Power and minimum sample size for two-way MANOVA can be calculated in the same manner as for one-way MANOVA (see MANOVA Power and Sample Size).
Example 1: What is the power for the interaction of the two factors for the two-way MANOVA in Example 1 of Two-way MANOVA Example.
The power is 89% as calculated in cell B18 of Figure 1.
Figure 1 – Power calculation
Real Statistics Functions: The Real Statistics Resource Pack provides the following functions.
MANOVA2Row_POWER(f, n, k, g1, g2, ttype, alpha, iter, prec) = the statistical power of the first factor (aka the row factor) for two-way MANOVA where the sample size is n, the number of dependent variables is k , the number of groups in the first factor is g1, the number of groups in the second factor is g2 and the effect size is f, where f = the partial eta-square effect size if ttype = 1, f = eta-square if ttype = 2 and f = Pillai’s V if ttype = 3.
MANOVA2Row_SIZE(f, k, g1, g2, pow, ttype, alpha, iter, prec) = the minimum sample size to obtain statistical power of pow of the first factor for two-way MANOVA where f, k, g1, g2 and ttype are as for MANOVA2Row_POWER.
The Real Statistics worksheet functions MANOVA2Col_POWER, MANOVA2Int_POWER, MANOVA2Col_SIZE, MANOVAInt_SIZE for the second factor (aka the column factor) and interaction between the factors are defined similarly.
alpha is the significance level (default .05), iter = the maximum number of iterations used in calculating the answer (default 1000) up to a precision of prec (default 0.000000001), the default for pow is .80.
The power for Example 1 can be calculated by any of the following formulas (with reference to Figure 3).
=MANOVA_POWER(B5,B9,B7,B6)
=MANOVA_POWER(B4,B9,B7,B6,2,B13)
=MANOVA_POWER(B3,B9,B7,B6,3,B13)
Example 2: What sample size would be required to detect a partial eta-square effect size of .2 for the interaction between the two factors with power 95% if the experiment in Example 1 of Two-way MANOVA Example is to be repeated?
The required sample size is calculated as shown in cell G8 of Figure 2.
Figure 2 – Sample size calculation
As we can see, the minimum sample size is 46. Since 46 is not divisible by 2 ⨯ 3 = 6, the number of interaction groups, if we require a balanced model, then the minimum sample is 48, the next highest number larger than 46 that is divisible by 6.