine variables associated with long term budget
decisions such as indebtedness, trends or ratios.
2. Examine more recent data because of changes due to
the reforms of 1984 to determine whether the changes in
mandates influence the predictability of school district
fiscal health.
93
3. Examine factors such as fiscal capacity and tax
effort relative to other school districts.
4. Examine and explore methods by which school
districts can pursue entrepreneurial activities to earn
money through cash and securities transactions and by
renting, buying and selling assets and properties whenever
feasible.
5. Examine means of reducing uncollectible tax
revenues.
REFERENCES
Berny, C.A. (1982) . Selected variables as discriminators between financially troubled and non-troubled rural Ohio school districts. Journal of Education Finance, 7, 473-483. ""
Burrup, P. E. & Education in Allyn and Bacon.
Brimley, Jr., V. (1982). a Climate of Change. (3rd ed
Financing Boston:
Candoli, I. (1984)
C , Hack, W. G., Ray, J. R. , & Stollar, D. H. School Business Administration: A Planning
Approach. Newton, MA: Allyn and Bacon.
Chabotar, K. J. educational Finance, 12,
(1987). Use of retrenchment. 351-368.
financial Journal
forecasting in of Education
Cornett, J. D. & Statistics for
Beckner, W. the Behavioral
(1975) . Sciences.
Charles E. Merrill Publishing Company.
Introductory Columbus, OH:
Costerison, D. L. Distressed
(1984) . State Assistance to Financially School Districts. (ERIC Document
Reproduction Service No. ED. 246 536) .
Dickmeyer, N. (1979). Assessing the financial health institutions. Education Record, 60, (2), 159-168.
of
Gaylord, T. A. (1983) Planning: Phase
An Approach to Quantitative Fiscal I Report
Department of Development. ED 239 551).
Juneau, AK: Alaska State Education, Statewide Office of Budget (ERIC Document Reproduction Service No.
Hartman, W. T. & Rivenburg, J. W. (19 85). Budget allocation patterns: school district choices for available resources. Journal of Education Finance, 2, 219-235.
Hentschke, G. C. & Yagielske, Jr. (1982a). Fiscal strain — past and future. Educational Horizons, 61, (1), 12-17.
Hentschke, G- C. & Yagielske, Jr. (1982b). School district fiscal strain: implications for state and federal financial assistance. Journal of Education Finance, 8, 52-82.
94
95
Hentschke, G. C. & Yagielske, Jr. (1983). Response to F. Howard Nelson. Journal of Education Finance, 9, 245-250. -~
Hull, C. H. & Nie, N. H. (1981). SPSS Update 7-9: New Procedures and Facilities for Releases 7-9. New York: McGraw-Hill Book Company.
Is Your Budget in Tune? (1981). The Executive Educator, 3, 25-29.
Jordan, K. F. (1985) . Education vital signs: finance. The Executive Educator, 7 (10), A 11-A 14.
Kerlinger, F. A. (1973). Foundations of Behavioral Research (2nd ed.). New York: Holt, Rinehart and Winston.
Kim, J. & Kahout, F. J. (1975) . Multiple regression analysis: Subprogram regression. In Nie, N. H., Hull, C. H., Jenkins, J. G., Steinbrenner, K., & Bent, D. H., Statistical Package for the Social Sciences. (2nd ed.), 320-367. New York: McGraw-Hill Book Company.
Lee, R. A. (1983). Financial and staffing ratio analysis: predicting fiscal distress in school districts. Journal of Education Finance, 9, 256-263.
Murphy, J. F. (1980) . An analysis of financially troubled school districts in Ohio. Dissertation Abstracts International, 41, 34219A-34220A. (Univeristy Microfilms No. 8100209) .
National School Boards Association (1985). Seventh annual survey of board members. American School Board Journal, 172, (1), 29-32.
Nie, N. H., Hull, C H., Jenkins, J. G., Steinbrenner, K., & Bent, D. H., Statistical Package for the Social Sciences. (2nd ed.). New York: McGraw-Hill Book Company.
Roland, C. (1986). Telephone interview. Austin: Texas Education Agency, Audit Division.
Smith, C. A. (1985) . Forecasting school district fiscal health. Dissertation Abstracts International, 46, 10-A. (University Microfilms No. AAD85-26254).
Texas Education Agency. (1981). 1980-1981 Texas School Directory. Austin, TX: Author.
96
Texas Education Agency. (1982). 1981-1982 Texas School Directory. Austin, TX: Author.
Texas Education Agency. (1983). 1982-1983 Texas School Directory. Austin, TX: Author.
Texas Education Agency. (1984). 1983-1984 Texas School Directory. Austin, TX: Author.
Texas Education Agency. (1985) . House Bill 72 and subsequent educational legislation: comprehensive references and explanations. Austin, TX: Author.
Texas Education Agency. (1986). Bulletin 679: Financial Accounting Manual (6th ed., change no: 19). Austin, TX: Author.
Texas Education Code, Volume 2, Vernon's Texas Codes Annotated, 23.45b (1978).
Thomas, J. A. (1980). Resource allocation in school districts and classrooms. Journal of Education Finance, 5 , 246-261.
Walker, B. D. (1986) . Telephone interview. Odessa, TX: Ector County Independent School District.
Ward, J. G. (1985). Predicting fiscal stress in large city school districts. Journal of Education Finance, 11, 89-104.
Wegenke, G. L. & Smith, D. B. (1983) . Data Needs for Financial Planners. Ann Arbor, MI: Paper presented at the annual meeting of the Michigan Education Research Association, (ERIC Document Reproduction Service No. ED 238 154) .
Zerchykov, R. , Owen, H., & Weaver, W. T. (1982). A Review of the Literature and an Annotated Bibliography on Managing Decline in School Systems. Boston: Institute for Responsive Education.
98
CN >
o o I
'sr rsj o o oj r>» CM 0> CM rH CN r-«-CN rH CM O ( N rsj
• • • • • • o o o o o o
CM ro vo »* vo rH r^ r^ ro vo ^ VD r^ in o o ^ o ro ro o
• • • • • t •
o o o o o o o I I
CN >
r H
• <
fa hQ OQ <: in
cn fa iJ fa m i-Q < OQ H < Pi H cn
X < Pi EH H > < U Pi > H in in P5 < IS EH EH s fa IS cn
P fa H IS IS P P O fa IS H P< fa hQ EH fa PH O < P fa O
ORREL
81 IN
982 D
L SCH
U CT r H hQ r H 1 <
1 r H O 00 00 as as rH
o CM >
as r H >
00 T-i
>
VD T-i
>
i n T-i
>
•^ T-i
>
ro r H >
CO'* cNrHrocr>r*-CM vocM cNrs jCMrors j ro O O O O O r H O O
o o o o
CTv in o r vo o o o f** cy> rH rH vo o
o o o o o
in t^ ro ro rH o 0^ CO CM 0^ ro ro CM CN CN rH CM O
r CM CT\ ro vo o o O O CN rH VO rH rH TH rH rH O O O O
.171
.461
o
.128
o o 1
VD VD CM O H O
O O
a\ ^ o r-* vo o
o o 1
rH CN rH rH O O
O O 1
CO 00 00 VD CM rH
O O 1
CM CN rH O O rH
O O
VO rH 00 O CN O
O O 1 1
as ro o o o o
o o 1
as vo 00 as rM CN
o o o o 1
rH ro CT\ ro in in ^ vo ^ O CM rH
o o o o
' ^ r^ r«- in o in rvj rs] rH o vo o
o o o 1
r* C3 r^ ^ Cr> rH o o o
o o o
rH ro r^ CM 00 r^ i n ' ^ o
o o o o o o
^ '^ CM 'sr in ra 00 VD CO o 00 <y» CM H CM O CM CM
o o o o o o o I I I
VD vo rH 00 O CM vo <y> in ro rH CM 00 VD o o VD o in r-
o o o o o o
O in CT\ ro ro o rH rH O vo O O 0 0 0 ^ * 0 0
o o o o o o o I I i
CN in in 00 o CN rH rsi o '* o in vo rH O O CM H rH H O
o o o o o o
cr> crs 00 rH i n cy r^ CN CTv (T» o " * o r-ro <T> <T> CM rH <X> O
O O O O O O
rH CM <Ti r o rH CO 00 VO r^ rH 00 CO CM rH CM O CN CM
O O O O O O O I I I
VO in ro o CN rH CT» in ro rH CM 00 in o o vo o in r
o o o o o o o
t ^ o o r o r H c r > o o o oo<y»cT>cr»vo'*vDrH ^ O ' s ^ i ' ^ o o r o o
o o o o o o
r^ 00 00 00 o^ in cr> vo t^ rH r* 00 rn \D T-i O T-i 1-i
