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Generally, the sign test is used to test the hypothesis that the difference median is zero between two continuous distributions (Sign test).

I am trying to understand whether it can be adapted to prove that the values from one distribution are generally lower than the other. Or are there better tests which can be designed for this purpose?

Data available: Suppose that I have the average GMAT scores from 50 universities. There are 2 averages per university, the first one being the average of those candidates who have studied mathematics at a graduate level while the second one is for those who have not.

A simple plot shows that students who have studied math score higher. However, I would like to prove this fact statistically using a test (and a p-value?). Conversely, I may also like to prove in another case that there is no difference.

Plot of average scores by universities separated by Math NoMath

Mozan Sykol
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  • Do you have the raw data that went into the averages? – Peter Flom Jan 20 '14 at 17:00
  • @PeterFlom Created a temporary version which should follow similar trends - http://pastebin.com/xzcKwRsA – Mozan Sykol Jan 20 '14 at 19:17
  • If you have the raw data, you can use a regression model. – Peter Flom Jan 20 '14 at 19:25
  • @PeterFlom Pardon my ignorance, but even if I build a linear regression model thus getting one as a function of the other, how do I prove that generally one series is "lesser" than the other? Just using the magnitude of the slope? – Mozan Sykol Jan 20 '14 at 19:35
  • What exactly do you want to prove? You can do quantile regression about many quantiles, if you want. – Peter Flom Jan 20 '14 at 19:37
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    What is the population about which you wish to make inferences? (It looks to me like you might even already have the population rather than a sample from it, but it depends on the type of statement you wish to make) – Glen_b Jan 20 '14 at 21:02
  • @PeterFlom I am trying to disprove the assertion: Students who have not studied math score as well or better in GMAT as compared to those who have. I am guessing this statement can be framed as a null hypothesis, and a p-value obtained. Please note that we cannot assume that the two distributions are normal. – Mozan Sykol Jan 21 '14 at 03:28

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