Normality tests

Four statistical tests for normal (Gaussian) distribution of one or several samples of univariate data, given in one or more separate columns or with a single data column and a group column.

If the p value is small (p<0.05), as marked in pink, the sample has a distribution significantly different from normal.

For each test, the test statistic and a p value according to published approximations are given, in addition to the result of a Monte Carlo simulation, comparing the test statistics to e.g. 9999 random samples from a normal distribution. The former is more traditional, while the latter is probably more accurate.

In most cases, the Shapiro-Wilk test is preferable. The other tests are given for reference and comparison with other studies. They are given in order of decreasing accuracy (Anderson-Darling, Lilliefors, Jarque-Bera).

See the Past manual for algorithmic details and references.

Example use of results for publication:

The distribution is significantly non-normal (Shapiro Wilk test, W=0.69, p<0.001).
The distribution is not significantly different from normal (Anderson-Darling test, A=0.44, Monte Carlo p=0.18).

Published Aug. 31, 2020 9:09 PM - Last modified Aug. 31, 2020 9:09 PM