Seeing with your eyes is but looking; seeing with your mind--knowing. -TJS • “The main value of bar graphs…and picture graphs lies probably in school publicity and in the motivation of learning.” – Statistical Methods (Glass and Stanley) • “A successful graph depends far more on careful thought and judgment than on techniques.” –Scates, 1942
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Seeing with your eyes is but looking; seeing with your mind--knowing. -TJS
• “The main value of bar graphs…and picture graphs lies probably in school publicity and in the motivation of learning.” –Statistical Methods (Glass and Stanley)
• “A successful graph depends far more on careful thought and judgment than on techniques.” –Scates, 1942
Presentation OrganizationSet 1: Mean Scale Score Comparison—Shoreline,
North Haven, and State
Set 2: Randomized DRG D Sample Mean Scale Score Comparison
Set 3: Randomized DRG D Sample Percent Change Comparison—From 2006 to 2009
Set 4: DRG D Complete Comparison Ranking Leveled by Quintile by Mean Scale Score and
At/Above Goal Percentages
Sets 1, 2, 3, and 4 display 3rd and 4th Grade Scores for Reading, Writing, and Math. Sets 1, 2, and 4 Contain Data for Years 2006 through 2009.
Branford Public Schools
Comparison of 4th Generation CMT Scale Scores for Years 2006 through 2009
Regarding Branford’s Elementary Schools
District-Wide 3rd and 4th Grade: Test Scores Over a 4 Year Period:
A Trend Analysis
Why Use Scale Scores?
Scaled scores are particularly useful for comparing test scores over time, such as measuring semester-to-semester and year-to-year growth of individual students or groups of students in a content area. http://www.pearsonedmeasurement.com/research/faq_2e.htm
Unlike percentile rank scores, the interval between scores is equal. This means that you can average scale scores to compare groups of students or schools. http://www.ncrel.org/tech/claims/glossary.html
Scale Scores
Scale scores are useful in comparing performance in one subject area across classes, schools, districts, and other large populations, especially in monitoring change over time. http://www.k12.hi.us/~atr/evaluation/glossary.htm
…they can be added, subtracted, and averaged across test levels. This cannot be done with percentiles or grade equivalents. Wisconsin Student Assessment System Wisconsin Knowledge and Concepts Examinations
Set 1: Shoreline, State, and North Haven
This is not a randomized sample. Although some districts are DRG
D districts, generalization to a target population is not
appropriate.
Grade 3 Writing CMT Trend Lines 2006-2009
• Slide 1: Branford and State Average
• Slide 2: Branford, North Haven, and Shoreline
Content Area Sequence
WritingMath
Reading
Sequence is the same for 3rd and 4th Grades
Grade 3: Writing CMT Scale Score Comparisons
Writing 3rd Grade Scale Scores 2006-2009
245
250
255
260
265
270
275
2006 2007 2008 2009
Years
Wri
tin
g S
cale
Sco
res
3rd
Gra
de
State Average
Branford
Grade 3: Writing CMT Scale Score Comparisons
Writing 3rd Grade Scale Scores 2006-2009
245
250
255
260
265
270
275
280
285
290
2006 2007 2008 2009
Years
Wri
tin
g S
cale
Sco
res
3rd
Gra
de
Branford
Clinton
Guilford
Madison
North Haven
Old Saybrook
Westbrook
Grade 3 Math CMT Trend Lines 2006-2009
• Slide 1: Branford and State Average
• Slide 2: Branford, North Haven, and Shoreline
Grade 3: Math CMT Scale Score Comparisons
CMT 3rd Grade Branford/State Math Scale Scores 2006-2009
Set 2 and Set 3 follow. These 2 sets use randomized samples from Branford’s
DRG (D).
Randomization is a powerful statistical technique which permits
generalizing results from a relatively small sample to the
larger target population.
The following 2 sets of charts (At/Above Goal: 2006 through 2009; and Scale Score Percent Change: 2006 to 2009) were based on District Reference Group D (Branford’s reference group). Two samples were randomly selected from this DRG allowing comparisons to Branford and Connecticut’s state average. The districts were randomly selected by assigning numbers to the 23 other districts in Branford’s DRG. A random number generator was then used to select the sample thereby eliminating selection bias to allow a generalization of the results to the population DRG.
* This table of 23 random numbers was produced according to the following specifications: Numbers were randomly selected from within the range of 1 to 23. Duplicate numbers were not allowed. A Seed number was not used.
District Reference Group (DRG)
1. Berlin 2. Bethel 3. Clinton 4. Colchester
5. Cromwell 6. East Granby 7. East Hampton 8. East Lyme
9. Ledyard 10. Milford 11. New Milford 12. Newington
13. North Haven 14. Old Saybrook 15. Rocky Hill 16. Shelton
A total of 15 districts were included in the 2 samples (62.5% of the DRGs in DRG D are represented in the 2 samples). Sample 1 was randomly assigned to Percentage Change Chart Data and Sample 2 was randomly assigned to At Goal/Above Chart Data.
