Discriminant AnalysisJames H. SteigerDepartment of Psychology and Human DevelopmentVanderbilt UniversityJames H. Steiger(Vanderbilt University)1 / 54
Discriminant Analysis1Introduction2Classification in One DimensionA Simple Special Case3Classification in Two DimensionsThe Two-Group Linear Discriminant FunctionPlotting the Two-Group Discriminant FunctionUnequal Probabilities of Group MembershipUnequal Costs4More than Two GroupsGeneralizing the Classification Score ApproachAn Alternate Approach: Canonical Discriminant FunctionsTests of Significance5Canonical Dimensions in Discriminant Analysis6Statistical Variable Selection in Discriminant AnalysisJames H. Steiger(Vanderbilt University)2 / 54
IntroductionIntroductionThere are two prototypical situations in multivariate analysis that are, in asense, different sides of the same coin. Suppose we have identifiablegroups, and they may (or may not) differ in their means (and possibly intheir 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 usto accurately assign an individual to one of several groups, dependingon their scores on the response measures?In this module, we will deal with the second problem, examining, indetail, a method known asdiscriminant 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 DimensionClassification in One DimensionThere are many situations in which we measure a response variable ona group of people, objects, or situations, and then try to sort theseinto 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 DimensionClassification in One Dimension – Some ExamplesYour response variable is the color of a test strip. You try to sortindividuals into:1Pregnant2Non-PregnantYour response variable is a brief sensation of change of illumination ina very dark backround. You try to decide whether a very dim signallight is1Present2Not PresentYou have individuals who are either male or female, and you havetheir heights. You try to devise a rule that will, with the highestpossible degree of accuracy, decide only on the basis of heightwhether a person is:1Male2FemaleJames H. Steiger(Vanderbilt University)5 / 54
Classification in One DimensionA Simple Special CaseA Simple Special CaseAs a simple special case, suppose we consider the whole population ofmen and women, and imagine that weknewthat both populationsare normally distributed with standard deviations of 2.5, but menhave a mean of 70, women of 65.