Talk:Shapiro–Wilk test
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Some questions:
editWhat is the criterion for W to be "too small"? What is the expected value for the order statistics? Is there a multi-variate generalization? PhysPhD 20:55, 16 May 2007 (UTC)
I think there should be some way of arriving at the a(i)'s...
I've seen it like this:
ai <- qnorm((i-0.375)/(n+0.25))
where qnorm is the inverse CDF. —Preceding unsigned comment added by 64.122.234.42 (talk) 21:35, 30 October 2007 (UTC)
I've found some table for critical values of criterion Wcrit in some old Russian book named "Основы математической статистики - Под ред.В.С.Иванова" which is roughly "Fundamentals of Mathematical Statistics - Edited by Ivanov V.S.". The table looks like this:
n | alpha | alpha | n | alpha | alpha | n | alpha | alpha |
---|---|---|---|---|---|---|---|---|
0.05 | 0.01 | 0.05 | 0.01 | 0.05 | 0.01 | |||
4 | 0.767 | 0.753 | 20 | 0.905 | 0.868 | 36 | 0.935 | 0.912 |
5 | 0.748 | 0.687 | 21 | 0.908 | 0.873 | 37 | 0.936 | 0.914 |
6 | 0.762 | 0.686 | 22 | 0.911 | 0.878 | 38 | 0.938 | 0.916 |
7 | 0.803 | 0.730 | 23 | 0.914 | 0.881 | 39 | 0.939 | 0.917 |
8 | 0.818 | 0.749 | 24 | 0.916 | 0.884 | 40 | 0.940 | 0.919 |
9 | 0.829 | 0.764 | 25 | 0.918 | 0.888 | 41 | 0.941 | 0.920 |
10 | 0.842 | 0.781 | 26 | 0.920 | 0.891 | 42 | 0.942 | 0.922 |
11 | 0.850 | 0.781 | 27 | 0.923 | 0.894 | 43 | 0.943 | 0.923 |
12 | 0.859 | 0.805 | 28 | 0.924 | 0.896 | 44 | 0.944 | 0.924 |
13 | 0.866 | 0.814 | 29 | 0.926 | 0.898 | 45 | 0.945 | 0.926 |
14 | 0.874 | 0.825 | 30 | 0.927 | 0.900 | 46 | 0.945 | 0.927 |
15 | 0.881 | 0.835 | 31 | 0.929 | 0.902 | 47 | 0.946 | 0.928 |
16 | 0.887 | 0.884 | 32 | 0.930 | 0.904 | 48 | 0.947 | 0.929 |
17 | 0.892 | 0.851 | 33 | 0.931 | 0.906 | 49 | 0.947 | 0.929 |
18 | 0.897 | 0.858 | 34 | 0.933 | 0.908 | 50 | 0.947 | 0.930 |
19 | 0.901 | 0.863 | 35 | 0.934 | 0.910 |
The null hypothesis is rejected if W < Wcrit. From this table we can deduce that Wcrit depends on so-called statistical significance level alpha (see article http://en.wikipedia.org/wiki/Statistically_significant), and on the actual number of experiments n. This test was specialized for small n (under 40-50), so if you have to test a larger sample, it's better to use other tests like Kolmogorov–Smirnov test (http://en.wikipedia.org/wiki/Kolmogorov%E2%80%93Smirnov_test) —Preceding unsigned comment added by 93.73.35.146 (talk) 07:47, 22 August 2010 (UTC)