o o o o o o o I I I
CJ CM -^ cn rH 00 i n r o rH rH O i n rH CO o o ro o ^ ^ CNJ o
o o o o o o o o
t ^ a > r ^ c T > o o o i n o i n aasc^asasO'^rn r^ ino>rocy>cT»o« j rHvoo
o o o o o o
ro 00 o ro CN o^ 00 r^ 00 rH CO 00 CM rH CM O CM CN
o o o o o o o I i I
vo i n ro * * CTi CN vo o> in ro rH rH CO r-o o VD o in ^ o
o o o o o o o o o o o o o o o o o o o o o o I I I
CM r H >
^ ^ ^ o o o ^ r ^ r o c ? ^ ^ * o o r ^ 0 O t ^ 0 O C M C O 0 O C M 0 0 C T > i n r O r H r o r H r o r o c N H O C M
O ^ ^ J rvj rH CT\ ro o ro r ro CN rH O rH O rH rH
O O '^ in rH -^ iH ro ** in 1* ro CN rH O "iT rH O O O
oooooooooo o o o o o o I I I I i i
o o o o o o o 1 1 I I I I
corHO<r>rHcocT» in in<T>r^ C r > r H V O O r O O O C N V D C T » r ^ O V O r O V O C N V O V D r H O C T \ 0
^ CM O rH CN r » rs) <y» CM r H r>a r>j rvj rH CM O CN CM
CN ^ vo ^ r^ CM 00 r^ ro vo ^ vo r^ in o o ' ^ o ro ro o
o o o o o o o o o o o o o o o o o o o o o o o o I I
fa
OQ < H Pi < >
cr»co<r»cy»cNCMCN i n r ^ v o c T i r H O O ^ V D C O r ^ r H r « V O r O r H O ^ C N r H r o o r O r H r o r o c N r H C M O
^ rH vo i^ VD ro r o r* 'sj' t^ r rH O rH O H rH
VD rH CN VD O O t <T» O VD ro rH O O O CM O rH rsj O
O O O O O O O O O O O O O O O O O O
r H C N r O - ^ i n V D O O C T v O r H C N ro r H r H r H r H r H r H H r H C N C M C : ^ Ql > > > > > > > > > > > >
^ in VD r^ cr» o
o o o o o o o I I
iH r j o CN ro ' ^ in ro ro in in in in in > > > > > > >
99
CN CN >
CM >
O rsj >
as T-i >
00 T-i >
VD T-i >
in rH >
rH >
ro T-i
>
CM rH >
fa
CQ
^ Z l ^ ^ Z l Z l ^ ^ ^ v D i H i n r H r H o o c o o c T . C M o o r ^ o r H r ^ c o r ^ c o t n ? ^ ? ^ S ^ i 5 r S r ^ S ^ " ^ ^ c M l n < 7 ^ o o o r ^ o o ^ o c M o k i n ^ o o r - ^ r H o o o o c N o v o i n o r o i n ^ c N r o o o o o o o v o C N O O O O O I H O O O ^ - ^ ^ * ^ ^ ~ * * o o o c p O O O O O O O O O O 0 < T > 0 0 0 o o o o o o o o o o
' ' I cn I i i I I I I I ^ o 15 J5; P; ^ ^ [;; S ; : : J 2 ? S ^ ^ i n o o v o r - v o ^ v o c n o cn CM r - ^ ro S o o S S r 2 S i C ^ 9 S: : :^ iQ: i^ :Z^ m o r o r n - ^ r v j o r o o o r j r o o o . - i O O O O O r H O O r H C N O O O O O O O O r H O O O O O O O O O O ^ ^ ^ * ^ ^ ^ * * ^ ? ? ? OOOOO ooooo ocnooo ooooo ooooo
' ' ' I I cn I i i i I II i Q ? ^ S l 5 J ^ i £ l ^ S 2 ! < 3 ^ ^ r o r o • ^ o o o r s i r o t ^ o o c n O r H ^ i ^ i ^ r - ^ S S ^ ?^ £ j J^ J^ E^ ^ H I S ^ ' D ' ^ r 0 O C N l H a ^ . - H O i n V O O i H r O C M r H C M O O O O r H C N C M r H r H C N O r H O O O O O O r H O O O O O O O O O O
• • • • ^ * * * * . . . . . • • • . . » . . . . o c p o c p o o o o o o o o o o o c T i O o o o o o o o o o o o o
• ' I I c: I I I I I I
^ ^ S ^ i S S S ^ C i i C C N C o o r H v o roocMCN<J^ c n c N ' ^ o r o c n o ^ v o i n o 2 S r ^ 2 2 ^ r ^ 5 ^ * ' ^ v o r ^ - ^ o o o o o o o v D c n o o o c o o o r H - " ^ ^ r H r n c N O O r H O r H V O O V D i n V D C M V O r H O r H O O O O ^ C N O O O O O r H O O O
OOOO OOOOO OOOOO OOOOOO ooooo ooooo • I CTi I I I I I I I
?!! ! ;^?^S2 v D 5 ; " ^ c M r M v o - ^ v o c N t ^ r o o r H l n c T ^ i n r H i n r H r H c n < y > r - i n c n CMOCMOO ' ^ ' ^ r H C N c n v o t ^ r o c o o o o o o v o c n o o o o o c o r H rr fT T-i T-i r-i O O r H O r H V O O V D i n V D C M V O r H O r H O O O O ^ C M O O O O O r H O O O O O O O O O O O O O O O O O 0 0 ^ 0 0 0 O O O O O O O O O O
I I c n I I I I I I I
CM'>PCNvo c o r o c o O r H rHiHTTVOrH f ^ o r ^ t ^ c M o i n i n o o v D cMcr>vo in r^ i - H r H i n i n ' i ^ O ^ r O ^ ' d ' ^ O C M r H C M O O r H V D a ^ O O ^ r O r H r H O r O O C M O O O O r H t — I r H r H r H C N O r H O O O O O V D C M O O O O O O O O O O
OOOO OOOOO OOOOO ocnooo ooooo ooooo I I C7 I I I I I I
c n r ^ o c n O ' s r c n c n o r ^ o r o r H v o rHOrHCTicy\ c N r H i n c N r H as t^ in m o C M O r O O O i n ' ^ r H r H C T i V O r ^ r O O O O O O O O O O O C O O O O O O r H ^ ' ^ r H r H C N O O r H O r H V O O V D i n V O C N V O H O r H O O O O C N O O O O O r H O O O
OOOO ooooo ooooo OCTNOOO O O O O O O O O O O
I I cn I i l l I I I o c N ' d ' V D o o c M o u o r H r o o H V D o o r o o c n u o c N C M r o o r o r o i n r ^ o c M O C N O o r - c M o o o o r o o c o r o r « - C N r - > o O o a > o o o r - i n r o i n u o ' ^ r n r o O O r H O o r o o r o r o r o r n r o o o C M O O O ^ r H O O o o r H r n o o o
OOOO ooooo ooooo oc3^ooo ooooo ooooo I (7\ I I I I I I
o t ^ r H O ( T i i n c n c n r H r ^ c N r o o i n O O O C M O O O rornvocMCM r o o ' d ' i n o r o o r o c h ' * r r r H r H a \ v o r ^ r o o o o r H o o o o o ^ c o o c o o o r H i n i n r H r H C N O O r H O r H V O O V D i n V D C M V O r H O 0 0 0 0 0 ^ C M O O O O O r H O O O
OOOO OOOOO OOOOO OOOOOO OOOOO ooooo I I cn I I I I I I I
^ r ^ r ^ c o ' ; r l n o o a ^ l n o m c M v o i ^ o o o - ^ o o c N ^ r c M r o i n C M ^ ^ O C M ' ^ T C M r ^ o i n r o ' * O r H a ^ v o c M r n r o o v o o c N r o o o roCT>Lnt^ in o o H O r H O o ^ ^ O O O r H C N V O r H r O O O O O O O r O r H O H O O O r H O O O
O O O O o o o o o O O O O O o c n o o o o o o o o o o o o o l l l l l I I I c n i l l l l I I
^ r o o o v o r o ^ r ^ v o c T t v o r H i n r H r H O O O O O O O c M c o r ^ o o r ^ c o v o c o L n «*rHO^vD r o r o ' i ^ i n c M c M L n a ^ c o o r ^ o o ' ^ o c N o r ^ u o r H o o r ^ i - n o o O O C N O v o i n o r o i n < * c M r o o o o o o o v o C M O O O O O r H o o o
OOOO ooooo ooooo oo^ooo ooooo ooooo I I \ as llll II
r H i n C N O O O O ^ r ^ ' S f i n r n r O r H C M i n r H O O O H O ^ ' i i ' ^ ^ t ^ r H C M r ^ r O O r H L j J i J ^ ^ C N ^ O C M O r ^ " < * C M r H r H C M O H r H V O r - O - ^ i n r O r H - ^ r H r H - « * O O O O o c M O C N C N r o r H C M r H O o o o o r o r H O O O O r o o o o o
, , , , • • • • •
O O O O o o o o o o o o o o o < y > o o o o o o o o o o o o o I I I ' r * ' I I I I
VD r- CO cn O rH CN ro ^ VD VO VD VD VO > > > > >
in VO r- 00 CT\ vo vo vo vo vo > > > > >
O rH
555? CN ro o r r- CO > > >
rH CM ro i n VD CO 00 00 00 00 > > > > >
r^ CO ^ o o> 00 C30 00 a^ 00 > > > > >
100
ro in >
in ** r^ ^ <7N in r^ vo ro o o o
O O O O
vo 0^ CN iH CM O t^ CT^ VD vo ro o o I-H o
'^r cr> 00 CM o in ro CM CO 'i r «* ro CM CM ro
o rH CM o r~-00 o CO o ro o o o o o
o o o o o o o o o o o o o <r» o as
CN i n >
o r^ in «H 'd' •^ T-i m T-i •<!r I-H TH O rH o
o o o o o
in o r* cn CM i n i n ^ o fH ^ rH rH rH vo
rH ^ *:}< rH VD O CM r^ rH rH O O O O O
O VD VO O CM ^ CM CM O O O O O O O
O O O O O O O O O O I I
o o o cr> o I I I cn I
o in >
CM ro >
ro >
o ro >
i n 00 ro
00 00 0^ rH rH CM CM CO O rH ro ro o rH o o o o o o
rH o «-i CO cn VD vo in in rH ro o CM «* ^
^ a^ o VD r-o CN o ro ro '^ ^ vo rH ^
vo ro cn o rH rH CN in o o ooooo
o o o o o o o o o o O O O (Ti o I cn I
.236
o
.180
o
.076
o
.074
o 1
.134
o 1
.129
o
.015
o
TOO
*
o 1
.018
o
.026
o 1
.043
o 1
.292
o
.012
o 1
.053
o 1
.235
o
600"
o .050
o
.194
o
rH rH
o o 1
.007
o 1
.005
o
.003
o
.016
o
.076
o
.026
o 1
.012
o 1
.056
o
.010
o 1
017
o .016
o 1
025
o 1
.038
o 1
035
o 059
o 1
070
o 1
104
o 007
o 1
010
o
021
o 1
033
o 1
079
o 1
291
o
014
o 1
061
o 1
219
o
037
o 1
102
o 1
090
o
096
o
224
o
957
o
047
o 1
085
o 1
272
o
186
o
071
o
377
o
008
o 1
015
o 1
013.