Percentage At Goal or Above 3rd and 4th Grade CMT 2006 - 2009
Goal and Proficiency are based on Scale Scores
3rd Grade: Goal ProficiencyMath 242 210
Reading 235 217Writing 240 212
4th Grade: Goal Proficiency Math 245 215 Reading 244 227
Writing 237 209
3rd Grade At/Above Goal
Trend Line Subject Sequence
Writing
Math
Reading
50
55
60
65
70
75
80
85
90
2006 2007 2008 2009
At G
oal
or
Ab
ove
Per
cen
tag
es
Years
3rd Grade Writing DRG D Sampling and State CMT At Goal or Above Percentages 2006-2009
State
Branford
East Lyme
New Milford
North Haven
Southington
Watertown
Rocky Hill
Cromwell
45
50
55
60
65
70
75
80
85
90
2006 2007 2008 2009
At G
oal
or
Ab
ove
Per
cen
tag
es
Years
3rd Grade Math DRG D Sampling and State CMT At Goal or Above Percentages
State
Branford
East Lyme
New Milford
North Haven
Southington
Watertown
Rocky Hill
Cromwell
50
55
60
65
70
75
80
2006 2007 2008 2009
At G
oal
or
Ab
ove
Per
cen
tag
es
Years
3rd Grade Reading DRG D Sampling and State CMT At Goal or Above Percentages 2006-2009
State
Branford
East Lyme
New Milford
North Haven
Southington
Watertown
Rocky Hill
Cromwell
4th Grade At/Above Goal
Trend Line Subject Sequence
Writing
Math
Reading
55
60
65
70
75
80
85
90
2006 2007 2008 2009
At G
oal
or
Ab
ove
Per
cen
tag
es
Years
4th Grade Writing DRG D Sampling and State CMT At Goal or Above Percentages 2006-2009
State
Branford
East Lyme
New Milford
North Haven
Southington
Watertown
Rocky Hill
Cromwell
45
50
55
60
65
70
75
80
85
90
95
2006 2007 2008 2009
At G
oal
or
Ab
ove
Per
cen
tag
es
Years
4th Grade Math DRG D Sampling and State CMT At Goal or Above Percentages 2006-2009
State
Branford
East Lyme
New Milford
North Haven
Southington
Watertown
Rocky Hill
Cromwell
55
60
65
70
75
80
85
2006 2007 2008 2009
At G
oal
or
Ab
ove
Per
cen
tag
es
Years
4th Grade Reading DRG D Sampling and State CMT At Goal or Above Percentages 2006-2009
State
Branford
East Lyme
New Milford
North Haven
Southington
Watertown
Rocky Hill
Cromwell
Bar Graphs of Scale Score Percent Change
4th Generation CMT Scale Scores Percent Change from 2006 to 2009
Percentage Change Calculation
Example: State Math Average Scale Score 2006 is 252.6
State Math Average Scale Score 2009 is 262.8
Dividing 262.8 by 252.6 results in an approximate percent change of +4% (less than .04 of one percent (.0004)
2006 2007 2008 2009Grd 3 2006 Writing 2006 2007 Writing 2007 2008 Writing 2008 2009 Writing 2009QT Dist. ID Group %Goal+ Rank Group %Goal+ Rank Group %Goal+ Rank Group %Goal+ Rank
40 East Granby 79.7 1 Old Saybrook 83.6 1 Newington 83.9 1 Old Saybrook 90.9 142 East Hampton 79.7 2 East Lyme 80.9 2 East Granby 82.5 2 Bethel 88.5 2
5 101 North Haven 78.9 3 New Milford 79.2 3 East Lyme 80.8 3 East Lyme 84.2 345 East Lyme 77.6 4 Berlin 78.3 4 Old Saybrook 80.6 4 Cromwell 79.4 49 Bethel 77.5 5 Clinton 77.9 5 Clinton 80.3 5 Rocky Hill 79.4 5
14 Branford 77.1 6 East Hampton 76 6 Berlin 80.2 6 East Granby 79.2 6131 Southington 75.9 7 Milford 74.4 7 East Hampton 79.5 7 North Haven 77.9 7
Branford Rank in DRG D 3rd Grade Writing CMT 2006-2009
ScaleScoreRank
%GoalAboveRank
Branford Grd 3 Math Scale Score DRG D Rank
2006 2007 2008 2009Grd 3 2006 Math 2006 2007 Math 2007 2008 Math 2008 2009 Math 2009QT Dist Group MeanSS Rank Group MeanSS Rank Group MeanSS Rank Group MeanSS Rank
5 45 East Lyme 76.1 3 Bethel 80.3 3 East Lyme 77.2 3 East Lyme 81.3 3131 Southington 76 4 Berlin 79.9 4 Waterford 75.8 4 North Haven 79.5 4
