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Table 5 Relative efficiency of ANCOVA and Mann-Whitney combining all sample sizes. Values less than 1 indicate greater power of ANCOVA; greater than 1 indicates superiority of Mann-Whitney.

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

Distribution Correlation between baseline and post-treatment score
  0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
Moderate positive skew: shift 0.9342 0.9257 0.8707 0.8532 0.8569 0.9030 0.9447 0.9538 0.9963
Moderate positive skew: ratio 1.1560 1.1300 1.1074 1.0800 0.8170 0.8656 0.9065 0.9231 0.9720
Moderate negative skew: shift 0.9392 0.9058 0.8837 0.8444 0.8799 0.9114 0.9421 0.9593 0.9885
Moderate negative skew: ratio 1.1766 1.1946 1.1467 1.0980 0.8851 0.9319 0.9671 1.0241 1.0390
Uniform: shift 0.9492 0.9170 0.8869 0.8480 0.8586 0.8977 0.9281 0.9723 1.0021
Uniform: ratio 0.9575 0.9384 0.8862 0.8499 0.8604 0.8849 0.9213 0.9467 0.9895
Extreme negative skew: shift 1.4019 1.3718 1.3339 1.3045 0.8987 0.9425 0.9475 0.9405 0.9345
Extreme negative skew: ratio 1.6914 1.6185 1.6101 1.5835 1.0153 1.0367 1.0247 1.0344 1.0062
Normal: shift 0.9700 0.9393 0.9142 0.8445 0.8372 0.8840 0.9065 0.9485 0.9734
Normal: ratio 0.9551 0.9506 0.9126 0.8791 0.8536 0.8859 0.9072 0.9293 0.9654