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This paper illustrates how expected mean squares needed in the analysis of variance can be arrived at via the use of only one rule: the E(MS) for any source of variation for any ANOVA model is the specified effect (main effect or interaction) plus the specified effect in combination with any random effect (including combinations of random effects). Once the procedure has been mastered, it can be quickly applied to ANOVA designs of any complexity.
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Kenneth D. Hopkins (1976) studied this question.
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