Probing interactions in repeated measures designs: Applications in clothing and textiles research

Mixed designs, which contain one or more repeated measures factors in addition to one or more independent groups factors, are used in a variety of disciplines, including the clothing and textiles discipline. While many researchers may adopt the conventional analysis of variance (ANOVA) procedure to test repeated measures hypotheses in such designs this approach is not recommended, particularly for omnibus tests of interactions, as it is known to be highly sensitive to departures from the derivational assumption of multisample sphericity. Furthermore, omnibus tests of interactions in mixed designs are not useful in providing specific information on the localized sources of these effects.

A content analysis of clothing and textiles literature published between 1987 and 1993 revealed that the conventional ANOVA approach is popular for testing repeated measures hypotheses. However in using mixed designs, clothing and textiles researchers do not take full advantage of the factorial structure of the data, either by not testing for the presence of interactions or by following omnibus tests of interactions with tests of simple effects which do not provide relevant information about the specific nature of variable interactions.

It is shown that in two-factor designs, tetrad contrasts are the only viable way to probe interactions. Monte Carlo simulation techniques were used to collect empirical familywise Type I error and power rates for ten procedures for testing multiple tetrad contrast hypotheses in mixed designs when the multisample sphericity assumption was violated. Only three procedures provided acceptable control of error rates; these relied on a test statistic formed using an estimate of the standard error of the tetrad contrast based on only those data used in defining the contrast (i.e., a nonpooled test statistic), in combination with either a Studentized maximum modulus, Hochberg (1988) step-up Bonferroni, or Shaffer (1986) modified sequentially rejective Bonferroni critical value. Minimal power differences between these three procedures were observed.

The application of these nonpooled tetrad contrast procedures to data from a hypothetical clothing and textiles data set was made with a computer program based on a general linear model approach to hypothesis testing using a nonpooled statistic.