A conventional cross-tabulation is a two by two table that subsets your counts in two categories (for both the rows and columns). You can use a cross-tabulation for calculating the odds ratio, risk ratio, prevalence, sensitivity, specificity, and other statistics that involve counts. You could generate a Chi-Square or Fisher’s Exact test because the cross-tabulation contains your observed data. The whole point of running a hypothesis using a cross-tabulation is to evaluate the difference between your observed data and the null hypothesis. Usually, your null hypothesis will contain your expected frequencies. So there is the cross-tab that you generate from your observed data. Then you have the cross-tab that you generate from your null hypothesis.
Some people try to make a cross-tab from variables that contain more than two categories.So the variables are re-structured because they realize more than two categories were not needed in the first place. The whole point of a cross-tabs is to analyze the people who had the disease or event under study. The people who did not have the event are only included for a comparison. And actually any frequency must take into account the healthy population for contrast.
And of course there is the idea of the central limit theorem for count data. In terms of a cross-tab, if the cells have at least 5 entities you can apply it to the normal distribution.
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