ANOVA AND ANCOVA OF PRETEST AND POSTTEST, ORDINAL DATA

With random assignment to treatments and standard assumptions, either a one-way ANOVA of post-test scores or a two-way, repeated measures ANOVA of pre- and post-test scores provides a legitimate test of the equal treatment effect null hypothesis for latent variable THETA. In an ANCOVA for pre- and post-test variables X and Y which are ordinal measures of eta and THETA, respectively, random assignment and standard assumptions ensure the legitimacy of inferences about the equality of treatment effects on latent variable THETA. Sample estimates of adjusted Y treatment means are ordinal estimators of adjusted post-test means on latent variable THETA.