A Handbook for Data Analysis in the Behavioral Sciences: Statistical Issues

By Gideon Keren; Charles Lewis | Go to book overview

I ANALYSIS OF VARIANCE AND MULTIPLE REGRESSION

Analysis of variance, multiple regression and other special cases of the general linear model enjoy great popularity in the social sciences. Chapter 1, by Tatsuoka, provides an accessible introduction to the subject. It takes the reader in careful detail through the problem of comparing the means of two independent groups, first showing informally how it can be recast as a regression problem and then spelling out the formal details. The setup for this case is re-expressed in matrix notation, thus allowing general expressions for the linear model to be introduced. The chapter concludes with a discussion of how factorial designs, multivariate problems and the analysis of covariance can all be expressed in the same framework.

In chapter 2, Zwick discusses the multiple comparisons problem in the context of one-way analysis of variance, focusing on the pairwise comparison of all treatment means for both the independent groups and repeated measures cases. She compares the best known procedures in terms of both power and Type I error probability, and describes alternatives that are available when there is concern about violation of the assumptions of normality and/or homogeneity of variance. Single-step methods of comparison are recommended because of their simplicity and the availability of associated simultaneous confidence intervals for the comparisons.

Several procedures for carrying out a repeated measures analy-

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