A comparison of normality tests towards convoluted probability distributions

Figures & data

Table 1. Type I error rate of normality tests against independent Normal (2, 1) distribution, and convoluted Normal (2, 1) and Normal (0, 1) distributions with varying sample sizes

Sample size	AD	SW	LF	DA	SF	JB
Independent Normal (2, 1)
20	0.0508	0.0513	0.0481	0.0590	0.0531	0.0600
30	0.0493	0.0513	0.0479	0.0580	0.0529	0.0591
50	0.0511	0.0509	0.0514	0.0572	0.0532	0.0585
100	0.0513	0.0505	0.0539	0.0564	0.0527	0.0594
300	0.0490	0.0506	0.0507	0.0537	0.0520	0.0599
500	0.0497	0.0515	0.0513	0.0543	0.0535	0.0594
1000	0.0500	0.0511	0.0472	0.0513	0.0513	0.0584
Convoluted distribution involving Normal (2, 1) and Normal (0, 1)
20	0.0508	0.0513	0.0481	0.0590	0.0531	0.0600
30	0.0493	0.0513	0.0479	0.0580	0.0529	0.0591
50	0.0511	0.0509	0.0514	0.0572	0.0532	0.0585
100	0.0513	0.0505	0.0539	0.0564	0.0527	0.0594
300	0.0490	0.0506	0.0507	0.0537	0.0520	0.0599
500	0.0497	0.0515	0.0513	0.0543	0.0535	0.0594
1000	0.0500	0.0511	0.0472	0.0513	0.0513	0.0584

Figure 1. Power of normality tests against independent uniform (left panel) and convoluted uniform-normal distributions (right panel) with varying sample sizes.

Figure 2. Power of normality tests against independent Student’s t (left panel) and convoluted Student’s t-normal distributions (right panel) with varying sample sizes.

Figure 3. Power of normality tests against independent exponential (left panel) and convoluted exponential-normal distributions (right panel) with varying sample sizes.

Figure 4. Power of normality tests against independent gamma (left panel) and convoluted gamma-normal distributions (right panel) with varying sample sizes.

Figure 5. Power of normality tests against independent beta (left panel) and convoluted beta-normal distributions (right) with varying sample sizes.