Can a weak Spearman's rank-correlation also indicate that 2 sets of values are different? I was wondering, if there is no correlation between 2 sets of values, like 2 sets of test scores from the same sample (pretest/post-test), then can you say that the 2 sets of values are also different?
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$\begingroup$ I'm not sure I follow your question. Can you clarify? Can you post some example data? $\endgroup$– gung - Reinstate MonicaCommented Dec 8, 2016 at 12:52
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$\begingroup$ I was wondering, if there is no correlation between 2 sets of values, like 2 sets of test scores from the same sample, then can you say that the 2 sets of values are also different? $\endgroup$– KokoCommented Dec 8, 2016 at 13:00
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1$\begingroup$ how do you define difference? With low correlation you could assume that the variables might be linear independent - but more ? $\endgroup$– DreyCommented Dec 8, 2016 at 13:20
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$\begingroup$ Could you explain what "weak" means and describe what kinds of differences you are looking for? $\endgroup$– whuber ♦Commented Dec 8, 2016 at 21:46
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Generally, no. Here's an example: Consider the following numbers. They are the pre-test scores for 12 candidates, and their post-test scores.
500, 499, 498, 497, 496, 495, 494, 493, 492, 400, 300, 200
500, 501, 502, 503, 504, 505, 506, 507, 508, 400, 300, 200
Clearly, the numbers pre-test and post-test are virtually the same - both overall and for each candidate. However, their ordering has changed dramatically: the p-value is now 61% two-tailed (i.e. no correlation).
But I think your question is kinda ill-posed. What do you mean by 'different'? If you mean you want to determine if two sets of samples are different, you probably want to use something like the two-sample Kolmogorov-Smirnov test or the Wilcoxon rank test.
However, it is true that if you replaced the post-test data with random numbers, you would get a weak Spearman's Rank correlation.
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$\begingroup$ Thanks. What I mean by "different" is different as would be found if a t-test was done. We had this case where there were only 14 samples (7 per treatment group). A t-test was done which showed no difference between their test results after 1 group received tutorials and the other didn't. The test results were skewed with outliers upwards which we thought would affect the mean. Thus we said it would be better to do a Spearman's rho and if the correlation would be weak or close to zero, then it 's likely the scores are different (since they do not correlate). Sorry if I confused you more. $\endgroup$– KokoCommented Dec 8, 2016 at 14:05
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1$\begingroup$ I agree that you have to define what you mean by "different". I wouldn't use correlation to compare pre and post-test scores. You could use a paired t-test. $\endgroup$– BryanCommented Dec 8, 2016 at 14:10