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JWBK119-11
160 2:57 Goodness-of-Fit Tests for Normality
Table 11.4 Critical values of EDF based statistics (Kolmogorov--Smirnov, Anderson--Darling
and Cram´er--von Mises).
(a) Critical values of D statistic (case where F 0 (x) completely specified and mean
specified, variance unknown)

F 0 (x) completely specified Mean specified, variance unknown
(from exact distribution) 6 (based on Monte Carlo simulation) 15
Sample
size, n α = 5% α = 10 % α = 5% α = 10 %
5 0.565 0.510 -- --
10 0.41 0.368 0.402 0.360
15 0.338 0.304 -- --
20 0.294 0.264 0.288 0.259
25 0.27 0.240 -- --
30 0.24 0.220 -- --
35 0.23 0.210 -- --
⎫ ⎫
50 0.185 0.165
√ √
⎬ ⎬
100 1.36/ n 1.22/ n 0.132 0.118
√ √
>100 ⎭ ⎭ 1.333/ n 1.190/ n
2
2
(b) Critical values for A and W statistics for Anderson--Darling and Cram´er--von Mises
GOF test (n ≥ 5) 15
Case when F 0 (x) completely specified
2
Critical values Modified W* and A statistic
Modifications α = 5% α = 10 %

2
2
W 2 W* = (W − 0.4/n + 0.6/n )(1.0 + 1.0/n) 0.461 0.347
A 2 -- 2.492 1.933
2 2
Case when mean specified, variance unknown and estimated from s = (x i − μ) /n
i
Critical values at α level of significance
α = 5% α = 10 %

W 2 0.443 0.329
A 2 2.323 1.76

absolute differences where the null hypothesis can be retained at the 5% level of sig-
nificance is shown in Figure 11.1 as well. This ‘acceptance’band is computed from the
critical values for the absolute difference based on equation (11.4). The critical values
d α are given by Barnes and Murdoch. 14 The critical values for the case where F 0 (x)
is completely specified and the case where the mean is specified and the variance
unknown given in Table 11.4(a). 6,15