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

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%.

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

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