o
003
o 1
025
o
113
o
O rH O CN O O
cn o cn
O CO o ro o o as o cn
O rH O CM o o as o cn
as CM >
00 i n 00 CM 00 cn in r^ CN rH (Tv CN O iH O
o o o o o
o 00 i n * * r-<y CN cn o r~-CN CM rH O O
CO r- CN .H rH in rH ro o CM O O O rH O
ro ro r^ VD ^ 00 rH CO in vo CM CM O cn CM
rH rH 00 O ro 00 rH t-H O rvi ro O rH o o
o o o o o o o o o o I I o o o o o o o o <r» o as
CN >
C5 i H * * VD CM 0 0 o^ o ^ ^ ' ^ o CM ro CM rH O O
00 ro rH i n "«T O ro O rH CM o o o o o
rH r^ -er in CN ro rH CM o ro o o o o o
vo "sr r- ^ VD o o o r-- o O O O CM O
o^ CO ro o vo rH ro VD O rH rH O O O O
O O O O O O I I
o o o o o o o o o o l l l l l
o o o o o I I
o o o cn o cn I
vo CM >
i n CN >
CM >
ro CM >
fa hQ OQ < H Pi < >
i n o ^ o o c T v r H O C o o o r ^ r o i n t ^ v o r ^ r H O C M r H r H v o i n c M T H C M O ^ O C S I c N a \ c n i n c o c N r H o o c N o ^ o ^ ^ i n r n r o o c N c o r H O o i n v o c O f H r H o r s i r o a ^ o ^ C M O r H O C M C M I H O O o o O r H O CMrs iocncM r o o H o o
O O O O O O O o o o o o o o o o o o o o o o O O O C T > 0 1 I I as
[ ^ c N v o r H i n c N r H r ^ o t ^ ^ H C M t ^ r o v o o i n C N ' ^ o ^ r o r o < r > r s i o ^ o r o V D i n v o r - r H r ^ c o r H ro<7^ ro rH ro r o i n o r o r o o r o r ^ v o H v o v o o o o o r o ^ r O f Y - ) , _ I O O O r H O r H O O O O O r H O r-i T-i a cn T-i O O r H O O
o o o o o o o o o o o o o o o o o o o o o o o o o o c r > o I I I as
l n a ^ v o o ^ ^ ^ o c M 1 H a ^ o o r ^ L n i n r ^ ^ ^ a ^ r ^ ' * c N r n r o o o i n c M o o ^ r o o c M a^CT^CNO^o^vDoo<NrH o o c N O ^ o ^ ^ i n n r o o c M o O r H O i n v o t ^ r n r s i o c M m 0 ^ r O O ^ O ^ C M O r H O C M C M r H O O O O O r H O C M C M O O N C M r O O r H O O
ooooooooo ooooo ooooo ooooo oooo^o I I I cn
o ^ c N r ^ o c M i n ' ! * o o r * ~ i n cN'«l 'CNa^ro C N t ^ r o r H o ^ c o r H r n r o o o o o r o t ^ o < * r H v D r H ^ ^ r H o a ^ c N ' 5 * ' ^ ^ a ^ r o c M ' * ' * CMOOO^VDVD as T-i T-i t^ cn i — l O ' ^ O r H ( v ^ , _ | f n r s l f * 1 f * 1 r H r H O r H r H r H O O O O O O O O O O r H C M O r H O O O O
C5000000000 OOOOO OOOOO ooooo oooovo
<: rLnvD^~*o^OrHCMOCM C M C N C N C N C M r o r o p L n i n > > > > > > > > > >
ro in VD r- CO 0> O rH (N in in VD VO VO > > > > >
ro in vo r VD vo VD VD vo > > > > >
00 0^ O rH CM
101
r r o 00 00 CO r-r^ CM 00 "sr «* o
r- r^ VD 00 o CM O rH cr, O rH ro ro
in >
CM in >
V5
0
CM
ro >
o • o
as in o • o
CN CM O
O
O T-i
o
in • o
rH CM O •
O 1
rH ro vo O
^ in o
CN • o
00 rH O • o 1
CN CM T-i
O
CM O fH
O • o 1
o CM O • o 1
r ^ o o
CM o o
o • o
r-cn o • o 1
CN as o o 1
vo T-i
o
o • o 1
^ VD O • o
ro vo o o 1
o o o
o • o
o in o • o
iH O O
O
VO CM O
O • o
r vo o • o
o in T-i
o
T-i T-i
o
o • o
ro vo o • o 1
cn ro rn o
00 T-i
o
o • o 1
r-rH O • o
o ro O
o
VD O o
o • o 1
00 rH o • o 1
.H CM O
o 1
o o o
o • o 1
in T-i
o • o 1
cn -^ o o 1
CN CM O
O O O O O O I I I I
O O O O O O l l l l
ro >
in CM vo in o ro r-i as '^ O T-i T-i O O CN O O O
• « • • • • O O O O O O I I I I
00 CN rH o cn 'sr VD CM ro CN O CO O O O O O O
• • • • • • O O O O O O
l l l l
o ro >
in * * cn cr> rH (Ti o cn o^ ro CM ro o CN cn o o o
• • . * • • O O O O O O I i I
r r ro ro r~ r^ CN r^ vo ^ o rH vo O O rH o o o
O O O O O O I I
as CM >
in r^ CO r-> rH o o 00 <J ro CM ^ o rsi cn o o o
O O O O O O I I I
rH ro rH r^ 00 t^ r- vo * * O H VD O O tH O O O
O O O O O O I I
CM >
r o CM CO r H VD r H 00 o o CM ro o rH o ro o o o
O O O O O O I I
o rH 00 CO in ro r^ CM rH in ^ rH O O O O O O
• * • • • • O O O O O O
VD CN >
o ^ CO r- CM o o CO C3 ro CN <* o CM a^ o o o
O O O O O O I I I
ro ro o in VD r^ (^ vo * * o rH vo O O rH O O O
• • * • < • O O O O O O
I I
rH r- ro O CM rH 00 in ^ r- cT\ in
V2
5
'^ CM >
ro CM >
fa i-q OQ < H Pi < >
o o • o 1
ro O o • o
r ro o • o 1
ro
5
vo rH O
VD CO CM
t
O
^ r~ o • o 1
o 00 >
ro • o
r as as
9
O
o rH ro • o
tH
g
O
o • o
r ro o • o 1
ro o rH • o
CM 00 >
o o • o
rH CM O • o
CM in o • o 1
ro g
o • o 1
rH ^ O • o 1 CM VO O • o 1
in CO >
fJS O • o
in r o • o
in o o • o
vo
I—I rH • o
r VD o • o
o o o • o 1
r
T-i 9
O
CM •d" rH .
O
cn T-i
o • o
00
IN O • o
»*
o o • o 1 VD VO o • o
^ 00 00 00 00 > > > >
V — ' 1—1
O O • • o o 1 1
VD in T-i VD
o o . • o o 1 o cn o o o o * • o o
o as ??
102
in VD >
ro rH ro in 00 ro rs] o o ^ o o
O O O O
in o CJ o vo r- o CM rH vo O O O O VD
VD ro r r ^ CM 00 r^ r^ CO rH O O rH o o
o cr> o o o cn I I o o o o o
I I I
ro CN vo ro CO 00 VD CM O CM O rH O O O
O O O O O I I
'sr VD >
r^ o r- TT CM 00 CN vo r^ o '?r CM ^ o o
o o o o o
"^ o ^ r^ VD ro o tH rH cy> rH o o o in
in ^ 'i r CM vo rH rH 00 r^ O CN O O O ^
o o^ o o o (y> I
o o o o o I I I
CM ro CM ro r^ r^ in «* rH o O rH O O O
o o o o o I I I
ro vo >
CM VO >
r H VO > .0
50
o 1
.033
o
.345
o
.467
o .015
o
.434
o
.407
o
.055
o
.581
o
.275
o
.014
o 1
.112
o
.430
o
.014
o .444
o
o rH T-i
O
.007
o 1
.051
o
.006
o 1
.009
o 1
.006
o 1
.071
o
.008
o 1
.080
o 1
.000
as as
.000
cn cn
.000
as as
rH T-i O o 1
.006
o 1
.024
o 1
TOO
o
TOO
o
.004
o 1
622
o
008
o
647
o
285
o 030
o 1
100
o
016
o 1
010
o 1
T-i rH o o
084
o 1
035
o
128
o
073
o 1
017
o
086
o 1
088
o
015
o 1
036
o 1
066
o
100
o
630
o
103
o
630
o 1
203
o
020
o 1
015
o
002
o 1
O T-i T-i O o o o o 1 1
r- o O rH
o o o o 1
CM CM o ro O o o o
1
o vo >
r^ 00 ro ' ^ CM rH in vo CM rH o rsj
O O O O
CO cn O VD VD vo a ro o o O O rH O O
CN o r* VD cn rH O O CM ^ O O O O rH
ro rsi cr> o CO ro rsi o o o o o o o o
o o o o o I I
O CT\ O O O I as
o o o o o I I
ro 00 'O' CO ro in ro o ro iH o o o o o
o o o o o
cn in >
VD "^ r^ O CN rH <! VD r^ in O rH o o o o o o o o
i I I
cr« o r^ cr> r^ in rH ro ro iH rH o o o o
in o ro in r-o o o O 00 o o o o o
in ro ' ^ ro rH tH ro vo r- o o o o o o
o o o o o l l l l l
o cn o o o i at I I
o o o o o I I I
ro VD 'd" o 00 rH VD 'a' tH O O O O O O O O O O O l l l l l
CO in >
^ ro * * r- ro CM tH ro ^ r^ o CM tH ro O CM tH CM
in CM vo ro CO ^ r- r- o CM O O rH o o
ro O rH VD O r^ o vo in ro O O O O rH
in r^ in rH VD in vo ** ro ro o o o o o
O O O O O O o o o o o I I I
o cn o o o as o o o o o
r- rsi ** vo CM in CO ro CM o o o o o o
o o o o o I I
in >
00 CN 00 vo a\ ro vo cn ^ rH vo CM O CM O O O O O O O
CN r- r^ in 00 r^ VD rH vo O o o o o o
o o o r^ r^ r^ o vo o o CM O CM O O
in o^ CM r^ ro r~> rH VD VD o O O rH O O
O O O O O O O o o o o o I I
O CT» O O O as
o o o o o
in cn CN o O CM CN o r^ o o o o o
o o o o o I I I
VD in >
V O ' ^ ^ C T t V O O O t H O O r H ^ t H r H i n C M ' * t H r H O O O O O O
00 O r - VD CM rH rH O t H rH O O O O O
CM o r^ vo o o o o H ro o o o o o
^ VD CO O "^ O H CO rH rH O O O O tH
CO in '?r r^ 00 o r^ CM o o o o o o o
o o o o o o o o o o o o o I I
o cn o o o as I
o o o o o I I
o o o o o I I I
in in >
in >
fa hQ
< H
c N i n v o r H r o v o r o r ^ t H r ^ r H r o r H r o t H C N O r o O O O O O O O r H C M o o o o o o o o o
I C 0 ' * ' * V O r H 0 0 r H < * C ^ V O r ^ t H C M r ^ c M O i H r ^ ' 3 < r H O O O t H O C M C N O ^ r O oooooooooo
I I
L n v D ^ * ~ o o o ^ O t H C N r o ^ i n i n i n i n i n v o v o v o v p v p > > > > > > > > > >
CO in vo vo 'd' rH ro ro CM o O CM O tH o
. . * • • o o o o o
I CM in ro 00 ro ro CM in rsj CN CN ro o o
• • • • • o o o o o
in VD r^ CO o^ vo vo vo vo vo > > > > >
CM o ro o r~ o o o o r-o o o o o
. • • • • o a> o o o
cn I I rH O i n vo CM rsi O r H CM CO o o o o **
• • • • • O CTi O O O
cn I •JC
o H CN ro o
^ o ON ro o as cn 1-i T-i as rH o o o ro
• • • • . o o o o o
I rH CM 00 VD t H ro in o in VO CN O O O O
• • • • • o o o o o
I I I
rH CN ro in VD 00 00 00 00 00 > > > > >
00 iH cx) rvj ';r O CM O O O o o o o o
• • • • • o o o o o
l l l l ro ro o VD CN ^ a> VD rH o o o o o o
• • • • • o o o o o
r- 00 -^ o <y\ 00 CO 00 a > > > >
103
ro 00 >
rvj ^ ro vo iH CM vo o o o
O O O O l l l l
r - 00 CM rH rH ro o o o
• • • o o o
CN 00 >
CO
>l
o 00 >
ro
>
CM
>
>
o
>
00 CM O
• o I
00 CM 00 O CM O
• • o o
I
rH VD CM VD O rH O O O
• • • o o o
I I
C7 rH ro in o o rM o O O O O
• • • * O O O O
I I ooooo ooooo ooooo
• • • . • as as as as as as as as as as
O ro ro ^ ro ro O O O 00 rH rH O O O rH rH O
• • • * . . o o o o o o a\ I I
CM r>- o 00 o tH rsi rsj rH ro o o o o o
• • • • * o o o o o
l l l l
O O VD rH rH CM CN r^ VD rr O O O O tH
• • • • .
