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I have a group A (about 100 people) that took a pretest and post test and were scored as the question correct or not correct. I also have separate group B (about 150 people) that did a post test and pretest and were scored as correct and not correct.

Group A went from 30% correct to 50% correct. Group B went from 20% correct to 17% correct. What statistical test can I do that shows that Group A was a better treatment than group B.

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You'll want to use a paired test of proportions.

Run the test separately for Group A and for Group B. The paired test takes into account that the data are from the same person (not independent). Since you are looking at correct versus incorrect, we'll use a proportion (versus a paired test of means).

Here is a link to a chapter discussing the topic.

If you look at this page from MedCalc you'll see a 2 x 2 table which in your case would be pre-test and post-test, and one table for group A and one table for group B.

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