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The chi-square goodness of fit test can easily be confused with other tests. Here are some distinctions to avoid any confusion.

Relationship to the chi-square analysis of contingency tables

Note that the chi-square test is used in two quite different contexts.

One use is to compare the observed distribution with an expected distribution generated by theory.

Another use is to analyze a contingency table. In this analysis, the expected values are computed from the data, and not from an external theory.

Relationship to normality tests

Normality tests compare the observed distribution of a continuous variable, with a theoretical distribution generated by the Gaussian distribution. Prism offers three ways to do this comparison, all offered as part of the Column statistics analysis.

Relationship to the Kolmogorov-Smirnov test

The Kolmogorov-Smirnov test can be used as a nonparametric method to compare two groups of continuous data. It compares the two observed cumulative frequency distributions, and does not compare either observed distribution to an expected distribution.

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