7 Berlin 74.4 5 East Lyme 79.2 5 North Haven 75.7 5 Cromwell 79.2 5
152 Waterford 73.7 6 Stonington 76.3 6 Berlin 72.7 6 Rocky Hill 78.4 684 Milford 72.9 7 East Granby 74.4 7 Ledyard 72 7 Old Saybrook 78.3 7
4 40 East Granby 71.9 8 Branford 73.1 8 Wallingford 71.5 8 East Granby 77.8 8137 Stonington 69.5 9 Milford 72 9 East Granby 71.4 9 Ledyard 77.1 927 Clinton 68.8 10 Waterford 71.4 10 Stonington 70.8 10 Berlin 75.6 10
119 Rocky Hill 68.3 11 Old Saybrook 69.5 11 Rocky Hill 69.8 11 Stonington 75.4 11106 Old Saybrook 67 12 Clinton 69.3 12 Clinton 67.3 12 Waterford 74.2 12
3 42 East Hampton 65 13 East Hampton 68.3 13 East Hampton 67.1 13 Newington 74 13 Median96 New Milford 63.1 14 North Haven 68.1 14 Newington 66.1 14 Colchester 72.5 14101 North Haven 62.4 15 Newington 67.1 15 Milford 65.8 15 East Hampton 72 15
2 137 Stonington 255.7 18 Stonington 257.9 18 Old Saybrook 258 18 Milford 263.9 1828 Colchester 255 19 State 256.9 19 North Haven 257.5 19 State 262.8 19
106 Old Saybrook 253.1 20 North Haven 255.9 20 New Milford 256.9 20 Clinton 259.8 20
0 State 252.6 21 Cromwell 253.9 21 Clinton 256.3 21 Branford 258.6 2142 East Hampton 249.7 22 Watertown 252 22 Shelton 256.2 22 Watertown 258 22
1 96 New Milford 248.8 23 New Milford 251.4 23 Watertown 254.6 23 Cromwell 254.9 23153 Watertown 246.9 24 East Hampton 251 24 Windsor 254.2 24 Windsor 252.3 24164 Windsor 246.1 25 Windsor 249.3 25 East Hampton 251.3 25 New Milford 247.6 25
Branford Grd 4 Math %Goal+ DRG D RankGrd 4 2006 Math 2006 2007 Math 2007 2008 Math 2008 2009 Math 2009QT Dist Group % Goal Rank Group % Goal Rank Group % Goal Rank Group % Goal Rank
119 Rocky Hill 63.5 16 Shelton 65 16 Clinton 62.7 16 Shelton 70.6 1633 Cromwell 62.3 17 Stonington 64.5 17 New Milford 62.6 17 Wallingford 68.2 17
2 28 Colchester 60.8 18 Cromwell 63.9 18 North Haven 62.6 18 Milford 64.1 18137 Stonington 60.2 19 Newington 63.6 19 Old Saybrook 62.6 19 State 63.8 1942 East Hampton 59.7 20 State 62.3 20 Wallingford 61.4 20 Clinton 62.2 20
0 State 58.8 21 North Haven 61.9 21 Watertown 61.1 21 Watertown 60.2 21106 Old Saybrook 58.7 22 Watertown 60.4 22 State 60.5 22 Cromwell 60 22
1 96 New Milford 57 23 New Milford 58.6 23 East Hampton 60.3 23 Branford 59.2 23164 Windsor 52.7 24 Windsor 53.1 24 Shelton 60.2 24 Windsor 55.7 24153 Watertown 49 25 East Hampton 51.5 25 Windsor 57.3 25 New Milford 50.5 25
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2006 2007 2008 2009
RA
NK
YEARS
Branford 4th Grade Math DRG D Ranking 2006-2009
ScaleScoreRank
%GoalAboveRank
Numerical Tabular Data may have hidden in the rows and columns valuable information that sometimes remains “in the shadows.” Data
displayed in a variety of graphical modalities may add clarity by showing the Data On The Surface
(DOTS). The responsibility of the reader becomes one of connecting the DOTS.
Great care was taken to assure the accuracy of the displayed data. Considering the amount of
data and the different display formats, some error may be present and as of yet unidentified. If so, the author apologizes for the inaccuracy and will make an attempt to correct the data as soon as
possible.
All data used is available by following this link http://www.Branford.k12.ct.us and then choosing
the second link from the bottom of the left-hand column’s list of links (http://www.ctreports.com/)