One-sample Kolmogorov-Smirnov Test

Advanced Statistics > Nonparametric Analysis > One Kolmogorov

Performs One-Sample Kolmogorov-Smirnov Goodness-of-Fit Test.

This procedure compares the distribution of a given sample to the hypothesized distribution defined by a specified cumulative distribution function. Like the chi-square goodness of fit test, the Kolmogorov-Smirnov one-sample test assesses the degree to which an observed pattern of categorical frequencies differs from the pattern that would be expected on the null hypothesis. The test statistic, designated D, is the maximum difference between the cumulative proportions of the two patterns.

An attractive feature of this test is that the distribution of the K-S test statistic itself does not depend on the underlying cumulative distribution function being tested. Another advantage is that it is an exact test


Applies to continuous distributions.

Tends to be more sensitive near the center of the distribution than at the tails.

The distribution must be fully specified.


Dialog box items

Variables: Choose the columns containing the variables to be included in the analysis. To select nonconsecutive columns, press and hold down CTRL, and then click each item. You can select many columns. Use the Ctrl key to select (or unselect) distant columns.


The display of outputs of VisualStat.



Use quantitative variables (interval or ratio level of measurement).



Distribution: Enter the hypothesized distribution.



Displays a histogram, a histogram with a normal curve, and a boxplot.

Choose to display a histogram for each variable

Histogram with Normal Curve:
Choose to display a histogram with a normal curve for each variable

Boxplot of data:
Choose to display a boxplot for each variable

Choose the options you want.

oExclude missing values: Check to excludes rows that have missing values.

oInverted Bar: Check to reverse the axes.



Confidence Level: Enter the level of confidence desired. Enter any number between 0 and 100. Entering 90 will result in a 90% confidence interval. The default is 95%.



1.Open the DataBook nonparam.vstz

2.Select the sheet ks1

3.Choose the tab Statistics, the group Nonparametric Tests and the command One Kolmogorov

4.In Variables, enter A

5.Click OK



Report window output


One-sample Kolmogorov-Smirnov Test


Kolmogorov-Smirnov test to compare the distribution of a given sample

alternative hypothesis: true cdf is not the Normal distribution with specified  parameters


    N     Mean  Std Deviation  Critical Value  alpha      ks  p-value  Alt Hypothesis

A  150  12.4336         3.2591          0.1097   0.05  0.0419   0.9510          Reject




See Also:


Web Resource: NIST e-Handbook of Statistical Methods, 2006

Getting Started: Numeric Formats