Goodness-of-Fit Test Analysis Object (Statistics Option)
You can use this analysis object to perform goodness-of-fit tests for samples from normally or exponentially distributed populations.
With the goodness-of-fit tests, you can check whether the independent observations present in a sample originate from a normally or exponentially distributed population. The analysis object offers you two different tests:
Description |
Procedure |
|---|---|
Chi-square Test |
A count is performed for the sample and compared with the expected distribution. Since the result depends on the number of classes, the test should be performed with different numbers of classes where appropriate. |
Kolmogorov-Smirnov Test |
The empirical density function of the sample is determined first and then the largest difference between this density and the density function of the distribution is formed for the test. This difference is compared to a critical value. The test is especially suited for small samples and reacts well to outliers. You can either directly specify the distribution parameters with which you would like to test your samples or have these estimated from the sample. |
The object uses the functions ChiSquareTest and KolmogorovSmirnovTest.
The class limits for the Chi-square test are set in such a way that if the exact distribution to be tested is present, then the classes are all equally occupied. You must select the number of classes in such a way that at least 5 values are allotted to at least 20% of the classes, and at least one value is allotted to all of the classes. If this is not the case, then no result can be determined.
The result can adopt the following values:
Value |
Interpretation |
|---|---|
0 |
The hypothesis was rejected, i.e. the sample does not originate from a population with the distribution specified. |
1 |
The hypothesis was accepted, i.e. the sample originates from a population with the distribution specified. |
2 |
No result could be determined (see above). |
References
Hartung, Joachim (1993). Statistik (Statistics), 9th Edition. Oldenbourg Verlag GmbH, Munich. ISBN 3-486-22055-1. Starting on pages 182 and 216.