The effectiveness of stepwise discriminant analysis as a post hoc procedure to a significant MANOVA.

摘要

This study examined stepwise discriminant analysis (DA) as a post hoc procedure to a significant MANOVA. Monte Carlo simulations were conducted under the assumptions of normality and homogeneity, using different levels of sample size, effect size, level of significance, number of dependent variables, and correlation structure among the dependent variables.;The results of this study indicated that stepwise DA has some limitations as a post hoc procedure to a significant MANOVA. High correlations among dependent variables and large numbers of dependent variables led to poor results for power and/or type I error using stepwise DA. In addition, stepwise DA was too aggressive when sample sizes were large, resulting in type I errors well above the set level of alpha. However, under certain conditions, stepwise DA performed quite well. The most important factor is keeping the number of dependent variables small, in this study no more than 3. Although type I error tends to be inflated using stepwise DA, observed values of type I error were very close to set levels of alpha when p was equal to 2 or 3. As values for p and sample size increased, type I error became too difficult to control, even for small alpha, and therefore stepwise DA is not recommended under these conditions.;The most important issue for future researchers to examine with regards to stepwise DA, is how to control type I error. Some possibilities include Thompson's (1995) adjustment to the degrees of freedom used in the calculation of the F statistic, Hawkins's (1976) "Bonferonni-like" adjustment to alpha, or the partial r-squared criterion as defined in the SAS procedure, STEPDISC.