The<unk> , named after Theodore Wilbur<unk> , Jr. (1918–?) and Donald A.<unk>  (1915–?), who invented it in 1952, is one of the most powerful statistics for detecting most departures from normality. It may be used with small sample sizes n ≤ 25.  Very large sample sizes may reject the assumption of normality with only slight imperfections, but industrial data with sample sizes of 200 and more have passed the<unk> .[citation needed]
The<unk>  assesses whether a sample comes from a specified distribution.  The formula for the test statistic 
A
{\displaystyle A}
 to assess if data 
{
Y
1
<
⋯
<
Y
N
}
{\displaystyle \{Y_{1}<\cdots <Y_{N}\}}
 (note that the data must be put in order) comes from a distribution with cumulative distribution function (CDF) 
F
{\displaystyle F}
 is
where
The test statistic can then be compared against the critical values of the theoretical distribution (dependent on which 
F
{\displaystyle F}
 is used) to determine the P-value.
The<unk>  for normality is a distance or empirical distribution function (EDF) test. It is based upon the concept that when given a hypothesized underlying distribution, the data can be transformed to a uniform distribution. The transformed sample data can be then tested for uniformity with a distance test (Shapiro 1980).
In comparisons of power, Stephens (1974) found 
A
2
{\displaystyle A^{2}}
 to be one of the best EDF statistics for detecting most departures from normality. The only statistic close was the 
W
2
{\displaystyle W^{2}}
 (Cramér von-Mises test) statistic.
Anderson-Darling test
Patrick's test
Breusch-Pagan test
Ascheim-Zondek test
Tine test
Schober's test
Posterior drawer test
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