Sometimes Pooling for Analysis of Variance Hypothesis Tests: A Review and Study of a Split-Plot Model

• Published in: The American statistician Vol. 54; no. 4; pp. 269 - 279
• Main Author: Janky, Denis G.
• Format: Journal Article
• Language: English
• Published: Alexandria, VA Taylor & Francis Group 01.11.2000; American Statistical Association
• Subjects: Analysis of variance; Conditional model; Degrees of freedom; Exact sciences and technology; Hypothesis testing; Linear inference, regression; Mathematics; Modeling; Multivariate analysis; Nonparametric inference; Parametric inference; Power gain; Power loss; Preliminary test; Probability and statistics; Random allocation; Recommendations; Response surface; Sciences and techniques of general use; Sequential test; Simulation; Simulations; Statistics; Teaching methods; Mixed distribution; Sequential test; Data analysis; Parameter estimation; Error estimation; Covariance analysis; Conditional model; Non parametric estimation; Statistical estimation; Review; Multivariate analysis; Variance analysis; Hypothesis test; Simulation; Mixed model; Response surface; Linear estimation; Preliminary test
• ISSN: 0003-1305; 1537-2731
• DOI: 10.1080/00031305.2000.10474559

This article presents a review of the technical literature on pooling in analysis of variance (ANOVA) models for the purpose of hypothesis testing, and compares these studies to corresponding discussions found in statistical textbooks. By following a clear prescription for pooling recommended in one book, a simulation study was conducted on a mixed model appropriate for a split-plot experiment. The results are summarized using response surface methods. It is found that pooling generally inflates Type I error and offers at best insubstantial gain in power (and often power loss) relative to the nominal test.