-
Views
-
Cite
Cite
Paul W. Mielke, Randomization Tests by E. S. Edgington and P. Onghena, Biometrics, Volume 63, Issue 4, December 2007, Pages 1303–1304, https://doi.org/10.1111/j.1541-0420.2007.00905_10.x
Close - Share Icon Share
Extract
An exact permutation test is based on all equally likely configurations of N distinct objects being placed into g disjoint groups with fixed sizes ni≥ 1 for i = 1, g (this is termed the complete reference set). If the complete reference set is extremely large as commonly occurs, then an approximate permutation test can be based on a reduced reference set resulting from repeated random assignments of the N objects to the g groups (this is termed a resampling approximation). A randomization test includes both the previously described exact and approximate permutation tests. If T is the statistic associated with either an exact (approximate) randomization test and To is an observed statistic, then the exact (approximate) P-value is the proportion of configurations in the complete (reduced) reference set yielding values of T that are either at least as large or at least as small as To, depending on the test in question. This book emphasizes the correct statement that no random sampling is allowed from an assumed artificial population such as a normal distribution in the case of classical t and F tests. Consequently randomization tests are termed data dependent methods since they strictly depend on the random assignment scheme of experimental units to treatments and the resulting data.
