Question

Define Discriminant Analysis. What are the assumptions we need to make to perform it. justify the assumptions.

Answer 1

DISCRIMINANT ANALYSIS:-

During a study, there are often questions that strike the researcher that must be answered. These questions include questions like ‘are the groups different?’, ‘on what variables, are the groups most different?’, ‘can one predict which group a person belongs to using such variables?’ etc. In answering such questions, discriminant analysis is quite helpful.

Discriminant analysis is a technique that is used by the researcher to analyze the research data when the criterion or the dependent variable is categorical and the predictor or the independent variable is interval in nature. The term categorical variable means that the dependent variable is divided into a number of categories. For example, three brands of computers, Computer A, Computer B and Computer C can be the categorical dependent variable.

As in statistics, everything is assumed up until infinity, so in this case, when the dependent variable has two categories, then the type used is two-group discriminant analysis. If the dependent variable has three or more than three categories, then the type used is multiple discriminant analysis. The major distinction to the types of discriminant analysis is that for a two group, it is possible to derive only one discriminant function. On the other hand, in the case of multiple discriminant analysis, more than one discriminant function can be computed.

ASSUMPTIONS AND IT'S JUSTIFICATION :-

The assumptions of discriminant analysis are the same as those for MANOVA. The analysis is quite sensitive to outliers and the size of the smallest group must be larger than the number of predictor variables.

• Multivariate normality: Independent variables are normal for each level of the grouping variable.
• Homogeneity of variance/covariance (homoscedasticity): Variances among group variables are the same across levels of predictors. Can be tested with Box's M statistic. It has been suggested, however, that linear discriminant analysis be used when covariances are equal, and that quadratic discriminant analysis may be used when covariances are not equal.
• Multicollinearity: Predictive power can decrease with an increased correlation between predictor variables.
• Independence: Participants are assumed to be randomly sampled, and a participant's score on one variable is assumed to be independent of scores on that variable for all other participants.

It has been suggested that discriminant analysis is relatively robust to slight violations of these assumptions, and it has also been shown that discriminant analysis may still be reliable when using dichotomous variables (where multivariate normality is often violated).