One-sample Kolmogorov-Smirnov test
Compares the distribution of a variable with a normal, uniform, Poisson or exponential distribution.
Menu: Analyze → Nonparametric Tests → Legacy Dialogs → 1-Sample K-S…
When should I use it?
- Checking normality (with the Lilliefors correction because the mean and SD come from the data).
- Checking whether counts follow a Poisson distribution.
What are the assumptions?
- Continuous data for the normal, uniform and exponential tests.
How do I run it in StatLab?
- Choose the variable(s) and tick the distribution(s).
How do I read the output?
| Output | Meaning |
|---|---|
| Most Extreme Differences | Largest gaps between the sample and the theoretical cumulative distribution. |
| Test Statistic | The largest absolute gap (D). |
| Asymp. Sig. | For the normal test with estimated parameters this is Lilliefors-corrected; '.200*' is a lower bound. |
Worked example
On the practice survey dataset (File → Sample dataset), this command — which the dialog's Paste button also produces — runs the procedure:
PROC npKS1 /vars=(score age) /normal=YES /uniform=NO /poisson=NO /exponential=NO /exact=NO.
Output tables: One-Sample Kolmogorov-Smirnov Test · One-Sample Kolmogorov-Smirnov Test.
Computed by StatLab's validated procedure code when this page was built. The example only illustrates the steps; choose variables that fit your own research question.
What are common mistakes?
- Treating a non-significant result in a small sample as proof of normality.
- Relying on the uncorrected K-S p-value when the mean and SD were estimated.