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Let’s talk about the Chi-Square. Before we start talking in STAT jargon – let’s discuss the contingency table. What is a contingency table? You know what I am talking about here. The square table that typically has two rows and two columns. There are numbers in each cell of that table.Those counts represent the number of times a particular row and column appear in your data. Do we really need to know how many counts there are? No not really. What we really want is the percentages for each cell. Why? Because the frequency counts are useful for the Chi-Square. the probabilities or frequencies  will be compared to our expected values to generate a Chi-Square test statistic. Specifically, the distance between our expected frequencies (calculated using our total row and columns) and our observed rates are of particular interest.

Now you don’t always need a Chi Square. Sometimes a Fisher exact is all you really want because the sample size is small. If one of the cells is less than 5 you want a Fisher’s Exact Test.

Another thing to note, your Chi Square or Fisher’s Exact is not going to tell you where the differences lie. Also please  make sure you run specific tests for ordinal outcomes. If you don’t account for the type of categorical variable you got- your interpretation will not be accurate. Mantel Haensel Chi Squares are typically constructed for ordinal data (with more than two categories).


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