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Table 4 Relative efficiency of ANCOVA and Mann-Whitney combining correlations 0.4 – 0.7. 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

Distribution Sample size
  10 20 30 40 60 100 200 400 800
Moderate positive skew: shift 1.0221 0.8751 0.8292 0.8004 0.8085 0.7887 0.7549 0.7497 -
Moderate positive skew: ratio 1.5001 0.9832 1.0161 0.8441 0.7973 0.8079 0.7755 0.7689 0.8389
Moderate negative skew: shift 1.0045 0.9793 0.8080 0.8300 0.8088 0.7810 0.7772 0.7494 0.7404
Moderate negative skew: ratio 1.7878 1.3025 1.1354 1.0737 0.9367 0.8763 0.8949 0.8766 0.8612
Uniform: shift 0.8611 0.8162 0.8360 0.7854 0.7787 0.7938 0.7560 0.7404 0.8137
Uniform: ratio 0.8285 0.8462 0.7789 0.7685 0.7759 0.7799 0.7401 0.7747 -
Extreme negative skew: shift 1.2952 1.0213 0.9250 0.9802 1.0610 1.0431 1.0477 1.0479 -
Extreme negative skew: ratio 1.5027 1.1288 1.1332 1.2639 1.3322 1.3808 1.3442 1.2769 -
Normal: shift 0.9601 1.0049 0.8356 0.7336 0.7850 0.7865 0.7797 0.7560 0.7516
Normal: ratio 0.8230 0.9140 0.8959 0.8114 0.7702 0.8166 0.7855 0.7961 0.7781