On Inverting Permutation Tests

Abstract

Polynomial time algorithms are presented for inverting permutation tests. The one-sample permutation test is inverted to make confidence statements about a location parameter, and the two-sample permutation test is inverted to make confidence statements concerning a shift in location or scale. These algorithms require polynomial time, as opposed to complete enumeration algorithms, which require exponential time. A computational method for the inversion of rank tests is also suggested. The algorithms extend to stratified experiments.

Key Words:

• Permutation test
• Fast Fourier Transform
• Nonparametrics
• Confidence interval
• Typical values
• Stratification