o o o o o
vo rH ro cr> o 00 CO rH ^ i n O O O O rH
• • I . *
O O O O O I I
o ro cn rH ro rsi O tH rH o o o o o o
• . . . • o o o o o
I I I
in 00 o '^ o CN O O O tH o o o o o
• • • • . o o o o o
l l l l
ooooo ooooo ooooo • . . • .
as as as as as as as as as as
CT\ r^ vo ro 00 tH rH rH CM O O O O O O
• « • • • o o o o o i I I
VD cn rH rsj O rH O rH O
• * • o o o I I
00 r^ ^ O tH VD o o o
• • . o o o I I
r^ i n rH rH rH CM o o o
• . . o o o I I I
rH ro r^ rH O O o o o
• t .
o o o I I I
CO rH r-O O 00 o o o
• • * o o o I I
o o o o o o o o o
• . * as as as as as as
CM rH CN OJ O O o o o
• . . o o o I I I
o cn >
00 >
ro o o
• o I
r^ as O rH o o
• • o o
I
0)
a o u <u
Xi
+J o c c fd u •p
c Q)
• H
u • H MH MH Q) O U C O
•H •P fC
rH Q) U U O U
as vo >
CO VD >
vo >
VD VD >
fa t-:i OQ < H
< >
i n o CM CM VO CM r^ O O O O O rH O O O O O O O O
•^ CN <r> CM VD rH rH O O tH O O O O O
O O O O cn as •K
O O O O I I
o o o o o
^ - o o a ^ O r H C N r o O l H C N v D v o v o r ^ r ^ r ^ r ^ o o c o o o > > > > > > > > > >
CM rH vo H O O O O O
.273
041
o
.403
000
o 1
.028
o 1
.024
o 1
.164
o
092
o
.111
as as
.000
cn a\
000
cn as
.000
o 1
.048
o
TOO
o
.018
o 1
.025
o
800'
o
.013
o 1
.180
o
640
o
.276
o
.380
o
99
3'
o
.957
o 1
.036
o 1
.012
o 1
.026
o 1
.024
o
.044
o 1
.017
o 1
.037
o 1
.046
o 1
.045
o 1
.009
o 1
.004
o 1
.092
o 1
173
o
.047
o
.080
o 1
.002
o 1
.167
o
.128
o 1
013
o 1
022
o 1
.027
o o 1 1
O rH T-i cn o in o o 1
in »* O CM o o o o 1 1
cn ro rH t^
o o o o o I I
r o i n v o r - c o " ^ o c r * pooopocopo co<y»co
CO 00 >
CO >
vo 00 >
in 00 >
fa hQ OQ < H Pi
i n o CO CM O rH o o o
• • • o o o I I
r^ rH r^ rH O CM O O O O O O
• • . . O O O O l l l l
ro rH ^ ^ r^ rH ro tH o o O O O O O
o o I
o I
o o I
i n 00 CM i n r^ ^ CM rH 'g' ro O rH O O O O O O
• • • * . . O O O O O O i I I I I I
VD r^ 00 ^ O <J 00 00 00 CO o^ 00 > > > > > >
4H •H
(D 4J C
•H U
Cu
cn •H o o o
• as as
rH
>
<
105
rsj rsj >
00 rH O^ OJ rH tH in ro O O O rH
VD cn ^ rsj rH in o in CO in O rH o o o
O O O O o o o o o
ro 00 r^ ro CM ro vo rH T-i cn T-i <z>
• t • .
O O O O
CM >
in in CM vo CO VD o ro o ^ CM O O O O
• • • • . o o o o o
in r^ ro ro rH o ^ o r j o O O O rH o
• . • . • o o o o o
r^ in cTt rH 00 rH ^ '?r •^ H o o
• • * • O O O O
o rsi >
as T-i >
rH • OQ
fa i-Q OQ < in
cn fa t-Q fa OQ hQ < OQ H < Pi H cn
X < Pi EH H > < U « > H in in Pi < IS EH EH s fa IS cn P fa H IS IS P P O fa IS H P< fa HQ EH fa P4 O < P fa O
ORREL
82 IN
983 D
L SCH
U O^ rH KI rH 1 < 1 CM rH 00 CO as as T-i
00 rH >
VD rH >
in rH >
'd' rH >
ro rH >
o rsj
i n T-i cn cn CM ' r
o o
00 o^ ^ VD cr» r o rsj cy> i H
o o o
CO CO i n ro rH r^ rH t ^ ^ rH ^ rH
O O O O
o^ o^ o o> r~~ cn as t^ as cn "«*• cn rsj (T» rH
o in CO CM vo o CN cy\ in rH CM in O ro CM
rH in ro r^ rsj in CO in ^ vo ro o ro o ro
O O O O O o o o o o
i n C3 00 CM CM ro t^ rsi vo " r rsj o o o o
rsj in ro o ^ vo O VD ^ '^ o o o ^ o
o o o o o
vo ro CO rH in o r*j cn in rH CN in O ro CM
o o o o o
O ' ^ rsj rH o in CO in ro vo ro o ro o ro
o o o o o
in o in r* * * cr» in o CM cn rsj rsi o rH o
o o o o o
vo cy» ro CO in rsi Tl* rH O rH rH i n tH O tH
o o o o o
CM ro r^ rH in rH rsi (y» in H rsj in o ro rsi
o o o o o
as CO T—i T—i as ' ^ cj> in ro in ro o ro o ro
o o o o o
as T—i as T—i T-i CO rH ro tH r* r J vo in rsi in o in o
o o o o o
O r^ CN O CM o r- rH " r ro oj ro o rsi vo
o o o o o
in ro VD ro rH rsj vo rsj rH ro rsj o rsi o CM
O O O O O O
CO as as as co oo r^ ro <y» ro cr» vo cr> ro in C3^ cy> rM (T> rH
o o o o o
^ vo in rsi 00 rH rsi cn in CM rsi in o ro CM
o o o o o
O CO CM tH O in o^ in ro vo ro O ro O ro
00 CO o • o 1
00 "«* ro
^ vo ro in r o O VD o • • • o o o i
o CM ro O ^ rH rH rH O
O O O O
^ o in ro r^ in r- o o o vo o
O O O O I I
vo ro rH CT\ o r- in "^ o o ro o
O O O O
ro r-* r-» ^ r-o ^ r^ o o o vo o
O O O O I I
in rH rsj TT rH O CT\ ^ o o rM o
O O O O I I I
ro vo in ro r^ ^ [^ o o o vo o
O O O O O O O o o o o o o o o o o O O O O I I
rsj rH >
L n ^ v o L n ^ ( T > c N C T > VOCNVOr^VOCNVOrO C M r H C M r H C M r H r s J r H
o^ iH ro ^ ^ * * rH O ro O rH O rsj rH O
vo rH r»- C7 in ro ^ ro o^ ro rH O rH O rH
O O O O O O O O o o o o o o o o o o l l l l l
Cr» O 00 rH <y» TH VD rH O rH ro CM
O O O O I I I
r H v o r ^ r o r H r o o o i n m r H r s l t ^ C M i n C N t ^ C M O o i n r o i n r s i i n o i n o
CO o^ o^ ro CM rH CT> i n H VD O CT» O rsj rH
rH o ro O C3 rH ' ^ rH i n rH CM O CN o rsj
O O O O O O O O O o o o o o o o o o o
vo rsj 00 un KD m T-i '^ o o ^ o O O O O I I
v D r o o ^ l n o L n o o f ^ v o c » l n r o o ^ ^ ^ o r o o ^ v o o ^ o ^ r H t H r o H ^ r s j r o H r o o
r* r* o H in ro in ^ ro r^ rH rH O CN rH
o rH 00 ro 00 ro vo CM <y> CM rsi rH rsi o rsj
55» vo vo r^ ^ CM 00 ^ o o rsj o
o o o o o o o o o o o o o o o o o o o o O O O O
fa
OQ < H pa < >
r H C M r o ^ i n v D r » o o < y i O
> > > > > > > > > >
rH rsi ro ^ in v o r - * o o c r » o r n r s i o r s j
106
rsi rsi >
r j >
o CN >
as T-i >
CO rH >
VO rH >
i n rH >
rH >
ro 1-i >
rsi rH >
fa
OQ < H Pi
>
2 J ^ ^ J ^ ! 5 ^ rii^S!?!:22 o o 00 rH ro o v o t ^ r s i ( T » ro t^ r o - ^ "^ r- rsi rH 3 2 S R R S S S ^ : ^ 2 V D O j O O r O C M C M r H O r O r H t H i n r o i ^ t H rH o ^ ^ r H r H O O O O O O r s I O r H O r H O r H O O O O O O C M O O O O O O O • • • • • • • • • . . .
