User Guide

492
Chapter 34
One-Sample K
olmogorov-Smirnov Test
The One-Sam
ple Kolmogorov-Smirnov Test procedure compares the observed
cumulative distribution function for a variable with a specified theoretical distribution,
which may be normal, uniform, Poisson, or exponential. The Kolmogorov-Smirnov Z
is computed
from the largest difference (in absolute value) between the observed and
theoretical cumulative distribution functions. This goodness-of-fit test tests whether
the observations could reasonably have come from the specified distribution.
Example. M
any parametric tests require normally distributed variables. The
one-sample Kolmogorov-Smirnov test can be used to test that a variable, say income,
is normally distributed.
Statistic
s.
Mean, standard deviation, minimum, maximum, number of nonmissing
cases, and quartiles.
Data. Use quantitative variables (interval or ratio level of measurement).
Assumpti
ons.
The Kolmogorov-Smirnov test assumes that the parameters of the test
distribution are specified in advance. This procedure estimates the parameters from
the sample. The sample mean and sample standard deviation are the parameters
for a norm
al distribution, the sample minimum and maximum values define the
range of the uniform distribution, the sample mean is the parameter for the Poisson
distribution, and the sample mean is the parameter for the exponential distribution.