I have a correlation of 0.777 but only a p-value of 0.069 (not significant) on my Pearson's test. My sample size was of 54. Should my hypothesis still be rejected even if there is a correlation? Is the non-significant p-value due to sample size? What can I say about the hypothesis in this case?
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1I think something's wrong with the p-value calculation. For a sample size of 50 an r of 0.27 should be a p-value of about 0.05. – Sal Mangiafico Mar 15 '23 at 15:36
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See, real-statistics.com/statistics-tables/pearsons-correlation-table/. Just approximately, for df = 52, r = 0.77, I get t = 8.8, p = 8e-12. – Sal Mangiafico Mar 15 '23 at 15:40
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1I apologise, I have made a mistake in my question. My sample size was of 6. – broccolops Mar 15 '23 at 16:05
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1Then, yes, with a sample size of 6, I think you would need an r of, say, 0.82 to get a p-value less than 0.05. – Sal Mangiafico Mar 15 '23 at 16:35
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2@broccolops in statistics, this is what we call a "game changer". – AdamO Mar 15 '23 at 17:07
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1It sounds like you might like to read the answers at https://stats.stackexchange.com/questions/31 concerning what p-values mean and how to interpret them. – whuber Mar 15 '23 at 17:08
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I'm sure this question is covered elsewhere on this site. But basically, for Pearson correlation, there is a relationship between sample size, the correlation coefficient, and the resultant p-value.
This relationship can be seen on tables like this one: real-statistics.com/statistics-tables/pearsons-correlation-table/, or can be found in many analysis of experiments textbooks.
For a given r value, the p-value becomes smaller as the sample size increases. This is basically a feature of how we do hypothesis testing.
Practically speaking, getting a relatively large r value with a small sample size is suggestive. Likely, there is a real correlation, but we have limited evidence against the possibility that this apparent correlation occurred simply by chance. Likewise, a p-value less than 0.10 is suggestive, but certainly not dispositive.
Sal Mangiafico
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1+1. Worth considering is that, with such a lack of precision in the estimate, there is a real chance that the true correlation is less than zero, despite the empirical correlation of $0.777$. – Dave Mar 15 '23 at 16:50
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When you do a significance test, you reject, or you fail to reject, the null hypothesis based on the p-value from the significance test.
Your p-value is not significant, therefore you fail to reject the null hypothesis. You have not found evidence that the null hypothesis is false.
You ask "Do I still reject the whole hypothesis?" No. You do not reject any hypotheses because of a non-significant test.
Jeremy Miles
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