O O O O O O o o o o o o o o o o o o o o o o o o o o O O O ' ' I I
S S J ^ Q j n S ^ H J S ^ ^ ' " ' o o r H i n v o o ^ •«a'r--vocorH r - r o r s i o i n r H f ^ r o o S § o S ^ R P ^ Z ) ; : ^ S ^ ^ 2 : i Q ^ r H r O O C M H i ^ t H ^ U ^ C M ? ^ O C N O r H O O O O O O r H O O O r H O O O O O O O O r H O O O O O O O
• • • • • • • • • » . • * • • . • • • • • • • > . . . . . O O O C I J O C p O O O O O o o o o o o o o o o o o o o o O O O
• • • I I I I I I n : ! r X 2 ! J 5 ' ^ ! r 1 corsjcy»rsicri o j r - r o o o r H ^ r s i o c r » i n as\o ID "^ cn T-i -^ i-i ^ ^ ° o ^ r i f ^ i n v o r o ^ ^ r o r - i n r s i c M r H ^ r M O c : ^ o ^ l n r ^ t ^ r H J ^ ^ J N i n i n o o o r H O r H v o o v o v o v o r o r ^ c N o o o o o c n r o o o o O r H r H
O O O O O O o o o o o o o o o o o o o o o O O C D O C J C 5 0 C D I I I I I I I
i f 2 ! 5 ^ ' ^ : : 1 ' ^ r s i r ^ r n r - r n r H c n r o c N r ^ o o ' ^ r o L n c s j r ^ i n r H v o v o r ^ v o o ^ ^ £ ^ ! I J £ ^ ' ~ ' c M o o c T i o c n i n r H r H i n v o r s j i n o ^ i n ^ i n c r ^ r o r s i r H o o r H r H O O O O O O r H O r H r H r s I t H r H r H O O O O r H C M O O O O O r H O
O O O O O O O O O O O o o o o o o o o o o o o o o o O O O I I I I
r H r ^ c N v o o o r H v D ' ^ o c M O cMoo 'd ' vo i n r o r o c T > r * - o cy>inoo«?j"CN o r - » o i n v o o o i n r H C M invD"<j<rHin r o r ^ i n r s j r M r H ^ ^ r H O o ( T i i n c N r ^ r H ro^*r^a i n i n O O O r H O r H V D O V O V O V O r O t ^ r s l O O O O r H c n r o o o o O r H r H
O O O O O O O O O O O o o o o o o o o o o o o o o o O O O I I I I I I I
( y » r ^ c o r o r o r H r n r ^ ' a ^ v o c n v o c o r o i n c o cNCT»cNrHO o i n r o o c M o o o i n r H ( y » r H r H t H r H C M i n i ^ O O r O i n r H r O V D O O O r * j r s I C M r H r O ^ O O O V O r H C N C M O O O O O r H r O O r O C M r O r H r O O O O O O O O r H O O O O O O
O O O O O O o o o o o o o o o o o o o o o o o o o o O O O l l l l I I I I
r H o ^ r H v o r ^ o vDvorocMrH r H o r o r ^ ^ cn cn as CO as as r^ co m -^ o v o c r * i n v D o o i n r H C M i n v D ^ r H i n rooo incNCN r H ^ r H O c y \ cy» in rs j r ^ rH r o r * r H i n i n o o o r H O r H v o o v D v o v o r o r ^ r s i o o o o o c r » r o o o o O r H r H
OOOOOO OOOOO OOOOO ooooo ooooo loo I I I I I I o
i n c N i n v o c M V D o i n r n r o i n v o i n r H i n c N m o i n o r - cMcr»r^ t^vD rHCMin i n c M i n o o i n r - r o c o m c M cNCNH<r»rH r H ' d ' r H o o c M r s i o v o o o o o o o C M C M O O O O O O r O O r O ^ r o r s i r O r H o o o o o i n C M O O O O O r H
O O O O O O o o o o o o o o o o O O O O O o o o o o O O O I I I I I I I I
o r ^ r H i n r ^ o r ^ i n ^ ^ r o o r o < T » r o r * ^ r o r o o ^ o o c o a \ L n c o i n ^ O V D C N i n v D c o i n r H C N i n v o ^ r H i n r o r ^ i n c M C M r H ^ a ' r H o c y i CT\incNt^rH r o r ^ c M i n i n O O O r H O t H V D O V O V O V O r O t ^ C N o o o o o < T » r O O O O O r H r H
O O O O O O O O O O O O O O O O o o o o o o o o o o O O O
o o v o L n r H a ^ c N i n c M O ^ i n ( T > C M O H C N r o r o i n c M r * - l n c o o ^ v D r H inrHCM c^ m T-i T-i \D '^ C M C N r o o o o r ^ o c n r * * ^ CNCMCMroro v o r o c N i n r * r o o c o O O O O O C N r H O ^ O r H C M V O O C M O O O O O O C N r H r H H O O O O
l O O O O O O O O O O o o o o o o o o o o O O O O O O O O l l l l I I I I I l l l l l I I I I
o ^ r o o ^ i n r H i n v o i n o r o o o i n c o o o r o r H O O ' * c M i n r H ' « * i n O C N O O v o r H o o r o r H ^ i n r H O O v o o r H r o r o o o o o r H H r o r s j r H O V D O ro ' s r cn c N f » i o o o c N o r ^ r o o r o ' ^ r o c M ^ r H o o o o o i n c M o o o O r H O
ocDCDCJCDCD o o o o o O O O O O O O O O O o o c D c p c D c p o o I I I I I l l l l
O N _ j , * c N C M r * r ^ r n r o r H i n (y>rsicocMro r s i i n o o c o v o t : r 0 0 * ^ 2 ! ^ 5 i ! 5 ' T ^ O ^ ^ ^ r H C M r H ivf O H - ^ r^ O V O i n O O i n rH rH rH rH rH 0^ CM rO O IQ 2 ^ 3 : i£^ S ^ O H O O o o ro o CM rsi ro rsi rsi rH o o o o o ro rsi o o o o ro o
. . . . • • . . . . . . . . O O O O O O o o o o o o o o o o o o c D c D O o o o o o c p o o
l l l l l I I I I
ro •«* in vo r* CO <y» o rH CM ro in vo vp vp vp > > > > >
';!< in vo t^ 00 vo vo vo VD vo > > > > >
c n o r H C M r o o r H C M r o ' ^ v o r ^ o o
107
IM rsj >
1-i rM >
o IM >
as r H >
CO r H
>
VD r H
>
i n r H >
^ r H
>
ro r H >
rg r H >
1—1
r H >
r H >
fa l-q OQ < H
VA
R
i n o o
• o
CO o o
o 1
r H o
• o 1
r H rsi o
• o 1
00 r H O
• o 1
o rH o
• o 1
00 r H o
o 1
-s * T-i
o
o 1
00 T-i o
• o 1
o CN O
• O 1
00
ro rsi o
o 1
i n rsi o
• o 1
as T-i o
. o
as o o
• o 1
as T-i
o • o
i n
o •
o 1
00 r H O
o
i n i n o
o
as r H o
• o
00 rsj o
. o 1
i n O 1-i O O
O O 1
i n ro r H 00 O ro
• • o o
1
o as
o i n >
CM ro >
r H ro >
o ro >
cn CN >
CO CN >
r^ rsi >
VD rsj
>
i n rsi >
<* rsi >
ro rsi >
rsj
CN >
fa a OQ < H
VA
R
rsj CO VD in CO ' ^ rsi in rM ^ in o
O O O rH ^ ' ^ o in o r o o ro o rsi
in 00 H 00 <T» ^ r H Tjt Tj< r H
in H ^ ^ vo O O O O
rH r>* rsj ro cy» o rsi o> -?}• o o o o o o
o o o o o I I
in rH o r- VD o in in ro o o o o o o
ooooo o o o o o
ooooo
CN O r* CT> CM ro in in in O O O O O . . . . . o o o o o I I I
.413
o
i n VD
o
rsj
o
1-i rM
o
o as cn CO "«* ro
o o
as vo cn CM cn CM
o o
1-i ^ 1-i CM •^ rsj
o o
.383
o
vo cn 1-i
o
cn T-i cn
o
VD o rsj
o
t H
o
r- rH rH ro rH O
O O 1 1
ro CM i n - ^ rsi o
o o
T-i in vo o o o
o o 1
m 1-i
rsj o
o o
^ vo CO ro o o
o o
i n o o ro o o
o 1
00 o ro
o
i n o o
o
rsj o ro
o
vo 00 o
o
o 1
rsj vo rg
o
rn o o
o 1
.007
o
00
rH
O
•>* O O
o 1
i n r» CM r H
o
i n as o
o
rsi rH o
o o 1
.024
o 1
vo o o
o
rsi o
o 1
i n o o
o
ro CM o o
1
045
o
i n o
o
00 ro o
o
i n o
o
o o
o 1
in in rH rH rsi CM O O O
O O O 1 1
^ rH 00 ro 'sr VO rH O O
O O O 1
rsi ro <T» CM O rH O O O
O O O 1
rsi o vo ro ' ^ VD rH O O
O O O 1
\D as as CM O O O O O
O O O 1
CO o < ^ T-i o o
o o 1
i n o ^ in 1-i o
o o
rH 00 ro ^ O 1-i
o o 1
o i n ^ in 1-i o
o o
in CM as vo o o
o o
^ o o rsi rsi o O O H
O O O i 1 1
^ ro r^ vo vo vo ro rsj rH
O O O
cn o r^ ^ VD in O O O
O O O 1 1
cn vo CM in in VD ro CM rH
O O O
CO vo in rH ro vo rH O O
O O O
vo o^ VD CO o 00 ro cr» vo cy> ro o " r <y> "^ cyi rsj CM
in CM rH f^ CM ' ^ ' ^ o i n t^ CM O ro CN rH
' ^ VD rsj o in o in ro •^ vo O O rH o o
rH VD CO ' ^ rH * * i n i n i n VO rH O ro CM rH
O O O O O O o o o o o O O O O O o o o o o
r H O C M O ' s T r H c n cTNOors joo in '<3«r^oocn cn as ^ cn as r ^ v o r - v o t ^ o ^ H i n i n i n r ^ cMrHCM's ro o o r s i r ^ i n r s i ^ r H ' S T r H ' ^ r H t H r H O r H O O O O O O O r H O r H r s l r H
O O O O O O O OOOOO OOOOO ooooo I I I
c N O ^ L n ( J ^ ^ c o o o i n o r H i n c N i n v o r H O * * i n i n o o r ^ r o cnc3^rocy^voo^rorH ^ ^ ^ o i n r * o i n r o ' ^ r v o " ^ m i n i n v o ' * c n ' * o > ^ c y > r s i c M o j o r o r s i r H o O r H O O r H o r o r s i r H
o o o o o o o o ooooo o o o o o o o o o o
cy>cMOorsjroCT\VDO^CT\ r « c n r o r o c N i n i n o o ^ v o C M r ^ r o r H i n r o o ^ r o c N r o c T ^ c M l n H i n r ^ m r H r H r o i n o r s j r - * c M H v o r s i o o ( v ^ ^ r o r o r o r s i r o r H r H o H r H r H O o o c M r H O o o o o o
CDOOOOOOOO ooooo o o o o o ooooo " llll lllll II
g > . f r ) o . , _ ( o r o o c r » v o r s j o o ' ^ O ' ^ o c n m n i n v o i n o r o o o i n r H V O r H ^ r H i n r H V O i n rH -^VOrHCO Cn i-i "^ ID rH C O V D O r H r O o c M ^ r s i o c M O C s j o o ^ o c M r o o o o r s j o r ^ r o o r o ' ^ r r o o o o o o o o o o o ooooo o o o o o o o o o o I I I I I I
r o ' s r i n v o r - ^ o o c n o r H rsi o rsi ro ^ in in in in uo in > > > > >
vo r^ 00 o^ o in in in in vo > > > > >
rH rsi ro ^ in VD VD vo vo VD > > > > >
108
o ID >
rH 00 r r o 00 VD rH O rH O CN VD rH O O
00 VD CM VD CO ro rM o r 1^ ^ in O O O VD CM rH
o j 00 rH ro CN ro r^ o ro rH r^ VD CM o O CM O CM rH O O
o o o o o O O O O O O O O O O O O O I I I
r«j ro >
o in ro o VD 00 CM ^ o o rH O O O O
CN CO r«- CO CN ro CN 00 rj« ^ rH CN O O O O CM O
O O O O O O O O O O O
00 VD r* ro r^ VD CO ^ rH ro Cy> '^r rH O H O O O O O O
. . . . . . . O O O O O O O
I I I I
ro >
o ro >
cn rsi >
00 rsi >
rM >
VD rsj >
inoor;»covD r^r -<yt^rorH roocovDcyivor^ ^^JdP iOO :Z!J£J^«^^f^ rHCN^CMSrHO r s j o o o o o o o o r M o o o o o o o o
• • • • • O C D O O O O O O O O O O O O O O O O
. ' ^ f ^J^ r2 : i ' c o o r - o c n r > - cnrHcoor>.'«*o iiJJ^f)J:i^2^ CMinrHVDcy>rsi r t r o o t ^ r o r s i m C J ^ r O i n O O O O O r O O ^ O O O C M r H r H O r s l o o o o o O O O O O O oooc3c:><i>c>
