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I want to make sure I am choosing the right statistical test. I am working with 7 semesters of exams scores for a particular course. Each semester the course ran with many sections. However, the students, no matter what section they were in, no matter which teacher, were given the same exams.

Let A = exam 1 and 2 average (two exams were given within the semester and they were averaged) Let B = final exam score (the course ends with a final)

Overall for each semester, I want to compare A with B to see if a significant difference is found. Which non-parametric test should I use? What should my level of significance be? Which test should I use to see if there is a correlation between A and B for each of the semesters?

I tested semester 1 (A & B) through semester 7 (A & B) and found that the data sets for all is not normal. I used the Shapiro-Wilk test (all p<.01).

Note: Just to clarify,... ** A is the average of exams 1 and 2 area given within the semester before the final exam The final exam score equals B. ** The data sets are not normally distributed as per the Shapiro-Wilk test for normality as well as histogram, box plots. ** Overall I wish to compare the averages to see differences if there are any.

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  • $\begingroup$ The average for A doesn't include the final right? These are two exams given before the final? I'd edit that into your question to clarify. $\endgroup$
    – Shawn Hemelstrand
    Commented Apr 6, 2023 at 1:41
  • $\begingroup$ "found that the data sets for all is not normal. I used the Shapiro Wilks test (all p<.01)." ... is not necessarily consequential. Original distributions are rarely (almost never) actually normal. In this case a test is pointless, since its obviously not normal without even seeing data, and in any case answers the wrong question. The question you should worry about is not whether the parent distribution is normal (no), but whether the resulting significance levels are close enough to what you choose them to be for your purposes ... $\endgroup$
    – Glen_b
    Commented Apr 6, 2023 at 2:02
  • $\begingroup$ ... (and you might also consider whether the power will still be reasonable). As George Box put it "Remember that all models are wrong; the practical question is how wrong do they have to be to not be useful." $\endgroup$
    – Glen_b
    Commented Apr 6, 2023 at 2:02
  • $\begingroup$ do you want to compare if the average of A is different than the average of B? because that's what "I want to compare A to B to see if there is a significant difference is found." would mean, but i am not sure if that's a meaningful research question. Can you elaborate? $\endgroup$
    – rep_ho
    Commented Apr 6, 2023 at 9:33
  • $\begingroup$ Thank you! revised my question to answer your responses. $\endgroup$
    – Tonya
    Commented Apr 6, 2023 at 13:18

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