Statistics and Algorithms / Simulations and Bootstrapping / Bootstrapping and Resampling Methods /

Approximate Randomization

Approximate randomization is a technique for testing “unrelatedness” in a fairly general way. It can be applied in place of analysis of variance tests and the like. The null hypothesis to be tested is that some variable \(X\) is unrelated to another variable \(Y\). The method of attack is to take random permutations of the sample \(X\)’s. If \(X\) is, indeed, unrelated to \(Y\), then the actual sample should be fairly typical of the population of permutations. Choose an appropriate test statistic and count the number of times the permuted samples produce a more extreme statistic than the actual sample. (In “exact” randomization, all permutations are examined. That is clearly only possible for very small sample sizes).

An example is provided in RANDOMIZE.RPF which looks the heteroscedasticity tests done in the HETEROTEST.RPF example but doing a bootstrapped p-value rather than using the asymptotic distribution.