I have some variables (all metric), most of them normally distributed but two are definitely not (gamma distributed). I now would like to compute Spearman (or Kendall) coefficient for this correlations. For the others I´d like to compute Pearson-correlations.
Now my question. Are these coefficients directly comparable? And do you know of References to cite for this? Maybe there are some significant tests for comparing these. But I couldn´t find them so far.
I hope someone can help me with these.
Thank!
The fact that the variables are metric does not matter. They could be in scruples and pennyweights, or any other unit. The numbers will be processed in the same way for all cases.
I suspect that you don't have enough data to compare correlation coefficients. This is better done using simulation and random number generators. However, I suspect that this has already been done, though maybe not with your specific application. Something like this (at least for methods):
Asymptotic Properties of Pearson's Rank-Variate Correlation Coefficient under Contaminated Gaussian Model
By: Ma, Rubao; Xu, Weichao; Zhang, Yun; et al.
PLOS ONE Volume: 9 Issue: 11 Article Number: UNSP e112215 Published: NOV 13 2014
I think this would be fairly easy in R, if you already have some experience with the software.
The Pearson r and the Spearman rho are mathematically identical, as far as I know. The difference is whether you input raw scores or rank orders.
However, if I was planning on comparing correlations for an assortment of variables, I would definitely use the same correlation coefficient for every analysis. That said, you can always use the Spearman or Kendall method for interval-type data that's normally distributed, but as you imply, you should not use the Pearson method for badly skewed data. So just run rank-order analyses for everything. (When the data are really, truly normally distributed, the results will be nearly the same as for Pearson anyway.)
Comparing them is trickier. If it was Pearson correlations, I'd suggest the Williams t test, but I do not know whether that is appropriate if you're starting with rank-ordered data.
I found a master thesis that answer your question:
PEARSON’S VERSUS SPEARMAN’S AND KENDALL’S CORRELATION COEFFICIENTS FOR CONTINUOUS DATA
by
Nian Shong Chok
attached
Spearman's rank correlation coefficient is a measure of a monotone association that is used when the distribution of data makes Pearson's correlation coefficient undesirable or misleading.
Spearman's coefficient is not a measure of the linear relationship between two variables, as some "statisticians" declare.
It assesses how well an arbitrary monotonic function can describe a relationship between two variables, without making any assumptions about the frequency distribution of the variables.
Unlike Pearson's product-moment correlation coefficient, it does not require the assumption that the relationship between the variables is linear, nor does it require the variables to be measured on interval scales; it can be used for variables measured at the ordinal level.
https://en.m.wikipedia.org/wiki/Spearman%27s_rank_correlation_coefficient
https://en.m.wikipedia.org/wiki/Pearson_product-moment_correlation_coefficient
Article Comparison of Values of Pearson's and Spearman's Correlation...
Hello to all of you. Again thanks for your help!
Here is a paper that might interest you. Its about a appriximative calculation of pearsons correlation from Kendallls Tau and from Spearmans rho.
Cheers Jan
I think this also depends on what problem you are trying to solve. They aren't directly comparable -- an ordinal level variable is not the same as a continuous variable. However, if I were to see a Spearman rho of .76 between two ordinal variable and a Pearson r of .71 between to continuous variables, I would feel comfortable that the strength of the relationship is approximately equal. The magnitude and direction of the associations give me confidnce that they are -- a statistical test and p-value would not really seem very useful to me.
But, that also depends on your field of study. I'm in the social sciences, so the differences are more likely due to precision in our measurements. If you are working doing research on devices that are used to fly to Mars, then that is an entirely different problem.
Hello
Difference between Spearman rank correlation coefficient and Pearson correlation coefficient :
1)Spearman correlation coefficient is used to investigate nonlinear relationships, while Pearson correlation coefficient is used to investigate a linear relationship.
2)Spearman correlation coefficient calculation is simpler and requires fewer assumptions than Pearson's coefficient
3)Pearson's correlation coefficient is used to calculate the correlation of two relative variables, but Spearman's correlation coefficient ,shows the correlation between the two ordinal variables.
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