Talk:Shapiro–Wilk test

Some questions:
What 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:

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)