A Monte Carlo study of alternative responses to intraclass correlation in community trials. Is it ever possible to avoid Cornfield's penalties?

Strategies to avoid the penalties of extra variation and reduced degrees of freedom in community trials were compared in Monte Carlo simulations. Three conditions were found necessary to ensure nominal Type I and II error rates: (a) Condition variation must be assessed against assignment unit variation, (b) the critical value for the test statistic must be based on the assignment unit degrees of freedom, and (c) estimation of negative intraclass correlations must be allowed in the analysis. Using other test statistics and other degrees of freedom, and fixing negative intraclass correlations at zero often gave Type I and II error rates far from their nominal levels.