Randall E. Schumacker University of Alabama SAGE Publications Contents Background Persons of Interest Factors Affecting Statistics R Software Web Resources

Multivariate statistics have been described as two distinct methods 1. Dependent 2. Interdependent Dependent methods define certain variables as dependent measures and others as independent measures (Y – dependent; X – independent) Examples: Multiple regression, analysis of variance, multivariate analysis of variance, discriminant, and canonical analysis Interdependent methods do not define a dependent variable. Examples: Factor analysis, cluster analysis, multidimensional scaling Alternative Definition Multivariate statistics has two approaches defined by testing mean differences or analyzing correlation (covariation) among variables. We proceed with this understanding using R functions to compute the multivariate statistics Copyright Using R with Multivariate Statistics 2

Biographies of Key Persons in Multivariate Statistics are included at the beginning of each chapter. There were many you contributed to the field, so any omissions are not intentional. Samuel S. Shapiro; Martin B. Wilk – Shapiro-Wilks test George E.P. Box - Box M test Harold Hotelling- Hotelling T 2, Canonical Correlation C.R. Rao- MANOVA William G. Cochran- MANCOVA Theodore W. Anderson- Multivariate Repeated Measures Sir Ronald A. Fisher- Discriminant Analysis Charles E. Spearman- Exploratory Factor Analysis Maurice S. Bartlett- Factor Score methods Theodore W. Anderson- Anderson-Rubin scores Herman Rubin Karl Pearson- Principal Component Analysis Warren S. Torgerson- Multidimensional Scaling (MDS) Roger N. Shepard-Shepard Diagram Joseph B. Kruskal-Kruskal STRESS test Herman O.A. Wold- Partial Least Squares Karl G. J ö reskog- Structural Equation Modeling 2016 Copyright Using R with Multivariate Statistics 3

Inferential statistics are not appropriate when: 1. Sample size is small ( n < 30) 2. N = 1 3. Non-random sampling (convenience, systematic, non-probability) 4. Guessing 5. Census is taken 6. Exact probabilities known (finite population; cards, dice) 7. Qualitative data (non-numeric) 8. Law (no need to estimate or predict) 9. Non-inferential (no inference from sample statistic to population parameter) 2016 Copyright Using R with Multivariate Statistics 4

Inferential statistics have certain assumptions, that when not met can bias results, that is we do not have a fair test of mean differences or correlation.  Restriction of range  Missing data  Outliers  Non-normality  Non-linearity  Equal variance  Equal covariance  Suppressor variables  Correction of Attenuation  Non-positive definite matrix  Sample size, power, effect size Can you define or explain each of these? 2016 Copyright Using R with Multivariate Statistics 5

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Install R R manuals, references, and information > help.start() R statistical packages > library(help = “stats”) Introduction to R (read data files, write data, statistics, graphics, and packages) Copyright Using R with Multivariate Statistics 7

Quick-R:Online information and functions R Tutorial Copyright Using R with Multivariate Statistics 8