Expected Mean Squares for a One-factor between-subject ANOVA (2 of 2)

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For example, if σ² = 100, n = 10, a = 3, µ₁ = 5, µ₂ = 6, and µ₃ = 10

then = 7 and



The expected value of MSB is σ² when the null hypothesis is true but is equal to a larger value when the null hypothesis is false. E[MSE] = σ² whether or not the null hypothesis is true.

For the example, E[MSE] = 100. Whenever the null hypothesis is false, E[MSB] > E[MSE] and relatively large values of F = MSB/MSE can be expected. Although you will rarely need to know the expected value of MSB or MSE, it is important to see that both expected values are the same when the null hypothesis is true and that the expected value of MSB is larger when the null hypothesis is false.

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