MAN_RM1 - The Multivariate Approach to the One-Way Repeated Measures ANOVA Analyses of variance which have one or more repeated measures\/within subjects

# MAN_RM1 - The Multivariate Approach to the One-Way Repeated...

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The Multivariate Approach to the One-Way Repeated Measures ANOVA Analyses of variance which have one or more repeated measures/within subjects factors have a SPHERICITY ASSUMPTION (the standard error of the difference between pairs of means is constant across all pairs of means at one level of the repeated factor versus another level of the repeated factor. Howell discusses compound symmetry , a somewhat more restrictive assumption. There are adjustments (of degrees of freedom) to correct for violation of the sphericity assumption, but at a cost of lower power. A better solution might be a multivariate approach to repeated measures designs, which does not have such a sphericity assumption. Consider the first experiment in Karl Wuensch’s doctoral dissertation (see the article, Fostering house mice onto rats and deer mice: Effects on response to species odors , Animal Learning and Behavior, 20, 253-258. Wild-strain house mice were at birth cross-fostered onto house-mouse ( Mus ), deer mouse ( Peromyscus ) or rat ( Rattus ) nursing mothers. Ten days after weaning each subject was tested in an apparatus that allowed it to enter tunnels scented with clean pine shavings or with shavings bearing the scent of Mus , Peromyscus , or Rattus . One of the variables measured was how long each subject spent in each of the four tunnels during a twenty minute test. The data are in the file “ TUNNEL4b.DAT ” and a program to do the analysis in MAN_RM1.SAS ,” both available on my web pages. Run the program. Time spent in each tunnel is coded in variables T_clean, T_Mus, T_Pero, and T_Rat. TT_clean, TT_Mus, TT_Pero, and TT_Rat are these same variables after a square root transformation to normalize the within-cell distributions and to reduce heterogeneity of variance. proc anova ; model TT_clean TT_mus TT_pero TT_rat = / nouni ; repeated scent 4 contrast ( 1 ) / summary printe ; proc means ; var T_clean -- T_Rat; Note that PROC ANOVA includes no CLASS statement and the MODEL statement includes no grouping variable (since we have no between subjects factor). The model statement does identify the multiple dependent variables, TT_clean, TT_Mus, TT_Pero, and TT_Rat, and includes the NOUNI option to suppress irrelevant output. The REPEATED statement indicates that we want a repeated measures analysis, with SCENT being the name we give to the 4-level repeated factor represented by the four transformed time variates. CONTRAST(1) ” indicates that these four variates are to be transformed into three sets of difference scores, each representing the difference between the subject’s score on the 1 st variate (tt_clean) and one of the other variates—that is, clean versus Mus , clean versus Peromyscus , and clean versus Rattus . I chose clean as the comparison variable for all others because I considered it to represent a sort of control or placebo condition. The Copyright 2008, Karl L. Wuensch - All rights reserved.

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