This article has discussed some of the ways that are available to increase the power of a t-test. There are some that it has omitted, such as increasing the strength of the treatment and decreasing the size of the standard deviation of the outcome measure. It has omitted them because they are not directly related to the design of the statistical analysis.
Each of the methods discussed, and the method's quantitative results, can also take place in the F test used in the analysis of variance or covariance:
- You might opt for a directional hypothesis when you plan a multiple comparisons procedure following a significant F test.
- You might calculate the power of an F test under a certain set of conditions (as discussed in the next two articles in this series) and decide that your power is not high enough to proceed. In that case, you might evaluate the power available if you were to increase your sample sizes.
- You might decide to conduct an analysis of covariance, which might allocate a substantial amount of error variance to the relationship between the covariate and the outcome measure. The result, a smaller degree of error variance, is the same as you get with a dependent groups t-test when the correlation is reasonably strong.
In each case, you can evaluate the power of the F test under a different set of conditions. The third article in this series takes up the problem of quantifying the power of the F test.