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I've been analysing data between cliff height and average erosion rate. The data is parametric so I used Pearson's correlation and found that I got a coefficient of 0.017. When I applied a 2-tailed t-test to the data I found that I had a t value of 28.22 with 128 degrees of freedom. The t-test is saying the data is significant when the correlation result is saying it is not

Any ideas?

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    $\begingroup$ What defines your two groups for the t test? Can you post the data? Note that data are not "parametric" or "nonparametric"; at best those are terms that describe methods. (FWIW, I have a persona as geomorphologist.) $\endgroup$
    – Nick Cox
    May 26, 2015 at 14:05
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    $\begingroup$ The t test is comparing two means; the correlation is quantifying linearity of relationship. They are asking different questions and there is no reason for the answers to be the same. $\endgroup$
    – Nick Cox
    May 26, 2015 at 14:07
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    $\begingroup$ What does it mean "the data is significant"? $\endgroup$ May 26, 2015 at 14:08

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The correlation coefficient appears to be what you're interested in here. If you entered these two measure types (height and erosion rate for each cliff) as two groups for a t-test, you'd almost certainly get a highly significant difference-- but all that means is that height measurements tend to be in a different range of numerical values from erosion rate measurements. That's an obvious, uninteresting result, and not the question you mean to ask.

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  • $\begingroup$ If that guess is right -- noting that the OP has apparently abandoned the question -- then your comments understate the main point, which is that such a t test is totally inappropriate. Means of variables with different units of measurement (indeed, worse, different dimensions) are not comparable, period. $\endgroup$
    – Nick Cox
    May 29, 2015 at 22:35
  • $\begingroup$ Right - this wasn't clear enough, but I suppose my point is that the result of conducting the wrong statistical test will often still mean something, and the absurdity of what the result really means can be instructive. (Congratulations, your paired-samples t test found that a person's height in meters tends to differ from his weight in kilograms!) $\endgroup$ May 29, 2015 at 22:40

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