# PROPHET StatGuide: 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.

### Assumptions:

Within the sample, the values are
independent,
and identically distributed.

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.
- 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.

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##### Last modified: February 20, 1997

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