I I I
i 2 ^ 5 ^ S ^ r-cy>r-roorH oorors icncnoo ^ C N r H i n O O r H C 3 ^ r H ' ; f ^ C M r O C M r s l C T l ^ O O ^ O ' ^ O O o o o o v o O O O O O O r H o o o o o O O O O O O O O O O O O O
I i I I I I I
vDO>^inro o^'i'corHcrtr^ OrHcr tocNroo intHrorHCTN cNinrHinCT^CN inrocMr^rocNin o ^ r o i n o o O O o r o o ^ o OOOrHrHOrs i
o o o o o O O O O O O O O O O O O O I I I
"ia r-CMoovD vDorsivDinr^ ininrHrH<T»rHr^ C O O ^ O O O C M r H r H O C O r H ' * r s l r H C M r O r H O m r O r H r H r H O O O O O O O O O O O O O O
o o o o o O O O O O O O O O O O O O I l l l l
inrHrovoro cr»rocoooooo OrHcncTvo oo incNrorHcn rsiinrHincrvrsi in rors jvororo^ < T > r O i n O O O O O r 0 < y » O O O O r H r H C M C M o o o o o O O O O O O O O O O O O O
I I I
i n rsi >
CN >
ro rsj >
rsi rsi >
fa hQ OQ < H Pi
r ^ V O V D C N C O ^ r s I r H t ^ ' ^ l ' r H C M r o i n c T i i n c M r H V D i n ' ^ T r H i n r H C M O r H I ^ O C N O C M r » V D r H < T t ^ r H C N O O O O O C N " ? r O O O O O H O r s I
O O O O O O O O O O O O O O O O O O I i I I I I
ID T-i cn ID cn o>ror^rHcoco as T-i as as cn c^ cn incMrorHcr* rsjinrHino^cN •sj'rocNvDrorsiin o ^ r o l n o o o o o r o o ^ o o o o H r H O C N
O O O O O O O O O O O O O O O O O O
o>OLnroo ^ ^ KD oo as as cxjinrHo^cNcovo c n o r ^ r H O CMtHro<y>rsirH CNororsirHorsi fvj,_l,_IOO O O O O r O O O O O O O O H
o o o o o O O O O O O O O O O O O O I l l l l I I I I I I
inoocororH o o ' ^ c N i n o ^ i n o c N c o o o i n CMOOOO rH rH ro rsj rH o VD o ro <«* cn O rH CNOrHOO O O O i n C N O O O O t H O O O cDOCDcJo O O O O O O o o o o o c p o
I I I I I I I
VD r* CO a\ o rH CN ro O rH CM ro "^ VD r 00 o o
109
ro VO >
ro o cy> ro ro CN o CN ' ^ TJ< CN CO o "^ i n ^ ro i n rH o o
cr» <y> VD a^ rH rsi CM O O ro ^ vo rsi ro o o o vo ro o o
00 00 as as c^ CO o ^ cy rsi o CM O O rH rH o o
O O O O O O O O O O O O O I I
O O O O O O I I
rsj VD >
1 ^ 1 ^ O O ^ r H r o V D O i n i n v D v o r o r H o r o o o O O O O O O
o o I I
O CM O ro O VD i n ro rH o H i n rH i n O O O O O O O
o i n CN vo rH rsj rH CM rsi rj< O CM O O O O O O
O O O O O O I I I
O O O O O O O I I I I
O O O O O O I I I I
VD >
VD r^ ro CO i n rH o ro ^
O O O
00 rH 00 rsi VD CTt cn vo ro cn rH CM un rH i n o o o
CM r^ VD ro rsi i n ro rsi CM CM ^ ^ rsj 00 O O O VD H rH O
00 i n o r^ rsi r-* H o o i n CM rsi rH O rH rH O O
O O O O O O I I
O O O O O O O I I I
O O O O O O I I
o VD >
<y> i n f^ o <T> ro i n ro rH rH O rH
O O O O
i n 00 r^ r- i n ^ cn O rH rH o o O rH CM O O O
^ ro ^ rsj VD H * * O O CN vo VD O O O O O H O O rH
O O rH VD O^ O rH O O rsi O rH O O H O O O
O O O O O O O O O O O O O I I I
O O O O O O I I I
as ID >
VD t ^ i n o o> CM i n cn ro rsi O rH O O O
o o o o o I I I
i n '<;»' rH o^ ro CO o ro CM rM rH rsi rH O O O O O
00 rH o^ r^ o^ o^ r^ i n o o i n ro rH vo O O O O O O O
CM t^ r^ (Ti r^ r* rsj "sr o i n o rsj O O O O O O
O O O O O O l l l l l
O O O O O O O I I I I
O O O O O O I I I I
00 i n >
ro O 'iJ' CN rH i n CO rH ro i n cn r^ rH ro O rH o o
r - »* CO i n cTt rsj CO ro ^ ro H r^ O rH rH o o o
vo in o cn ^ rr O vo CO H ^ o oj O O O rH rH O rH
VO <y» VD rH cn 00 ro - ^ 00 rsi o o O O H O O O
O O O O O O O O O O O O O O O O O O O I I
O O O O O O I I
i n >
o rH ro o vo ^ r>-rM VO ro rH rH O 00 rH O O O O O O
CO CM i n rsi VD rsj vo VD ro rH o i n o o o o o rsj
r^ 00 'sr 00 00 rH CM O "^ rH rH i n H ' ^ O CM O O O O H
^ * * ro t^ ^ rH O t ^ rsi O O rH O H O O O O
O O O O O O O O O O O O O O O O O O O O I I
O O O O O O I I I
VD i n >
r o r H O O ' ^ r o i n r o r H i n r H C M V D C M i n o O O O O O O O O O
VD rH ro r* VD H ^ ro H O O H O O O O O O
' ^ rH CM i n VD CO CM o o o i n o o rH O O O O O O O
CN vo rH ro i n ^ O - ^ VD CM CM rH O O O O O O
O O O O O O O O O O O O O O I I
O O O O O O O I I I
O O O O O O
in in >
in >
i n r H r * ^ i n r ^ c M o r s i V D C M C M O r M O r H O C O O O O O O O O r H r H
CM r r rsj cr» CM rH rsi vo r* o o o O rH O rH O O
CN ^ i n ro t ^ cy> rH o o o 00 r^ o rH O O O O rH O O
rH rsi O 00 ' i ^ VD o o o rH rsi o O CM O O O O
o o o o o o o o o I I
CN ascni-iy£>oii-ti-*^asi-i v D ' s f i n o r o o r o o ^ ^ O O O C N O C N r O t H O r O
. . . . . . . . . . O O O O O O O O O O
O O O O O O
o ' ^ i n H rH ro 00 i n (Tv CT\ rH rsj ro rM "^ o o o
. . . . . . O O O O O O
O O O O O O o I I I I
rsj 00 ^ cy» o ro CM O CN VD vo VD r o ^ o o o i n CM o o
• • • • • • • O O O O O O O
I I I
O O O O O O I I I
rH 00 CM ^ ro ro CO ro o 00 o o H o rsi o o o
• • • • • • O O O O O O
ro i n >
rsj i n >
fa (J OQ < H Pi
^ i n r ^ o o r ^ o r o i n o v o o ^ v o o ^ ^ o o O L n v D O ^ v o
^ O r H O r O r H H C M O - ^ r O
O O O O O O O O O O O
c n o o i n ' ^ r ^ ' ^ o c M V D o o v o c N V O n O O C M r H O C y » V D O r s I ^ O r H r H O O r H i n O J r H r H r H O O
. . . . . . . • • • • • o O O O O O O O O O o o
I I I
r o ' ^ i n v o r ^ c o o ^ O r H C M c*};^'
00 o^ rH ro "^ rsi r - rH i n o CN ' ^ CM ro 'sr rH O O
. . . . . . O O O O O O
VD o^ CO CO o r^ rH ro r* rH O rH rH O O O O O
. . . . . . O O O O O O
I I
i n VD r^ 00 as o VD VD vo VD VD r^ > > > > > >
rH o o CN VD ro ro rsi CM H in o ^ as o o rH in ro o o
• . . . . . . O O O O O O o
I rsi o o rH rH ^ r^ rH o o^ o ^ i n vo O O O O O O rH
. . . . . . . O O O O O O o
rH rsj ro O rH CM ro
as as cn yo cn CO ro rsj o r^ ro ro o o rsj o o o
• • • • • • O O O O O O
I VD i n ro r^ ro o CM r-- VD ro o ro O O rH O O O
• • • • • • O O O O O O I I I
^ VD t^ CO o <y>
110
CO >
CO O rH O CN in ro ro O O O O
. . . . O O O O I I
O ' i j ' r r 00 f^ ro CN rr tH rH O CM
. . . . O O O O
o 00 >
in VD ro o in CN r rH ro ro o o o o
. . . . . o o o o o
I I
^ o 00 cn r>- CM rH rH rH rH O O
. . . . O O O O
ro
>
rsj
>
in r o 00 in ' f O^ tH O "^ O CN O O O O O O
• . . . . . o o o o o o
CM 00 CN cr> in o r o o in o *!* o o o o o o o o o
• » . . . . . o o o o o o o
i I I I
VD ^ O 00 og o o o O O O O
. . . . O O O O
I i I
rH r f rH r^ O rH O O O O O O
. . . . O O O O
I I
>
f^ rH O O O CM O O O
. . . O O O
I I
o vo CN ro o rsj o o o o o o o o o
. . . . . o o o o o l l l l l
ro cyt CM in rH O O O O O O O
. . . . O O O O l l l l
o >
rH o ro CM rsj o o '^ O O O O
. . . . O O O O
ro VD in o 00 cn rH rH rH ro o o o o o
. . . . . o o o o o
I I I
00 O t ^ 00 O ro O rH O O O O
. . . . O O O O
I I
o cr» >
i n o o
• o I
as VD >
ro O CN rH ^ 'sr O O O rH O O O O O
. . . . . O O O O O
l l l l
^ rsi r ro r H O rH o o O O O O O
• • • • • o o o o o
I I I
cn T-i 1-i ^ O rH o o O O O O
. . . . O O O O l l l l
00 00 >
00 r-o rsj o o
• • o o I I
00 vo >
rH VD ro i n rH O rH rH rH rsj ro CN O O O O O CM
. . . . . . O O O O O O I I
i n 00 CO o VD rsi O O rH o in o o o o
• • • • • o o o o o
I I I
r^ CO 00 rH vo ro rH cn rsi o o rsi
. . . . O O O O
CO >
vo r o o o o
rsj
O O O
VD >
i n 00 rH rH rsj ro VD <y> rH ^ O rH VD CN o o o o o o r-
ro in 00 r 'jj* rsi oj o ro rH ro o o o o
O O O O O O O I I I
o o o o o
CM ^ O VD rH i n rH O rsi rH o O
O O O O I I
VD 00 >
o rH r r rH TJ* O O O O O O
. . . . O O O O l l l l
VD VD >
r ^ o o C T \ c o o i n r o o v D r H c r > c M ' * o i n r o i n o o o o o r o
i n ro *!»• CO rH in rsi '^ o ro o o o o o
o o o o o o o o o o o o o
ID •^ ID 1-i 1-i 1-i C^ T-i OJ rH o ro
O O O O
CO >
'^ rsj cy» r H c n rH O O O O o o o o o
. . . . . o o o o o
l l l l l
i n VD >
VD >
fa
OQ < H Pi
^ ^ o r ^ o c r > v o ' * o ^ r^"5;t«orMrHCNrorHr^ r H i n r H O O O O O V O
cn r^ oo T-i a\ vo 00 ro vo o rH O rH O O
ooooooooo l l l l
^HOO^cooo^*LnvDO^rH inr^cr i rHrHvorHcsirs j ro i n r M ^ r H O O O O O V D
o o o o o I I
o ro rH rsi in VD 00 rH rH VD CN O H o ro
o o o o o o o o o o I I I
o o o o o I I
L n v D r - c o a > O r H C N r o o rH rsi ro - r VD
i n o <T» r^ r in rsi o rH rH o o
O O O O I
^ i n o (Ti ID T-i C^ ID rH rH O O
O O O O
r- 00 o cr>
ro 00 >
rsj 00 >
fa hQ OQ < H
Pi
>
00 r ro vo rH r 00 o CO r^ i n CM O O O O O O
. . . . . . O O O O O O
I I ro ^ ^ rH VD vo r>> O O O rH CM O O O O O O O O O
. . . . . . . O O O O O O O
I l l l l
ro ' ^ vo r^ 00 o <T>
112
o vo >
rH O rH rsj CO r * ^ ^ ^ <yi r H rH O rH O
. . . . . O O O O O
o r* ^ rsj o in o ^ o rH O CM rH o o
^ cn as O O rH O O O
o o o o o O O O
as in >
t^ ro 00 rsi o O ro 'd' rH o in rsj O H rH rH O rH
. . . . . . o o o o o o
I I I
<y> cn VD ^ ro CM rH ro o vo o o o o o
. . . . . o o o o o l l l l
VD cy> CM
o in o O rH O
. . . O O O
00 ID >
r o 00 CN 00 vo O CM o rH VD a^ '^ (y> ^ CM r o O rH O O rH
o o
1-i T-i <D cn \D cn rH in o r-» O rH O O O
o o o o o i I
o o o o o
r^ VD '^f o '^ r^ O O O
O O O
in >
r H .
