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The exercise is about testing if there is a correlation between the town the student comes from and the score at a certain competitive exam. For each town in a set of five $A,B,C,D,E$ one is provided the means and the standard deviation of the scores of the inhabitants of the town, and no other data is given.

I browsed wikipedia on tests but could not find the test I was looking for. The nearest I could find was Pearson’s $\chi^2$ test, but this one needs more data.

Any help appreciated.

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  • $\begingroup$ What do you mean by "mean"? Isn't it just a single number for each town? E.g. 123 students from A-Town were admitted. $\endgroup$ – Hans Engler Mar 28 '13 at 14:29
  • $\begingroup$ @HansEngler : I misstated the problem, hopefully the question is clearer now after my edit. $\endgroup$ – Omar Ibrahim Mar 28 '13 at 14:41
  • $\begingroup$ Have you tried making a scatterplot of the data with the town on your $x$ axis and mean on your $y$ axis? See if there is any obvious correlation and you can run a general regression test. $\endgroup$ – Alti Mar 28 '13 at 14:46
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    $\begingroup$ @Alti Your suggestion looks doubtful to me, for two reasons : 1) there is no “natural” numbering of the towns. 2) This uses only the means and not the deviations. $\endgroup$ – Omar Ibrahim Mar 28 '13 at 14:59
  • $\begingroup$ You're right, I didn't take into account the standard deviation. $\endgroup$ – Alti Mar 28 '13 at 15:20
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I think what you are looking for is an anova, i.e. Analysis of Variance (An extension of the t-test for multiple groups).

The ANOVA test basically tells you if the groups have the same mean (which then leads into more elaborate schemes to determine which groups have higher means than the others - Fishers Least Significant Difference, among others).

Source: classes in experimental design, An Introduction to Statistical Methods and Data Analysis, Longnecker, Ott, p. 463

"Correlation" is explicitly asked for here but I dont think it is appropriate to use R-square correlation coefficient to address this problem as Omar already noted that towns have no hierarchy. I think the "correlation" they are looking for is whether there is any sort of relationship, ergo ANOVA.

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