## Quick Reference

A general test, published in 1952, that compares the fit of the observed cumulative distribution function with that expected. It was derived by Anderson and David A. Darling as a modification of the Cramér–von Mises test. The test statistic *A*^{2} is given by where F is the hypothesized cumulative distribution function, *n* is the sample size, and *x*_{(j)} is the *j*th ordered observation (*x*_{(1)}≤*x*_{(2)}≤…≤*x*_{(n)}). The statistic can also be used to test for normal and exponential distributions with unknown parameters estimated by their sample equivalents. In some cases, as shown in the following table, an adjusted test statistic is required.

test statistic

upper tail probability

0.10

0.05

0.025

0.01

Specified distribution

*A*^{2}

1.933

2.492

3.070

3.857

Normal, estimated mean (*n*>20)

*A*^{2}

0.894

1.087

1.285

1.551

Normal, estimated variance (*n*>20)

*A*^{2}

1.743

2.308

2.898

3.702

Normal, estimated mean and variance

0.631

0.752

0.873

1.035

Exponential, estimated mean

1.062

1.321

1.591

1.959

*Subjects:*
Probability and Statistics.