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.
For the Kolmogorov-Smirnov test, the mean and variance of the
hypothesized 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.
Guidance:
Ways to detect before performing the
normality test whether your data violate any assumptions.
Ways to examine normality test
results to detect assumption violations.
Possible alternatives if your data or
normality test results indicate assumption violations.
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.
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