ESTIMATING STATISTICAL POWER FOR A TWO-FACTOR ANOVA DESIGN WITH MISSING DATA THROUGH MULTIPLE IMPUTATION

Abstract

Missing data is a common issue in experimental research that can undermine the statistical power and validity of results. Procedures for estimating statistical power for a two-sample t-test for incomplete data have been documented in the literature. This study extends the existing procedures to more than two samples. A power estimation formula is derived for a two-factor ANOVA model with missing values addressed through multiple imputation (MI). The within-imputation variance from Rubin’s rules was substituted into the power calculation formula. Experimental data on the antifungal properties of plant extracts was analyzed in a two-factor design using SPSS version 27. Statistical power was investigated at 8%, 16%, and 40% levels of missingness; 0.2, 0.5, and 0.8 effect sizes and 20, 30, 40, and 100 number of imputations. The study reveals that the number of missing observations, the effect size, and the number of imputations have an impact on statistical power in a two-factor ANOVA design; as effect size and the number of imputations increase, statistical power increases but decreases with higher missingness. The power analysis presented in this study can be extended to higher ANOVA models.