The Wilcoxon, normal-scores, and sign tests also lose power by losing information. For instance, the Wilcoxon test ranks data points by their absolute distances from M 0 . This loss of information generally produces a loss of statistical power. The Wilcoxon and normal-scores tests also don't deal well with ties, which are very common in a wide range of problems. For instance, if 20 people respond to a 7-point attitude scale, the number of ties is necessarily large.
Permutation tests are either exhaustive or nonexhaustive .
Exhaustive permutation tests are often impractical even with very fast computers, while nonexhaustive tests are only approximate, and also have the unpleasant property that two different investigators will typically find different significance levels from the very same data. To introduce it, I first give a quick review of permutation tests for the Wilcoxon hypothesis. The variable may be either absolutely continuous, allowing scores like 7.3265, or may be discrete such as number of offspring or score on a 7-point attitude scale. We then examine all 2 N sums that could be computed by independently changing the sign of each of these differences. For instance, making all 4 signs positive yields a sum of 33, while making just the first two positive yields a sum of -19, and so on.