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ANOVA and ANCOVA of pre- and post-test, ordinal data

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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 Θ. In an ANCOVA for pre- and post-test variablesX andY which are ordinal measures ofη and Θ, respectively, random assignment and standard assumptions ensure the legitimacy of inferences about the equality of treatment effects on latent variable Θ. Sample estimates of adjustedY treatment means are ordinal estimators of adjusted post-test means on latent variable Θ.

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Davison, M.L., Sharma, A.R. ANOVA and ANCOVA of pre- and post-test, ordinal data. Psychometrika 59, 593–600 (1994).

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