The Shapiro-Wilk test for normality is a very powerful test. This test is a regression-type test. It assesses how well the observed cumulative frequency distribution curve fits the expected cumulative frequency curve. The Shapiro-Wilk test is sensitive to both skewness and kurtosis. The Shapiro-Wilk and Anderson-Darling tests are comparable in power, with Shapiro-Wilk having a slight edge in many situations.
Order the observations from low to high.
S² = (n-1)s²
where s² is the sample variance.
where a(n+i+1) for i = 1 to k, are found in tables.
W = b² / S²
The algorithms used by MVPstats are those of Patrick Royston, Applied Statistics, vol. 44 no. 4 (1995).
Accurracy is claimed for samples size from 3 to 5000. Sample size less than three will not produce a Shapiro-Wilk statistic.