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Is it 'normal' to have two Pearson correlation coefficients which are statistically significant on their own but not when compared with each other.

Example

  • r=.9083 (n=45) for females who buy ice-cream and yoghurt
  • r=.8382 (n=60) for males who buy ice-crean and yoghurt

(The above correlation is between buying ice-cream and buying yoghurt for the two groups)

Based on the above, my interpretation is that both males and females who buy more ice-cream also tend to buy more yoghurt but there is no difference whether one group buys more or less than the other group.

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    $\begingroup$ I notice this is the latest in a long list of questions that use correlation coefficients to assess relationships. Using correlation coefficients in this way is at best a weak approach and at worst it is wrong and misleading. Have you considered using more conventional analyses? $\endgroup$ – whuber Sep 15 '11 at 16:28
  • $\begingroup$ @whuber Thanks. Could you point me to some methods. I don't have a statistical background, so I am going for the simplest approach (which may not be appropriate, as you point out). $\endgroup$ – Adhesh Josh Sep 15 '11 at 20:25
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    $\begingroup$ After all these questions, I still don't know, because I haven't been able to figure out what your data look like (you have referred to them elsewhere as "responses," but that's too vague) or what your objectives are. Why don't you open a new question where you briefly describe your project, your data, and what you want to learn, and then ask (a) what an analysis of Pearson correlations could accomplish and (b) what some simple, effective approaches might be. $\endgroup$ – whuber Sep 15 '11 at 20:48
  • $\begingroup$ @whuber I will do this! $\endgroup$ – Adhesh Josh Sep 16 '11 at 4:11
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I assume the test you do when compared to each other is indeed such a thing: it is a test whether the correlations differ between the two groups.

As such, imagine comparing a group where there is a strong correlation, with itself: hopefully, a test for correlation will show a significant result for 'both' groups, but when you compare them and you get a significant difference according to some test, there is something seriously wrong.

So: indeed, it is very normal to find significant correlations but insignificant differences between them.

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The answer to your question is "Yes, why not?" @Nick answered this for you.

The first part of your interpretation is correct. The second part is not correct. You have no indication, from the above, of how much ice cream or yogurt men and women buy. The strong correlations could be over different ranges.

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  • $\begingroup$ Thanks. How do I interpret the second part. Any pointers? $\endgroup$ – Adhesh Josh Sep 15 '11 at 20:28
  • $\begingroup$ If you want to know about how much ice cream men and women bought, you have to look at how much ice cream men and women bought. Means, standard deviations, medians, t-tests and so on. $\endgroup$ – Peter Flom Sep 15 '11 at 23:34

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