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**Discriminant Analysis**

Introduction Types of DA Assumptions Model representation, data type/sample size Measurements Steps to solve DA problems An numerical example SPSS commands (to p2) (to p3) (to p4) (to p5) (to p6) (to p10) (to p11) (to p16)

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**Discriminant Analysis**

is a powerful statistical tool used to study the differences between groups of objects Here, objects could be an individual person or firms, and classifying them can be based on prior or posterior factors or characteristics (to p1)

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**Types of DA Two groups Three or more group**

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 (to p1)

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**Assumptions 1) multivariate normality, 2) equal covariance matrices**

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 other observations". (to p1)

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**Model representation Data type:**

Dependent variables = non-metric format Indep variables = metric format Sample size : between 5-20 obs for each independent variables (to p1)

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**Measurements Group categorizations Hit ratio Discriminating power**

(to p7) (to p8) (to p9) (to p1)

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**Group categorizations**

(to p6)

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**Hit ratio Used to measure the model fitness**

Is a maximum chance criteria (to p6) 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**

(to p6) 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 (to p1)

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Example (to p12) 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 (to p13) (to p14) (to p15) (to p1)

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Step 1, refer to p 762 (to p12)

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Step 2, refer to p763 (to p12)

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Step 3, refer to p763 (to p12)

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SPSS commands SPSS Windows (to p17)

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**SPSS windows Learn from iconic base – Pls refer to my website**

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

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Section 8.1-1 Copyright © 2014, 2012, 2010 Pearson Education, Inc. Lecture Slides Elementary Statistics Twelfth Edition and the Triola Statistics Series.

Section 8.1-1 Copyright © 2014, 2012, 2010 Pearson Education, Inc. Lecture Slides Elementary Statistics Twelfth Edition and the Triola Statistics Series.

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