Hi.
In my correlation data, sample (A)'s correlation coefficient is r = 0.7160 and the p-value is p = 0.0458 (*) (n=8), when analyzed by Pearson's correlation test. On the other hand, sample (B)'s correlation coefficient is r = 0.7500 and the p-value is p = 0.0663 (n.s.) (n=7), when analyzed by Spearman's correlation test, due to normality rejection.
This made me wonder how the sample (B)'s correlation is less significant than that of (A) when the coefficient 'r' of (B) is larger than that of (A).
What is the criteria of determining significance by p-values in Pearson's and Spearman's test, respectively? How are the p-values in the correlation tests related to the correlation coefficient 'r'?
Thanks.
Sung-Jun Lee Because the n-size of sample 1 (n = 8) is larger than sample 2 (n = 7). The statistical significance (p-value) of Pearson correlation is based on both the correlation coefficient and degrees of freedom (n - 2).
The correlation test for sample 1 is based on df = 6. The correlation test for sample 2 is based on df = 5. This means the correlation needs to be stronger in the second test in order to be statistically significant.
If you're conducting a two-tailed test the critical value for correlation test 1 is r = .707. The critical value for correlation test 2 is r = .754.
Apart from the fact that the p-value is a function of the sample size (and the sample sizes are not equal) - as Blaine noted above, you are comparing apples with peaches. Pearson'r measures the linear association using the quantitative information, Spearman's rho measures the monotone association using the rank-order information. These are different statistics with a different meaning. You should not compare their values.
Simple correct answer: there is no association between r and p values, since the former measures association, the latter significance, two different things. Except, for there to be a significant correlation, you require high r AND low p values :)
While correlation indicates the association between variables, p-values explain if the association is statistically significant or not. Usually a p
The correlation coefficient ‘r’ is a measure of the strength and direction of the linear relationship between two variables. The p-value is used to determine whether the correlation coefficient is statistically significant. The p-value is the probability of observing a correlation coefficient as extreme as the one calculated from the sample data if there were no correlation between the two variables in the population1.
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