How to perform a Kolmogorov-Smirnov test?

To perform a Kolmogorov-Smirnov test, calculate the test statistic and compare it to the critical value.

The Kolmogorov-Smirnov test is used to determine if a sample comes from a specific distribution. To perform the test, first, state the null hypothesis that the sample comes from the specified distribution. Then, calculate the test statistic, which is the maximum difference between the empirical distribution function of the sample and the cumulative distribution function of the specified distribution.

To calculate the test statistic, first, order the sample data from smallest to largest. Then, calculate the empirical distribution function (EDF) by dividing the number of observations less than or equal to each data point by the total number of observations. Next, calculate the cumulative distribution function (CDF) of the specified distribution. Finally, find the maximum difference between the EDF and CDF.

Once the test statistic is calculated, compare it to the critical value from the Kolmogorov-Smirnov table. If the test statistic is greater than the critical value, reject the null hypothesis and conclude that the sample does not come from the specified distribution. If the test statistic is less than or equal to the critical value, fail to reject the null hypothesis and conclude that there is not enough evidence to suggest that the sample does not come from the specified distribution.

In summary, to perform a Kolmogorov-Smirnov test, state the null hypothesis, calculate the test statistic, and compare it to the critical value.