I'm stuck trying to figure out how to compare Spearman's correlations for dependent samples.
I have an n of 57, and I want to compare two dependent Spearman's correlations with one variable in common. I use SPSS.
I can find a lot of info on how to compare Spearman's correlations in independent samples (eg SPSS support page https://www.ibm.com/support/pages/differences-between-correlations) but nothing on how to do this between dependent correlations.
I've found this web utility (http://quantpsy.org/corrtest/corrtest2.htm) for calculation for the test of the difference between two dependent correlations with one variable in common, which uses Fisher's z-scores. First, each correlation coefficient is converted into a z-score using Fisher's r-to-z transformation. Then, they use Steiger's (1980) Equations 3 and 10 to compute the asymptotic covariance of the estimates. These quantities are used in an asymptotic z-test.
It doesn't specify whether it's appropriate to use for Spearman's or Pearson's correlations, and as it seems using Fisher's z-scores is appropriate for comparing independent Spearman's correlations, and the tool doesn't specifically say it's for Pearson's correlations, I'm wondering if this method is appropriate for what I'm trying to do.
Any help or advice would be much appreciated!
Let's think about this for a minute. How can two different correlations (I assume you mean coefficients) be dependant? I eagerly await your reply. David Booth
Hello Jess,
I have prepared a guide using SPSS to carry out Spearman's correlations for dependent samples.
I do not know about your dependant variables, therefore, imagine you are interested to identify whether those who do better in Mathematics also do better in Physics. Follow the screenshots herewith attached. Let me know if you have anything to clarify further.
Cheers.
I explain briefly the difference between dependent (overlapping or non-overlapping) correlations in this blog post:
https://seriousstats.wordpress.com/2012/02/05/comparing-correlations/
In essence correlations can overlap if they share a variable e.g., AB overlaps with BC because B is common to both or because samples are correlated. e.g., AB is computed in mothers (AB) and in their children (ab). The AB correlation in the mothers and ab correlation in the children is not independent even though A != a and B != b.
At the bottom of the blog I refers to the nonparametric and robust approach that Wilcox developed. That seems like the most principled way to do this. There are links to the R functions for this (as well as my R functions based on Zou's approach).
The robust and nonparametric approaches use bootstrapping and are therefore not trivial to set up. The performance of approaches for Pearson's r should be similar I'd guess - but it is well known that the simple Fisher z approach isn't the best approach for Spearman's rho when data are non-normal (often the reason for using rho).
This R code snippet gives functions for computing a CI for rho and a link to a paper explaining the problem.
To compare correlations between dependent samples with one variable in common, you could check out Lee and Preacher's (2013) web utility. Here it is fully cited.
Lee, I. A., & Preacher, K. J. (2013, September). Calculation for the test of the difference between two dependent correlations with one variable in common [Computer software]. http://quantpsy.org/corrtest/corrtest2.htm
Good luck,
Hello Jess S. Aitken. Syntax file #6 on the page given below has SPSS syntax for comparing two non-independent correlations with one variable in common:
https://sites.google.com/a/lakeheadu.ca/bweaver/Home/statistics/spss/my-spss-page/weaver_wuensch
NOTE that the method it implements was intended for comparing Pearson correlations. Having said that, a Spearman correlation is equivalent to a Pearson correlation computed on the ranks. So I think it is not too unreasonable to use it for comparing your Spearman correlations. (But I'd be happy to be educated if I'm wrong about that!)
HTH.
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