One-Sample Kolmogorov-Smirnov Test
The One-Sample 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. Many parametric tests require normally distributed variables. The one-sample Kolmogorov-Smirnov test can be used to test that a variable (for example, income) is normally distributed.
Statistics. Mean, standard deviation, minimum, maximum, number of nonmissing cases, and quartiles.
One-Sample Kolmogorov-Smirnov Test Data Considerations
Data. Use quantitative variables (interval or ratio level of measurement).
Assumptions. 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 normal 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. The power of the test to detect departures from the hypothesized distribution may be seriously diminished. For testing against a normal distribution with estimated parameters, consider the adjusted K-S Lilliefors test (available in the Explore procedure).
To Obtain a One-Sample Kolmogorov-Smirnov Test
This feature requires the Statistics Base option.
- From the menus choose:
- Select one or more numeric test variables. Each variable produces a separate test.
- Optionally, click Options for descriptive statistics, quartiles, and control of the treatment of missing data.
This procedure pastes NPAR TESTS command syntax.