Introduction Q Ti A

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Quantitative Techniques in Analysis (QTiA)

Introductory LectureSaturday, 02nd October 2010

M. Shahnawaz Adil Assistant Professor & Course Advisor (Strategies & Management)[email protected]

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Reference BooksLocation: \\Fileserver\Shahnawaz Adil\6. QTIA

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Reference BooksLocation: \\Fileserver\Shahnawaz Adil\6. QTIA

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Common Statistical Packages

• S.P.S.S. (originally, Statistical Package for the Social Sciences)

• S.A.S. (pronounced "sas", originally Statistical Analysis System)

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Three Measurement Levelsin S.P.S.S.

1.Nominal2.Ordinal3.Scale

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LoM: Key points

Objects

Events

People

Assigning the discrete categories Called

CATEGORICAL MEASUREMENT

Identifying the attributes on numerical scale called

METRIC MEASUREMENT

Nominal

Ordinal

Interval

Ratio

In SPSS: Scale

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1) Categorical Measurement

1.1 Nominal Level Categories must be homogeneous, mutually

exclusive and exhaustive. Dichotomous / Binary

1.2 Ordinal Level The categories are ranked order along some dimension (high to low) e.g. Social class (upper, middle, lower) e.g. Likert Scale (strongly agree, agree, neither agree not disagree, disagree, strongly disagree)

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2) Metric Measurement

2.1 Interval Level The categories or scores on a scale are of

the same distance apart whereas in ordinal level, the numbers only indicate relative position.

It has an arbitrary zero. e.g. Attitude scale from 10 to 50 (may be

taken from 5 responses). It can be range from 0 to 40.

Temperature 0 C= 273 Kelvin = 32 F

2) Metric Measurement

2.2 Ratio Level Same as Interval level except it has an

absolute zero point. e.g. height, volume, income/salary in PKR, time, etc.

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Key Points to Ponder

• For ordinal string variables, the alphabetic order of string values is assumed to reflect the true order of the categories.

• For example, for a string variable with the values of low, medium, high, the order of the categories is interpreted as high, low, medium, which is not the correct order. In general, it is more reliable to use numeric codes to represent ordinal data.

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Key Points to Ponder (cont’d…)

• New numeric variables created during a session are assigned the scale measurement level. For data read from external file formats and SPSS data files that were created prior to version 8.0, default assignment of measurement level is based on the following rules:

• Numeric variables with fewer than 24 unique values and string variables are set to nominal.

• Numeric variables with 24 or more unique values are set to scale.

Refer: SPSS User Guide 16.0 for further details

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Time Dimension in Research

• Three types of data may be available for empirical analysis:

Time Series data

Cross-Section data

OR ORPooled data

Time Series data

Cross-Section data

and

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1. Time Series data (TS)one subject's changes over the course of time

• A time series is a set of observations on the values that a variable takes at different times.

• Such data may be collected at regular time intervals such as:– Daily (e.g., stock prices, weather reports);– Weekly (e.g., money supply figures);– Monthly (e.g., the unemployment rate, Consumer

Price Index (CPI));– Quarterly (e.g., GDP)– Annually (e.g., government budgets);– Quinquennially, i.e., every 5 years

(e.g., the census of manufactures); or– Decennially, (e.g., the census of population).

Australian Budget

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TS Data: Important Points

• Sometimes data are available both quarterly as well as annually, as in the case of the data on GDP and consumer expenditure.

• With the advent of high-speed computers, data can be collected over an extremely short interval of time, such as the data on stock prices, which can be obtained literally continuously (the so-called real-time quote)

• Application: Econometric studies

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• Assumption: most empirical work based on time series data assumes that the underlying time series is Stationary (loosely speaking a time series is stationary if its mean and variance do not vary systematically over time)

• Example: on next slide…

TS Data: Important Points

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M1 Money Supply: United States, 1947-97

The M1 money supply shows a steady upward trend as well as variability over the years, suggesting that the M1 time series in NOT stationary.

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2. Cross-Section data (CS)

• Data on one or more variables collected at the same point in time or without regard to differences in time, such as – census of population conducted by the Census

Bureau every 10 years (the latest being conducted in year 2000;

– The surveys of consumer expenditures conducted the University of Michigan); and

– Opinion polls by Gallup, etc.

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CS Data – an exampleWe want to measure current obesity levels in a population. We

could draw a sample of 1,000 people randomly from that

population (a.k.a a cross section of that population), measure

their weight and height, and calculate what percentage of that

sample is categorized as obese (mean: overweight). For example,

30% of our sample were categorized as obese. This cross-

sectional sample provides us with a snapshot of that population,

at that one point in time. Note that we do not know based on

one cross-sectional sample if obesity is increasing or decreasing;

we can only describe the current proportion.

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Panel Data

• In statistics and econometrics, the term panel data refers to multi-dimensional data. Panel data contains observations on multiple phenomena observed over multiple time periods for the same firms or individuals.

• TS and CS data are special cases of panel data that are in one-dimension only.

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Balanced vs. Unbalanced Data

In the example above, two data sets with a two-dimensional panel structure are shown. Individual characteristics (income, age, sex. educ) are collected for different persons and different years. In the left data set two persons (1, 2) are observed over three years (2003, 2004, 2005). Because each person is observed every year, the left-hand data set is called a balanced panel, whereas the data set on the right hand is called an unbalanced panel, since Person 1 is not observed in year 2005 and Person 3 is not observed in 2003 or 2005.

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Compulsory Home Reading Assignment

• Chapter No 2: Data Coding & Exploratory Data Analysis from

• Chapter No. 1 and 02 from