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Discriminant Analysis

1. Introduction

2. Types of DA

3. Assumptions

4. Model representation, data type/sample size

5. Measurements

6. Steps to solve DA problems

7. An numerical example

8. SPSS commands

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Discriminant Analysis• is a powerful statistical tool used to study

the differences between groups of objects

• Here, objects could be 1. an individual person or firms, and

2. classifying them can be based on prior or posterior factors or characteristics

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Types of DA

• Two groups

– refer to as two-group discriminant analysis

– Its dependent variable is termed as dichotomous

• Three or more group

– Refer to as multiple discriminant analysis (MDA)

– Its corresponding dependent variables are termed as multichotomous

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Assumptions

1) multivariate normality, – uses the normal probability

plot approach

– uses the most common statistical tests are the

calculation of skewness value

2) equal covariance matrices– Use covariance to check their

corelations

3) multicollinearity, among independent variables

– That is to check independent variables are not correlated to each other

4) Outliers– "the observations with a

unique combination of characteristics identifiable as distinctly different from the

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Model representation

Data type:Dependent variables = non-metric formatIndep variables = metric format

Sample size : between 5-20 obs for each independent variables

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Measurements

1. Group categorizations

2. Hit ratio

3. Discriminating power

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Group categorizations

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Hit ratio

• Used to measure the model fitness• Is a maximum chance criteria

Note: We need to compute this value for our original sample size and then compare to the value that produced by the SPSS; and computer value should not be less than the formal value in order to claim the significant of fitness of model

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Discriminating power

References: refer to “hit ratio” for details

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Steps to solve DA problems

• Step 1: Assess the assumptions

• Step 2: Estimate the discriminant function(s)

and its (their) significance

• Step 3: Assess the overall fit

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Example

You can obtain this paper by clicking Discriminant paper from my web site

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• Objective:– To discriminate the difference practices between the high and

low performance of firms practicing TQM is ISF– Use score of overall satisfaction as a mean for discriminating

factor

• Steps:– Step 1, refer to p 762

– Step 2, refer to p763

– Step 3, refer to p763

– Discussion, you can refer to the “discussion” section

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Step 1, refer to p 762

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Step 2, refer to p763

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Step 3, refer to p763

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SPSS commands

SPSS Windows (to p17)

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SPSS windows• Steps to compute Discriminant Analysis• Step 0• Prior the study of analysis, we need to firstly define a new variable as follows:• - Define “group” and assign a value of either 0, 1, 2 to them, as 0 as

neural• Step 1• Select “Analyze”• Select “Classify”• Select “Discriminant”• click “group variable”

– and select “group” variable as above• click “define range”

– state its max and min ranges– (this range same as min=1, and max=2 for above case)

• click “Independent”– select “variables”– that a group of factors that wish to be clustering

• Click option “use stepwise method”• select “Statistics”

Learn from iconic base – Pls refer to my website