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Table 6 Relative efficiency of ANCOVA and Mann-Whitney combining all sample sizes. Mann-Whitney is always analyzed using the post-treatment score. 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 postive skew: shift 0.9397 0.9184 0.8831 0.8433 0.8012 0.7384 0.6701 0.5627 0.4214
Moderate postive skew: ratio 1.1430 1.1415 1.1036 1.0849 1.0541 0.9759 0.9090 0.7662 0.5947
Moderate negative skew: shift 0.9293 0.9281 0.8844 0.8326 0.7973 0.7256 0.6631 0.5556 0.4077
Moderate negative skew: ratio 1.1724 1.1871 1.1453 1.1103 1.0568 0.9867 0.9004 0.7665 0.5783
Uniform: shift 0.9324 0.9136 0.8926 0.8609 0.7741 0.7341 0.6483 0.5632 0.4147
Uniform: ratio 0.9475 0.9385 0.8957 0.8497 0.8191 0.7507 0.6659 0.5723 0.4297
Extreme negative skew: shift 1.4043 1.3724 1.3504 1.2859 1.2534 1.1947 1.0992 0.9472 0.7523
Extreme negative skew: ratio 1.6803 1.6120 1.6265 1.5843 1.4941 1.4206 1.2697 1.0932 0.858
Extreme negative skew: shift. ANCOVA log transformed 0.9709 0.9600 0.9638 0.9043 0.8940 0.8633 0.8109 0.7443 0.6680
Extreme negative skew: ratio. ANCOVA log transformed 0.9502 0.9298 0.9317 0.9077 0.8662 0.8282 0.7834 0.7161 0.6408
Normal: shift 0.9712 0.9258 0.9081 0.8618 0.7841 0.7272 0.6423 0.5349 0.3896
Normal: ratio 0.9550 0.9557 0.9183 0.8692 0.8139 0.7652 0.6527 0.5427 0.4131