In the secondary data analysis for categorical data, situations often arise in which the estimated cell variances are available, but not the full matrix of variances. In this case researchers are often inclined to use Pearson-type test statistics for homogeneity. However, for a complex sample observed cell proportions are not distributed as multinomial and Pearson-type test statistic generally is not distributed asymptotically as chi-square distribution. This paper evaluates powers for Wald test and Pearson-type test and the first order corrected test of Pearson-type test for homogeneity. The resulting power curves indicate that as the misspecification effect increases, the amount of inflation of significance level and the loss of power Pearson-type test are getting more severe.