Sample size choice
Sample size choice is an important, not just a statistical, but also an ethical problem in designing an experiment or a trial. On one hand, the sample size should be big enough to have a chance to detect a difference in treatments, on the other hand small enough to ensure that subjects are not unnecessarily treated with harmful irritants. In general, sample sizes are determined via controlling the power of the utilized test at a specified alternative where the power of a test is the probability that the null hypothesis will be rejected if it is in fact false. The power of the ANOVA F-test, as it is the same for any other statistical test, depends on the distribution of the test statistic when the null hypothesis is false, that is we have different means of TEWL in the treatment groups. It turns out that this distribution is noncentral F and this distribution importantly depends on the actual means in the treatment groups, the population variance σ 2 , the significance level α and the number of observations in the sample. To become concrete we have, under the assumption of a balanced design which is usually the case in the planning phase of a study, the power of the F-test as π(ϕ; k-1, n-k) = p (F (k-1,n-k; ϕ) > F 1-α (k-1,n-k)), where F (k-1,n-k; ϕ) is the noncentral F-distribution with noncentrality parameter ϕ and k-1 and n-k degrees of freedom, F 1-α (k-1,n-k) is the (1-α)-quantile from the regular F-distribution with the respective number of degrees of freedom, k is the number of treatment groups and n is the sample size to be determined. If we specify further the α-error, the β-error, the clinical significant difference in the means we want to detect and the population variance σ 2 (which we have to guess or estimate from a small pilot study) we can calculate the required sample size. Further insight into sample size choice can be gained through the book of Desu and Raghavarao (1990).