Estimating Variance Components from Mean Squares for Random and Mixed Effects Analysis of Variance Models

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Abstract
The analysis of variance can be used for: (a) F tests of the null hypothesis; (b) investigating theoretical models; and (c) estimating, from mean squares, the relative contributions of variance components. The methods of estimation of variance components enable the researcher not only to test significance but to attribute the relative contribution (percentage of variance) of each source to the total variation (sum of variance components). Discussion concerns the advantages, disadvantages and limitations of random and mixed effects models. The study concludes that each researcher must logically choose the model which best describes his experiment. Three-way random and mixed effects models with one observation per cell are compared and illustrated using data from a multidimensional personality inventory.