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In my class I have groups of students making presentations and the rest of the class evaluates them. Since their scores are curved the students do have an incentive to collude and mark other teams down.

My hunch is that there is no collusion and if there were I would see it obviously. A histogram comparing the scores in this class to another section of the same class shows no obvious skews. I would like to prove that collusion was highly unlikely to have taken place.

To do so, I think, all I need to show is that if there were any collusion then the standard deviation of the victims' scores would be (statistically) significantly lower than the other groups' or that of the class. (The class size is 56 and each group has 7 students.)

I test this with the Levene´s test but I have to reject the null that all variances are the same. However, this doesn't mean that there was collusion. It only suggests that some groups were easier to judge than others.

So I then do the test to compare the standard deviation of each group to the average standard deviation across the groups in the class. Thinking about an "average standard deviation" raises alarm bells that my thought process is flawed and decide to come to this forum.

  1. Is my thinking right? if yes what should I compare against to show that no group had a significantly lower standard deviation, Or that the distribution of standard deviations is no different from the other section?

  2. Is there a better way to rule out systematic collusion.

kjetil b halvorsen
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K R
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  • If you are comparing variances you can use an $F$-test. – user2974951 Oct 25 '18 at 08:15
  • Thanks! I think it is more than just comparing two variances. What I want to do is compare a distribution of variances among the 8 groups of one section to the distribution of variances to another class with its own 8 groups....Unless there is a better way to prove that there was no collusion. – K R Oct 29 '18 at 11:31
  • update: this is the answer that led me to Levene's test rather than an F test in the first place https://stats.stackexchange.com/questions/24022/why-levene-test-of-equality-of-variances-rather-than-f-ratio/24024#24024 – K R Oct 29 '18 at 11:44

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