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OTE/SPH
OTE/SPH
August 31, 2006
Char Count= 0
JWBK119-11
168 2:57 Goodness-of-Fit Tests for Normality
Table 11.6 Coefficients and critical values for the Shapiro--Wilks GOF test. 17,18
(a) Coefficients a i,n computing the W statistics
Sample size, n
i 5 10 20 30 40 50

1 0.6646 0.5739 0.4734 0.4254 0.3964 0.3751
2 0.2413 0.3291 0.3211 0.2944 0.2737 0.2574
3 0.0000 0.2141 0.2565 0.2487 0.2368 0.2260
4 --- 0.1224 0.2085 0.2148 0.2098 0.2032
5 --- 0.0399 0.1686 0.1870 0.1878 0.1847
6 --- --- 0.1334 0.1630 0.1691 0.1691
7 --- --- 0.1013 0.1415 0.1526 0.1554
8 --- --- 0.0711 0.1219 0.1376 0.1430
9 --- --- 0.0422 0.1036 0.1237 0.1317
10 --- --- 0.0140 0.0862 0.1108 0.1212
11 --- --- --- 0.0697 0.0986 0.1113
12 --- --- --- 0.0537 0.0870 0.1020
13 --- --- --- 0.0381 0.0759 0.0932
14 --- --- --- 0.0227 0.0651 0.0846
15 --- --- --- 0.0076 0.0546 0.0764
16 --- --- --- --- 0.0444 0.0685
17 --- --- --- --- 0.0343 0.0608
18 --- --- --- --- 0.0244 0.0532
19 --- --- --- --- 0.0146 0.0459
20 --- --- --- --- 0.0049 0.0386
21 --- --- --- --- --- 0.0314
22 --- --- --- --- --- 0.0244
23 --- --- --- --- --- 0.0174
24 --- --- --- --- --- 0.0104
25 --- --- --- --- --- 0.0035
(b) Critical values for W statistics

Critical values at α-level of significance

Sample size, n α = 5% α = 5%

5 0.762 0.806
10 0.842 0.869
20 0.905 0.92
30 0.927 0.939
40 0.94 0.949
50 0.947 0.955