Connections between permutation and t-tests: relevance to adaptive methods.

A permutation test assigns a p-value by conditioning on the data and treating the different possible treatment assignments as random. The fact that the conditional type I error rate given the data is controlled at level α ensures validity of the test even if certain adaptations are made. We show the connection between permutation and t-tests, and use this connection to explain why certain adaptations are valid in a t-test setting as well. We illustrate this with an example of blinded sample size recalculation.