Tests for the Difference Between Two Means in a 2×2 Cross-Over Design

Description:

When calculating the sample size for tests for the difference between two means in a cross-over design, the one option that can be a bit difficult is the specification of the standard deviation. For this reason, 3 options are given for entering the standard deviation. Each of the options is functionally related to the other two, so the choice is for the user’s convenience. If you mouse over the drop-down, a description of each of the choices is shown in the Option Info area, as well as the functional relationship. The most common selection is the square root of the within mean square error from a repeated measures analysis of variance, since it is typically output in an analysis of cross-over designs.

Suppose that researchers wish to find the sample size necessary to achieve 90% power in a balanced cross-over design using the two-sided T-test approach, with alpha equal to 0.05. They assume the difference of the means under the null hypothesis is 0, and that the standard deviation of the period differences is 10. They wish to calculate sample sizes for assumed mean differences of 3 to 10.

Note that ‘N’ is the total sample size of all sequences, not the sample size for each group.

As expected, the required sample size decreases as the mean difference increases.

The same result is achieved if the procedure is run with a standard deviation of paired differences, of 20. Or, an SW of 14.14.