## Saturday, 21 September 2013

### Critical value of W statistic for Shapiro-Wilk test

One of the tests in SciStatCalc is the Shapiro-Wilk test for Gaussianity/Normality. Below is a table of the number of samples against the critical value of the statistic $W$ for this test, derived from Table 10-3 in Appendix D, from the document that is accessible at the following website

http://www.epa.gov/osw/hazard/correctiveaction/resources/guidance/sitechar/gwstats/unified-guid-app.pdf

The alpha level is 5%, for a two-tailed test. The $W$ statistic needs to be greater than the critical value for the null hypothesis that the samples are drawn from a Gaussian distribution not to be rejected. Sample values up to 50 are shown.

Number or Samples W(critical)
3 0.767
4 0.748
5 0.762
6 0.788
7 0.803
8 0.818
9 0.829
10 0.842
11 0.850
12 0.859
13 0.866
14 0.874
15 0.881
16 0.887
17 0.892
18 0.897
19 0.901
20 0.905
21 0.908
22 0.911
23 0.914
24 0.916
25 0.918
26 0.920
27 0.923
28 0.924
29 0.926
30 0.927
31 0.929
32 0.930
33 0.931
34 0.933
35 0.934
36 0.935
37 0.936
38 0.938
39 0.939
40 0.940
41 0.941
42 0.942
43 0.943
44 0.944
45 0.945
46 0.945
47 0.946
48 0.947
49 0.947
50 0.947