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I have demographic data for a specific group of students. I then have the demographic data for a subset of these students who have failed their courses. How to I test whether or not particular demographics are under-represented/over represented in the failed group?

Melissa
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I would suggest taking a look at What is the relationship between a chi squared test and test of equal proportions?.

I'm assuming here that your demographic data is categorical - for example, race or gender.

If you had the following data, for example:

       Pass Fail
    M    10   90
    F    90   10

This contingency table counts the number of students that fall into each situation; e.x. 10 male students passed.

The test I would suggest in this case is a chi-squared test; in this test you would attempt to determine if the difference in proportions between the two groups is statistically significant / if the two groups' proportions are statistically significant. This test can be done on any number of groups; so it'd be also useful for other demographic data as long as you're still looking at pass/fail rates)

Kontorus
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