Analysis of Variance of Multiply Imputed Data

Area of Science:

• Statistics
• Data Analysis
• Biostatistics

Background:

• Missing data is a common challenge in statistical analysis.
• Multiple imputation is a technique to handle missing data by creating multiple complete datasets.
• Pooling results from analysis of variance (ANOVA) F-tests with multiply imputed data lacks established guidelines.

Purpose of the Study:

• To propose and validate a procedure for pooling F-tests from ANOVA on multiply imputed datasets.
• To provide explicit rules for combining ANOVA results when using multiple imputation for missing data.
• To demonstrate the application of the proposed method with real-world examples.

Main Methods:

• Reformulating the ANOVA model as a regression model using effect coding.
• Applying existing combination rules for regression models to the imputed datasets.
• Illustrating the procedure with three distinct example datasets.

Main Results:

• The proposed method provides a clear procedure for pooling ANOVA F-tests from multiply imputed data.
• Pooled results from example datasets yielded plausible F- and p-values.
• The approach facilitates robust analysis of incomplete datasets.

Conclusions:

• The developed procedure offers a statistically sound method for analyzing multiply imputed data in ANOVA.
• This work addresses a critical gap in statistical methodology for handling missing data.
• The findings support the use of this method for reliable interpretation of research results.