## Wednesday, 31 August 2011

### Doing Discriminant Analysis on SPSS

Discriminant analysis is done to differentiate between groups usually between 2 groups. Discriminant analysis is based on regression. The effect of independent variables is studied on dependent variables.

The steps for a discriminant analysis are as follows:

1. Formulate the problem

2. Determine the discriminant function coefficients that result in the highest ratio of between-group variation to within-group.

3. Test the significance of the discriminant function.

4. Interpret the results.

5. Determine the validity of the analysis.

The steps to be followed in the SPSS software to get the relevant data are:

1. First enter the grouping variable. Then, define the lowest and highest coded value for the grouping variable by clicking on Button Define Range. Then, select the independent variables in the ‘Independents:’ box.

2. Button Statistics: Here you can indicate those statistics that are desired in discriminant analysis. Often these include means, univariate ANOVAs, unstandardized Function Coefficients.

3. Button Classify: Many classification options can be selected here, such as prior probabilities and plots. Also, a summary table can be requested.

4. Button Save: This option allows you to save as new variables: Predicted group membership, Discriminant Scores and Probabilities of group membership.

5. From the data received one of the most important value is the 'eigen value' and it is a canonical discriminant function. An eigenvalue indicates the proportion of variance explained. A large eigenvalue is associated with a strong function. The canonical relation is a correlation between the discriminant scores and the levels of the dependent variable. A high correlation indicates a function that discriminates well.

6. The Wilks Lambda is another important value. Wilks’ Lambda is the ratio of within-groups sums of squares to the total sums of squares. This is the proportion of the total variance in the discriminant scores not explained by differences among groups. A lambda of 1.00 occurs when observed group means are equal (all the variance is explained by factors other than difference between those means), while a small lambda occurs when within-groups variability is small compared to the total variability. A small lambda indicates that group means appear to differ. The associated significance value indicates whether the difference is significant.

7. ‘Functions at Group Centroids’ indicates the average discriminant score for subjects in the two groups. More specifically, the discriminant score for each group when the variable means (rather than individual values for each subject) are entered into the discriminant equation.

8. The ‘Canonical Discriminant Function Coefficients’ indicate the unstandardized scores concerning the independent variables. It is the list of coefficients of the unstandardized discriminant equation. Each subject’s discriminant score would be computed by entering his or her variable values (raw data) for each of the variables in the equation.

Author: Gayatri Nair

Group: Marketing - Group 4