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Some Differences Between Fixed, Mixed, and Random Effects Analysis of Variance Models

Summary: The analysis of variance is a technique for comparing treatment means or for estimating components of variation. The former is called fixed effects analysis of variance and the latter is called random effects analysis of variance. Many nonstatisticians who use canned analysis-of-variance computer programs do not appreciate this difference and incorrectly perform a fixed effects analysis when a random effects analysis is needed. The same set of data can lead to opposite conclusions, depending on whether a fixed or random effects analysis is appropriate. This article discusses differences in the assumptions, analyses, and inferences for fixed and random effects analysis of variance models. The mixed effects model, which is a combination of the fixed and random effects models, is also briefly described. The main message is that not all analysis of variance models are fixed effects models and that random effects require different treatment from fixed effects. The entire discussion is illustrated by practical examples.

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  • Topics:
  • Keywords: Fixed-effects model,Random effects,Statistical methods
  • Author: Feder, Paul I.
  • Journal: Journal of Quality Technology