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I am teaching a programming course at the university where I am working. I would like to do a statistical test to see if students marks (exam grades) are significantly better compared to the previous semester (e.g., summer semester vs. winter semester).

There are three exams each semester, and the grades are scored from 1 (best mark) to 5 (fail). There are about 24 students that take the exam each time.

What is the right test to use, in order to assess that the marks from the summer semester are significantly better than those from winter semester, considering 3 exams per semester?

(I would like to run the test in R, so if someone happens to know how it's called in R that would be perfect. But I think I can find that out myself.)

Background: I would like to apply for a teaching award. Although marks are probably not a good test of teaching performance if the course design improved, I would like to provide the statistical results as a indication of the merit of my nomination along with the student feedback from the instructor evaluation questionnaire.

EDIT:
The students are different each semester (except possibly for those who fail multiple times). The instructor is different (I am the second instructor). The test is the same. Yes, the difference in the capabilities of the students is a potential confounding factor. I would like to run the test anyway and perhaps I can state that its the difference in the set of students in the classes is not a major factor affecting the difference in the distribution of sources and average scores.

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    $\begingroup$ Are the students different each semester? If so couldn't a difference in the capabilities of the students be a confounding factor? Are you comaring yourself with the same class given in the previous semester by a different professor. Please make it clear what you are comparing. $\endgroup$
    – Michael R. Chernick
    Commented Sep 8, 2012 at 3:55
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    $\begingroup$ I have made a considerable modification to your edit as well as to your original post. I did this because I am pretty sure that what I wrote more clearly expresses what you intended. But please look it over to make sure that I didn't misunderstand something. $\endgroup$
    – Michael R. Chernick
    Commented Sep 8, 2012 at 4:39

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If the marks 1 through 5 can be reasonably called interval-level, a t-test should be fine. (Interval level data means that the gap between 1 and 2 is the same as that between 2 and 3 and so on). In r this is t.test.

If the marks 1 through 5 can only be assumed to be ordinal, then some test of the median is probably going to be good. See this post and its many comments for some ideas on this.

(Note, I added ordinal to your tags, as I suspect that these are only ordinal).

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  • $\begingroup$ Just to be sure, if I want to use for instance the "wilcox.test", I would treat all students from a semester (3 different exams) as one group? $\endgroup$
    – mrsteve
    Commented Sep 10, 2012 at 22:43
  • $\begingroup$ Yes, that's rightg\ $\endgroup$
    – Peter Flom
    Commented Sep 11, 2012 at 10:06
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I know this is not an answer to your statistics question, but you might find certainty based marking a useful criteria to employ. You'd probably get more detailed information than just the 1-5 grade. More data might mean a more informative statistical analysis. In particular, students giving a certainty score of 3 and being right could arguably be the result of good quality teaching that instills confidence as compared to students who may get the right answer but with lower certainty that they know they are right.

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