# Documentation

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## Perform Kolmogorov-Smirnov Test

MATLAB live scripts support most MuPAD functionality, though there are some differences. For more information, see Convert MuPAD Notebooks to MATLAB Live Scripts.

For the Kolmogorov-Smirnov goodness-of-fit test, MuPAD® provides the `stats::ksGOFT` function. This function enables you to test the data against any cumulative distribution available in the MuPAD Statistics library. The Kolmogorov-Smirnov test returns two p-values. The null hypothesis passes the test only if both values are larger than the significance level. For example, create the following data sequence `x` which contains a thousand entries:

```f := stats::normalRandom(1, 1/3): x := f() \$ k = 1..1000:```

Use the function `stats::ksGOFT` to test whether the sequence `x` has a normal distribution with the mean 1 and the variance 1/3. Suppose, you apply the typical significance level 0.05. Since both p-values are larger than the significance level, the sequence passes the test:

`stats::ksGOFT(x, CDF = stats::normalCDF(1, 1/3))`

Test the same sequence, but this time compare it to the normal distribution with the variance 1. Both p-values are much smaller than the significance level. The null hypothesis states that the sequence `x` has a normal distribution with the mean 1 and the variance 1. This hypothesis must be rejected:

`stats::ksGOFT(x, CDF = stats::normalCDF(1, 1))`