ABSTRACT
This chapter introduces different sources of random variation, and examines how these arise from design considerations and how they affect the model form and data analysis. It discusses a model with one random effect besides error. The chapter explores a test for variation among classes, drawing analogies to comparison of group means in the fixed model. The one-factor random model includes two random mechanisms which may affect the response. The partition of total variation is exactly the same for the one-factor random model as for the one-factor fixed model. While the error sum of squares always has a nice form, the distribution of the model sum of squares can be complicated in the case of unbalanced data. Quick and easy estimates of variance components for random effects are possible with the method of moments, or anova method, by simply matching up expectations.
