Tests for Normal distribution

Tests available in MedCalc

MedCalc offers 3 tests for Normal distribution:

The D'Agostino-Pearson test (Sheskin, 2011) (recommended) computes a single P-value for the combination of the coefficients of Skewness and Kurtosis.
Kolmogorov-Smirnov test (Neter et al., 1988) is based on the greatest discrepancy between the sample cumulative distribution and the Normal cumulative distribution.
The chi-square goodness-of-fit test is applied to binned data (the data are put into classes) (Snedecor & Cochran, 1989) and requires a larger sample size than the other two tests.

The result of this test is expressed as 'accept Normality' or 'reject Normality', with P value.

If P is higher than 0.05, it may be assumed that the data have a Normal distribution and the conclusion ‘accept Normality’ is displayed.
If P is less than 0.05, then the hypothesis that the distribution of the observations in the sample is Normal, should be rejected, and the conclusion ‘reject Normality’ is displayed. In the latter case, the sample cannot accurately be described by arithmetic mean and standard deviation, and such samples should not be submitted to any parametrical statistical test or procedure, such as e.g. a t-test. To test the possible difference between not Normally distributed samples, the Wilcoxon test should be used, and correlation can be estimated by means of rank correlation.
When the sample size is small, it may not be possible to perform the selected test and an appropriate message will appear. In this case you can visually evaluate the symmetry and peakedness of the distribution using the Histogram, Cumulative frequency distribution, or Box-and-whisker plot.

Neter, Wasserman, Whitmore (1988) Applied statistics. 3rd ed. Boston: Allyn and Bacon, Inc.
Sheskin DJ (2011) Handbook of parametric and nonparametric statistical procedures. 5th ed. Boca Raton: Chapman & Hall /CRC.
Snedecor GW, Cochran WG (1989) Statistical methods, 8th edition. Ames, Iowa: Iowa State University Press.