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Table 7 Relative efficiency of ANCOVA and Mann-Whitney for the extreme asymmetry distribution. Values less than 1 indicate greater power of ANCOVA; greater than 1 indicates superiority of Mann-Whitney. In blank cells, the power of one or both tests was 100%.

From: Parametric versus non-parametric statistics in the analysis of randomized trials with non-normally distributed data

Sample size Post-treatment score Change score
  ANCOVA v. Mann-Whitney log ANCOVA v. Mann-Whitney ANCOVA v. Mann-Whitney log ANCOVA v. Mann-Whitney
  Shift Ratio Shift Ratio Shift Ratio Shift Ratio
10 3.0404 4.1864 0.8862 1.1179 1.2586 1.9736 0.5567 0.539
20 1.2037 2.6045 0.8073 1.2589 0.5480 0.7372 0.3473 0.2983
30 1.1503 1.7717 0.9409 1.2707 0.3084 0.3860 0.2472 0.2701
40 1.1730 1.4786 1.0233 1.4105 0.2643 0.2772 0.2446 0.2421
60 1.1853 1.2015 1.1118 1.4062 0.2115 0.2121 0.1898 0.2586
100 1.2682 1.0648 1.1842 1.4789 0.2224 0.1753 0.2065 0.2545
200 1.2880 0.9257 1.2570 1.5437 0.2078 0.1496 0.1985 0.2544
400 1.3576 0.9089 1.3112 1.5308 0.1961 0.1358 0.1816 0.2418
800 1.4222 - 1.4116 - 0.2038 - 0.1783 0.2444