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With either test, you have a number of categories and for each you have an expected number of observations. The expected number is based either on the variable being independent of some other variable, or determined by some know (or hypothesised) distribution. You will also have a number of observations of the variable for each category. The test statistic is based on the observed and expected frequencies and has a chi-squared distribution.

The tests require the observations to come from independent, identically distributed variables.

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