Analysis of variance with ipsative measures

Measures with more than 1 score per participant, when the total for each participant equals the same constant, are said to be ipsative. Ipsativity occurs when data are percentages, with each participant's total equal to 100%, or when data are ranks, with each participant's total equal to the sum of the ranks. When ipsative measures are analyzed with analysis of variance (ANOVA), certain sums of squares equal 0, and the average intercorrelation among measures is negative. These characteristics of ipsativity may result in violations of ANOVA assumptions, producing an inflated Type I error rate and affecting power. The purpose of this Monte Carlo study was to empirically examine the extent to which ANOVA is affected by ipsative data. Findings indicated that, with few exceptions, ANOVA worked quite well with ipsative data. Not only were Type I error rates well preserved, but power was nearly equivalent to that with nonipsative data.