DiscriminantAnalysis - Discriminant Analysis James H...

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Discriminant Analysis James H. Steiger Department of Psychology and Human Development Vanderbilt University James H. Steiger (Vanderbilt University) 1 / 54
Discriminant Analysis 1 Introduction 2 Classification in One Dimension A Simple Special Case 3 Classification in Two Dimensions The Two-Group Linear Discriminant Function Plotting the Two-Group Discriminant Function Unequal Probabilities of Group Membership Unequal Costs 4 More than Two Groups Generalizing the Classification Score Approach An Alternate Approach: Canonical Discriminant Functions Tests of Significance 5 Canonical Dimensions in Discriminant Analysis 6 Statistical Variable Selection in Discriminant Analysis James H. Steiger (Vanderbilt University) 2 / 54
Introduction Introduction There are two prototypical situations in multivariate analysis that are, in a sense, different sides of the same coin. Suppose we have identifiable groups, and they may (or may not) differ in their means (and possibly in their covariance structure) on one or more response measures. How can we test whether the groups are significantly different? If the groups are different, how can we construct a rule that allows us to accurately assign an individual to one of several groups, depending on their scores on the response measures? In this module, we will deal with the second problem, examining, in detail, a method known as discriminant analysis . However, the first problem, related to a technique known as MANOVA (Multivariate Analysis of Variance) is closely related to the first. James H. Steiger (Vanderbilt University) 3 / 54
Classification in One Dimension Classification in One Dimension There are many situations in which we measure a response variable on a group of people, objects, or situations, and then try to sort these into one or more groups depending on their score on that variable. Some examples? (C.P.) James H. Steiger (Vanderbilt University) 4 / 54
Classification in One Dimension Classification in One Dimension – Some Examples Your response variable is the color of a test strip. You try to sort individuals into: 1 Pregnant 2 Non-Pregnant Your response variable is a brief sensation of change of illumination in a very dark backround. You try to decide whether a very dim signal light is 1 Present 2 Not Present You have individuals who are either male or female, and you have their heights. You try to devise a rule that will, with the highest possible degree of accuracy, decide only on the basis of height whether a person is: 1 Male 2 Female James H. Steiger (Vanderbilt University) 5 / 54
Classification in One Dimension A Simple Special Case A Simple Special Case As a simple special case, suppose we consider the whole population of men and women, and imagine that we knew that both populations are normally distributed with standard deviations of 2.5, but men have a mean of 70, women of 65.