An Assessment of Statistical Power for Analysis of Variance with Missing Data using Multiple Imputation
DOI:
https://doi.org/10.62054/ijdm/0104.9Keywords:
Analysis of variance (ANOVA), Arbitrary, Incomplete data, Monotone, Multiple imputation, Statistical powerAbstract
This study proposes a framework for statistical power assessment in the analysis of variance (ANOVA) models with missing data handled through multiple imputation. While existing literature has examined the power for t-tests with missing data, extending these techniques to ANOVA designs with multiple group means remains an open challenge. The methodology involves incorporating the variance component into an existing power model derived for a pairwise test, enabling explicit power estimation for two-factor, three-factor, and split-plot ANOVA designs with incomplete data. Empirical evaluations across varying effect sizes, missing data rates (8%, 16%, 40%), and numbers of imputations (20, 30, 40, 100) were conducted for both monotone and arbitrary patterns of missing data. The findings reveal that while power remains high at low missing data rates, it declines substantially with increasing missingness, particularly for higher proportions of missing data. Furthermore, arbitrary patterns of missing data exhibit slightly lower power compared to monotone patterns. The number of required imputations to achieve desired power levels depends on the missing data rate, with more imputations needed for higher proportions of missing data. This study provides a framework for power analysis in ANOVA models with missing data, addressing the critical need for reliable guidance in designing studies with incomplete data
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