Normal Distribution Tests
The Kolmogorov-Smirnov test, the Shapiro-Wilk test (for sample sizes up to 2000), Stephens' test (for sample sizes greater than 2000), D'Agostino's test for skewness, the Anscombe-Glynn test for kurtosis, and the D'Agostino-Pearson omnibus test can be used to test the null hypothesis that the population distribution from which the data sample is drawn is a Gaussian (normal) distribution.
- Within the sample, the values are independent, and identically distributed.
- For the Kolmogorov-Smirnov test, the mean and variance of the ypothesized normal distribution should be specified in advance. If the mean and/or the variance must be estimated from the data, the Kolmogorov-Smirnov test becomes conservative, and thus less likely to reject the null hypothesis. The other normality tests listed above do not assume a specified mean or variance for the hypothesized normal distribution.
To properly analyze and interpret results of normal distribution tests, you should be familiar with the following terms and concepts:
If you are not familiar with these terms and concepts, you are advised to consult with a statistician. Failure to understand and properly apply normal distribution tests may result in drawing erroneous conclusions from your data. Additionally, you may want to consult the following references:
- Conover, W. J. 1980. Practical Nonparametric Statistics. 2nd ed. New York: John Wiley & Sons.
- D'Agostino, R. B. and Stephens, M. A., eds. 1986. Goodness-of-fit Techniques. New York: Dekker.
- Daniel, Wayne W. 1978. Applied Nonparametric Statistics. Boston: Houghton Mifflin.
- Daniel, Wayne W. 1995. Biostatistics. 6th ed. New York: John Wiley & Sons.
- Rosner, Bernard. 1995. Fundamentals of Biostatistics. 4th ed. Belmont, California: Duxbury Press.
- Sokal, Robert R. and Rohlf, F. James. 1995. Biometry. 3rd. ed. New York: W. H. Freeman and Co.
- Zar, Jerrold H. 1996. Biostatistical Analysis. 3rd ed. Upper Saddle River, NJ: Prentice-Hall.