Multivariate Statistical Methods: A Primer

About this book

This edition includes increased coverage on measuring distances between cases based on on presence-absence data, a new section on logistic regression, new exercises and two completely new chapters on graphical methods and ordination. The author has taken into account the major shift in the way in which computer software is used. The emphasis is on the underlying principles rather than the use of particular programs.

Contents

THE MATERIAL OF MULTIVARIATE ANALYSISExamples of Multivariate DataPreview of Multivariate MethodsThe Multivariate Normal DistributionComputer ProgramsGraphical MethodsChapter SummaryReferencesMATRIX ALGEBRAThe Need for Matrix AlgebraMatrices and VectorsOperations on MatricesMatrix InversionQuadratic FormsEigenvalues and EigenvectorsVectors of Means and Covariance MatricesFurther ReadingChapter SummaryReferencesDISPLAYING MULTIVARIATE DATAThe Problem of Displaying Many Variables in Two DimensionsPlotting index VariablesThe Draftsman's PlotThe Representation of Individual Data P:ointsProfiles of VariablesDiscussion and Further ReadingChapter SummaryReferencesTESTS OF SIGNIFICANCE WITH MULTIVARIATE DATASimultaneous Tests on Several VarablesComparison of Mean Values for Two Samples: The Single Variable CaseComparison of Mean Values for Two Samples: The Multivariate CaseMultivariate Versus Univariate TestsComparison of Variation for Two Samples: The Single Variable CaseComparison of Variation for Two Samples: The Multivariate CaseComparison of Means for Several SamplesComparison of Variation for Several SamplesDiscussionChapter SummaryExercisesReferencesMEASURING AND TESTING MULTIVARIATE DISTANCESMultivariate DistancesDistances Between Individual ObservationsDistances Between Populations and SamplesDistances Based on ProportionsPresence-Absence dataThe Mantel Randomization TestComputer ProgramsDiscussion and Further ReadingChapter SummaryExerciseReferencesPRINCIPAL COMPONENTS ANALYSISDefinition of Principal ComponentsProcedure for a Principal Components AnalysisComputer ProgramsFurther ReadingChapter SummaryExercisesReferencesFACTOR ANALYSISThe Factor Analysis ModelProcedure for a Factor AnalysisPrincipal Components Factor AnalysisUsing a Factor Analysis Program to do Principal Components AnalysisOptions in AnalysesThe Value of Factor AnalysisComputer ProgramsDiscussion and Further ReadingChapter SummaryExerciseReferencesDISCRIMINANT FUNCTION ANALYSISThe Problem of Separating GroupsDiscrimination Using Mahalanobis DistancesCanonical Discriminant FunctionsTests of SignificanceAssumptionsAllowing for Prior Probabilities of Group MembershipStepwise Discriminant Function AnalysisJackknife Classification of IndividualsAssigning of Ungrouped Individuals to GroupsLogistic RegressionComputer ProgramsDiscussion and Further ReadingChapter SummaryExercisesReferencesCLUSTER ANALYSISUses of Cluster analysisTypes of Cluster AnalysisHierarchic MethodsProblems of Cluster AnalysisMeasures of DistancePrincipal Components Analysis with Cluster AnalysisComputer ProgramsDiscussion and Further ReadingChapter SummaryExercisesReferencesCANONICAL CORRELATION ANALYSISGeneralizing a Multiple Regression AnalysisProcedure for a Canonical Correlation Analysis

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