u
fa f j OQ < b^
cn fa cn i-:i fa OQ f-q < m H <c Pi H cn
X < oi in H > < u Pi > H in in Pi < IS EH EH S fa IS cn
P fa H 2 IS P P O fa IS H PH fa hQ EH fa P< O < P fa o
ORREL
83 IN
984 D
L SCH
U 0^ rH KP rH 1 < 1 ro
OJ 00 CO cn as rH
vo in >
in in >
^ in >
ro in >
rsi in >
00 ' ^ rH cn r^ CM O O O O O O
as 1^ cn as •^ in r^ in O rH o o
O O O O
00 CO ro vo in CM rH VD o rsj o o o o o
cn o rH o 00 00 ^ in vo r^ o o o o o
o ' * vo '^ ro 00 r* rsi CN 00 o o o o H
o o o o o I I I I
H ro O VD i n rH CM rH ro CM O O O O O
o o o o o
VO ro ro in O O rsi rH rH 00 o o o o o
o o o o o
ro i n H C3> "^ o o 00 in rH o o o o o
o o o o o
CM 00 00 o i n O 00 ro O O rH O O O O
o o o o o
VD i n o i n t ^ CM ' ^ r** r o VD r J cn O O O rH O rH
o o o o o
ro rM r* ro cn vo H -"^ CM [^ CN o ' ^ ro ro
o o o o o
rsi ro VD in ro CN o o CT\ r j CM in rH o o
O O O O O O
rH ro ro ^ in r^ ro ';r in ro 00 vo OJ o^ ^ O tH O CN rH O
o o o o o
00 VD rsi rH in ro ro O vo ro rH o ro OJ rsi
o o o o o
VD cn r» o o ' ^ CM rH r o CO CM ' ^ rH O O
O O O O O O O
v D v o r ^ r s i r ^ v D V D i n o v o c M O H ' ^ r ^ r o r H O O t H r H ' s r r s J r H
o o o o o
rH CM 00 i n 00 a^ ro CM ro O H O O rH
O O O O O
^ i n o C3 OJ ^ ro rH ro ro o o o o o
i n CM CN o in OJ O O O
O O O
VD '^r <T> o vo in O O O
O O O
rH r^ r^ o in o O O O O O O
ro o ^ Ol CM ro O O O
O O O I I
«* in vo O rH 00 O O O
O O O
^ ro CN O O VD O O O
o o o o o o o o O O O O O I I I
o o o o o O O O
in >
c M r ^ c n ^ i n o o i r H r H O i n r H O O ' ^ O O C T * O H r H O r O O r H O O
00 o ro 00 [^ VD CM vo r^ cr> O O rH O O
ro t^ CM VD in ro rH ro o o^ O rH O O O
o o o o o o o o o O O O O O o o o o o
r-. o 'a* O O O O O O
O O O I I I
o in >
C N ' * o o v D O r o a ^ r H V O « * r o ^ ' * r o o ^ v D O O ^ o o ^ r H C N r O ' ^ O O O C N O C M
i n ^ 00 <T> r-o o r^ CO cn in o '^ ^ vo
in cy> r* o ^ VD •<* r o O rH rn KD T-i rn <Z3
O O O O O O O O O O o o o o o O O O O O
cn o vo ro o ro O O O
o o I
fa hQ OQ < H Pi < >
C M ' * ' * o o o ^ o o o o o ^ * L n c N ^ O r O r H r H H C M O O ' d ' H r O r H o r o r o o o o o o o
(TV r^ ro r^ r-« ro OJ rH vo Ol
ro o ro CM ^
o vo o in o 00 r^ 00 rH rH 01 ro rH rH O
ooooooooooo I I I
Q , _ l r s I r O " « : r l n v D ^ * o o c T ^ o
o o o o o
rH OJ ro ' a* in vo vo vo VD vo > > > > >
o o o o o
vo r^ 00 <T> o VD VD VD VD r^ > > > > >
ro o^ 00 O rH ro O O O
O o I
rH Ol ro
555
113
o vo >
cn in >
CO in >
in >
VD in >
in in >
in >
ro in >
rsi in >
in >
o in >
fa hQ OQ < H Pi
r H O ' ^ o j r H o i r o o r ^ r o r H o r o r H i ^ r o i n o i n v o c o i n o r H O v o r H ^ t H r H r H o o as T-i KD CO cn rOCMOO r H O O O O O r H O O O O t ^ t ^ O O r H O O O r H
O O O O O O O o o o o o O O O O O O O O I I I I l l l l
C M r ^ ^ r H o i n r o o o r ^ o o c o v o " ^ r ^ o c o c y * o ^ v o VD'<3< ' *CT\0 ' * rH inrHCMrOVD i n r H r H V D O o i r^vo O O O O O O O o o o o o O r H r H O O O O O
O O O O O O O o o o o o o o o o o O O O I I I I I I I I I I I I I I I I
O I O O i n o r O C M ' ; * * inCNtHCNVO (J\<T\CMrsirsI O H r H r H O O r O r O V O C N r O O C » O r O ^ i n v O r H C N ' * ^ O C N r H O O H O O r H O O O O O J C M O l C N r H O Q i-i i-i
O O O O O O O O O O O O O O O O O O O O I l l l l
c N C N O c N r H i n o i n v o ^ r o o ' s r o o i n r H r o v o * * O V O r H V D r H t H C N r H O O r O O J rHOOVOrHCM ^ ( N r H O O O r H O O O O O H O O O O O O O O O O
O O O O O O O o o o o o O O O O O O O O I I I I I I I I I I
o c M i n r M v D o v D i n o i v o r ^ r * o o i r ^ i n c r ^ o j ^ r v o i n o c N o r o v D O r o r H O j o c N r o ^ C M ^ o j <o rn -^ O O O O O O O o o o o o o o o o o O O O O O O O O O O O O O O O o o o o o O O O
I I I l l l l i n v o c M r o c M o i n ' s r r s i o o o c o r H r H o i v o o ^ cMvor^ c y » O r H r o o r o o r H O r H O < T » o c N r H O O o j r o o O r H O O O O O o o o o o r H O O r H O O O r H
O O O O O O O o o o o o o o o o o O O O I I I I I I I l l l l
i n C N r H O O i n C O O r H VOrHVOrOCN O O r O O r H ^ rOrOCM V D C N O r O ^ C r i C N V O O O r O O O OOCOVOVOrO OCNVD i n c N o o o o c M o o o o c M c M o o i n o o o i n
O O O O O O O o o o o o o o o o o O O O I I I I I
r o o r ~ r ^ c N o o i n r - r n r o o j i n o o o o r - r o ^ v o t n ^ o i n r o u o ' ^ ^ o oorHrHCMin i n ^ ^ r ^ o r * * o o o i n C N O O O O C N O O O O H r H O r H i n O O C M i n
O O O O O O O o o o o o o o o o o O O O I I l l l l
f O o o o i n c N V D v o r o r H v o c N O * c T i r o i n r H o o 0 ( y » r H O ^ r ^ r O O O V O V O C M r H r H l ^ CX3<y»rOrHCM O H r H O O r H r H O O r H O O O O O O H H O O CDCDO
C 3 C I > C I > C D < D O O o o o o o O O O O O O O O I I I I I I I
r ^ o o r ^ m r H r H o i r o r H H ' ^ r H ojcM««j'<y»rH Hr ; : :2? o S c N O ^ J S c g oorH<y>rHcr> a^ ^ OJ cy» Ol fN oo a^ S o O O H O C D o o o o o O O O H O O O r H
. . . . . . . . . . . . • • • O O O O O O O o o o o o O O O O O c p o o
I I I I I I l l l l
r o r f t v o r s i o r ^ c n vocr»r^ rHoo v o c o o o r o o j o i n i n
I^ rH O tH O O Ol rH O O O ^^ '^ ' ^ O r- O O Ol r-
O O O o ' o ' O O O O C^ CD O O O C> O CD O O O
.«««««r t / -^ i r> r r \ m c T » r o o o " ^ r o r o t ^ r * - o r ^ r ^
O O O O O O O O CD O O O o o o o o O O O
O rH CM ro VD r- 00 o H a> ro ^ CM ro in VD ro H Ol ro ro > > > > >
r^ CO <?> ro ro ro > > >
114
CM
>
ro tH r^ vo O O rH O O O O O
O O O O I I
vo <r> i n ro o^ O^ rH r^ O CM tH O O O O
ro o CM ro r-O rH rH rH O O O O O O
O 00 rH ro ro ro rH o o 'sr o o o o o
o o o o o o o o o o l l l l l
o o o o o I i I
>
o
>
cr> vo >
CO VD >
vo >
r^ ro in o r^ O O rH rH O o o o o o
00 in tH ro cn O O OJ o o o o o o o
000
o o 1
O r-l iH O
O O O 1 1 1
OJ O OJ CN "^ CM O O O
O O 1
VO ^ ro CM o o
o o 1
OJ CM O O O O
O 1
048
rH in in r* in o ro o o o o o o o o
• • • • • o o o o o I I I I
vo vo ^ cn cn o o o o o o o o o o
a in vo in 00 1-i r-i 1-i CD O O O O O O
• • • • • o o o o o l l l l
00 00 i n CO rH ^ O ro CM rH o o o o o
.144
.007
o
.049
.007
o 1
.008
o
.018
•
o
TO
O'
o 1
1-i rH o o 1
.025
o
.005
o
.022
o
.004
o
.006
o .047
o
.035
o
.068
o .253
o
.798
o
.026
o
.504
o
.228
o 1
.006
o
.019
o
.007
o
.026
o
069
o .079
o 1
.018
o 1
.021
o .032
o 1
.024
o
003
o 1
.065
o
.062
o
401
o
.203
o 1
.013
o 1
014
o 1
.131
o 1
004
o 1
017
o 1
.003
o
006
o 1
073
o
.021
o 1
042
o
413
o
.039
o 1
010
o
210
o
.393
o 1
010
o
214
o
.386
o 1
099
o
040
o 1
.351
o 1
on
o 1
288
o
.073
o
073
o
334
o
.773
o o 1
CO o O -J
o o o o 1
tH as cn CM O 1-i
o o 1
VD in in o o o
O O O O o o o o o o o o o o I I o o o o o o o o o o
I I
VD VD >
in rH ro in in CM vo CM i n rH CN in o o o
o o o o o
o> r^ r^ rH CM rH O O vo H o o ro cn o
rH in in vo CM i n rH rH 00 rH O O O CM rH
cn r^ rH VD rH o ro CO ro ^ O O rH rH rH
CM ^ CO ' ^ 00 Ol r~- VD ro o tH ro " r o o
o o o o o I I
o o o o o o o o o o o o o o o I I
in VD >
<D 1-i rn as iD as rH OJ CM r^ i n CN rH vo rH O O O
i n rH VD 00 o ro o o CN Ol O O r^ rH o
Ol in vo in CN rH ^ r^ ro VD CN O O CM tH
<r> 0 0 CT\ VD ';r O rH rH Ol O O O O ro ro
CJS (T CM 00 r-r- o r- ' ^ rH vo rH VD O O
O O O O O O I I
o o o o o I I
o o o o o o o o o o o o o o o
VD >
i n CO ^ 00 i n CO <? CN O^ CT> i n 00 O CM in o ^ o o o o
o> ^ cn r^ VD cn cn as as cn o o ">* o o
^ vo vo ro '«* rH rH r^ Cr» rH rH O OJ O H
O ro ro VO cn O O O Cr> 00 O O O CM CM
O O O O O O O O O O O O o o o o o o o o o o I I
r- rH r^ ^ ro in rH r^ CT> r--ro o ^ o o
o o o o o I I
ro vo >
r o r H ' ^ r o c M i n v o r o o o o o c N v o i n o o r r i n c N i n r H O O o
o^ o^ vo "^ ^ r r H ro cn r^ o o vo CM o
Cr> 00 CM rH o cn rH r- o r-* O O rH CM rH
VD O in ^ CM VD rH r- r-- VD O O O OJ CM
ro o 'S* cn 00 i n CM ro VD o rH O VD O O
o o o o o o o o I I
o o o o o o o o o o o o o o o o o o o o I I
CM VD >
C N O ^ o o o c ^ r M r o o ^ t H i n r H C N O r H O O r H C M O O r H O O O O O ' ^ r
o o o o o o o o o I I I I I I
in - r ro o^ ro rH O ro O rH o o o o o
• • • • • o o o o o
r o^ 00 ** o CO ro rH o CM o o o o o
. . . . . o o o o o
I I I
in " r cn ro rH rH rH CM vo r^ o o o o o
• • • • • o o o o o I I
o^ o^ 00 ^ tH CM r^ CM rH O rH O O O O
• • * • • O O O O O I I I
vo >
fa hQ OQ < H
Pi
>
r o c M l n ^ ^ ( ^ c M r ^ o o ^ c M r H C n ^ C N r H i n r ^ O r O t H r H r O ' ^ r V O r H i n r H O O O
o o o o o o o o c p c p I I I
ro CM O rH CM CM O rH rH ro O O VO rH O . . . . .
O O O O O
cn CM CO cn o vo CM 'r o vo rH O O rH rH . . . . .
O O O O O
rMr^'«rlnvD^-cocT^OrH C^'JTl^^J^ S S S VD VD vo vp vp {^ i: r^ r^ on m m
ro ^ VD r-- CO r ^ r ^ o o o o o o OOOOOOOOOO
' r in r^ r^ vo rH o 00 r^ in o o o ro ro
. . . . . o o o o o
o 1-i as cn ^ as as CO cn cn > > > > >
in in ro o 00 o ro 00 r^ in ^ o in o o
. . . . . o o o o o
CM ro in so r^ rH rsi ro ro ro > > > > >
115
rsi
>
^ T-i CM O O O
. . o o
I
as CO >
o CM CM ro rH rH CM i n O O O O
. . . . O O O O
in 00 VD 00 in O rH cn rH O H O O O rH
. . . . . O O O O O
I I
>
vo >
O r H o o
. . o o
I I
o o
00 vo >
ro o T-i
'«*' ro ro
• o o
r^ vo vo r^ CM r*-
. . o o
cn >
o l"^ >
cn vo >
ro o
• o
ro o o
ro o
• o
ro r--o
o as >
CO 00 >
00 >
VD CO >
o ro o
• o 1
CM r H
o • o
1
CM * * O
• o
o o o
• o 1
VD r H O
• o 1
in 1—i
o •
o
';r o o
. o 1
r H CM O
• O 1
in o o
• o
o o o
• o
r^ ^ ^ ^ VD
O o o ** ro o o o o o
. . . . . o o o o o
l l l l
CO VD ro ro O O O rH o o o o o o
. . . . . o o o o o 1 1 1
r ^ ro o vo rH CO r^ Ol o O O O rH o
• t • • •
o o o o o 1
00 r o^ ro in ' ^ cn o^ o ro rH rH rH O O
. . . . . O O O O O
r- o 00 in ro rH CM CM 00 rH o o o o o
• • • • • o o o o o 1 1
ro in ro o ro r-i CD T-i 1-i T-i O O O O O
. . . . . o o o o o
1
r o r - Ol rH rH O O CM t ^ O o o o o o
. . . . . o o o o o
1 1
r^ C7 CM i n i n rH CN O ON rH rH O O O rH
. . . . . O O O O O
1 1
O rH O rH CM i n '53" rH 00 i n CN O O O CM
. . . . . o o o o o i 1
CM ^ in '^ o CM i n rH i n Ol o o o o o
• • • • t
o o o o o 1
vo VD >
o^ cn r-o vo T-i ^
o o 00 >
cn rH rH rH cn O CM CM rH CM O O O O rH
O O O O O I i I
ro <y> Ol CM r^ ro o rH ro o o o o o o
o o o o o I I I
rH 00 r^ CM ^ CM O i n CM CN o o o o o o o o o o I I
in vo >
O ' J'
CM vo . .
o o
ro 00 >
00 o VD in ro o\ CN o o in rH roo o o o o o
r^ o rH vo ro rH 00 r - r^ rH O O O rH O
in ro CN ro VD o o CM ro o tH O O O rH
O O O O O O I I I I
o o o o o I I I
o o o o o I I I
vo >
as VD CN ^
. . o o
OJ 00 >
in VD in r^ in rH r^ CN rH ^ r o CM CM rH O O O O O O O
rH in CO VD ro r o O O rH o o o o o o
r- in o o r^ O rH O CM O o o o o o
O O O O O O O I I I
o o o o o I I
o o o o o
ro vo >
O CN in ro ro vo
• • o o
00 >
V D C O ^ ^ i n r H r ^ r H O ' ^ C N O r O H O r H O O O O C M t H O O
in r^ ro ro VD vo ro '5j« CM cn rH rH rH rH r o
Ol o ro CM ro 00 r o CM 00 00 ^ O O rH ^
o o o o o o o o I I
o o o o o o o o o o
CN VD >
vo r^ Ol CN o o o o
I I
o 00 >
v o r ^ r o o o ^ r s i r ^ " ^ ^ r H O r H r H C N C M O O r H r O O r H O O C M r H O O
rH CM i n VD CO 00 r - VD 00 VD O ^ ^ Ol o
o o o o o o o o o I I
o o o o o
rr r- VD VD in r^ r ta* CM r^ o^ o o ^ o^
o o o o o
vo >
fa
OQ < H Pi < >
CM ro in 00 CN in
. . o o
00 as cn cn > >
cn
>
fa iJ OQ < H
>
i H r ^ v D c n r o c M r o o i n v o O O r H O C M r H r H r H O O O O O O O O O O O O O
in VD in o (7 o Ol CM ^ ro o o o o o
oooooooooo l l l l l
O H r s i r o ' j ^ v D r ^ o o o r H o o o o o o c o o o o o o o o o a ^ o ^ > > > > > > > > > >
o o o o o I I
<* tH 00 cn o r^ tH o ^ r-O O O rH O
o^ ro ^ CN ro 00 ro ro rH CM > > > > >
o o o o o
in VD r CO cn ro ro ro ro ro > > > > >
116
CO ro >
o CN
ro >
vo ro >
in ro >
080
182
• o
065
ro in o *r o o
• • o o 1
OJ o rH 00 o o
• • o o 1 1
r^ cn ^ cn <* as
O O O O
ro CM >
^ in ro in CM rH rH r o r o rH o o o o o
. . . . . o o o o o
Ol 1-i
>
in o CM o vo OJ 00 "«;r ro CM ' ^ «!j* tH CM O O O CM
. . . . . . O O O O O O
'S3'
ro >
a^ in in rH o "* ^ o ' r vo ro CM VD VD O O *^ O O CN "^
o o o o o I I I
o o
ro ro >
fa hQ OQ < H Pi < >
• t r i n c M r H r o r H r o c n c r > c M ' * r ~ r O ' - i v o v o ( r > o o ' ! f O O C M ' *
O O O O O O O O I I I
r r c M r o i n v o r - o o o j f O f H C M r o r o r p c n C ?