Rank-biserial correlation

[Manar Serageldin]

Hello,
I have an independent binary variable & a dependent ordinal variable. I want to test the correlation between them & found that rank-biserial correlation coefficient will be the most suitable. I can't find it in STATA. Can anyone please tell me how to perform rank-biserial correlation test in STATA version 14.
Thank you.

[Leonardo Guizzetti]

This correlation is a special case of Spearman's rank correlation (which is Pearson's correlation computed over the ranks and average ranks of your two variables). It assumes you have a binary variable (call this x) and an at least an ordinal variable (call this y). Then you may compute the rank-biserial correlation as either:

egen y_rank = rank(y)
corr x y_rank
spearman x y

[Mike Lacy]

In my view, ranks are not the most conceptually "nice" way to think about most ordinal variables, which commonly only have a few categories. I'd instead suggest using an explicitly ordinal measure, with Somers' D (-ssc describe somersd-) being my preferred choice here. In the current case, the rank-biserial correlation gives the same result as Somers' D, but I think the theoretical foundation of Somers' D, as well as some of the options offered by the -somersd- community-contributed program, are advantageous. (See Newson, R. 2008. Identity of Somers’ D and the rank biserial correlation coefficient.
http://www.imperial.ac.uk/nhli/r.new...s/ranksum1.pdf)

[Manar Serageldin]

Leonardo Guizzetti
Thank you for your reply.
I tried it but I'm confused which correlation coefficient value should I use ?

[Manar Serageldin]

Mike Lacy

Thank you for your reply.
I think I should have both the dependent and independent variables as ordinal variables to perform Somer's D?

[Leonardo Guizzetti]

They are the equivalent, so use whichever you prefer.

[Mike Lacy]

Re #5: All binary variables are ordinal (e.g., if coded 0/1, individuals in category 1 have "more" of category 1 than they do of category 0.)

[Manar Serageldin]

Mike Lacy
Re #7: I tried to perform Somer's D test but I couldn't because it needs STATA version 16 and I'm working with version 14.2.
Would you please explain to me how to perform rank-biserial correlation as an alternative?
Thank you.

[Mike Lacy]

Something is strange here. I started my old copy of Stata version 14.2, and -somersd- works fine for me. Further, the Stata version specification in -somersd- is version 9, at least for the most up to date version of -somersd-, which is 23 April 2006.

What did you experience or see that leads you to believe that -somersd- requires version 16? Try the following and post back here what you find:

which somersd
sysuse auto
somersd foreign rep78

[Rich Goldstein]

. which somersd
/Users/rich/Library/Application Support/Stata/ado/plus/s/somersd.ado
*! Author: Roger Newson
*! Date: 15 April 2020

[Mike Lacy]

Good find by Rich. I wondered if there might be some newer version I wasn't finding.

[Rich Goldstein]

I believe that the problem is that there are versions at each of SSC and SJ; ideally, they would be the same, but ...

[Manar Serageldin]

RE #9: Here is what I get

. which somersd
c:\ado\plus\s\somersd.ado
*! Author: Roger Newson
*! Date: 15 April 2020

.
. sysuse auto
(1978 Automobile Data)

.
. somersd foreign rep78
this is version 14.2 of Stata; it cannot run version 16.0 programs
You can purchase the latest version of Stata by visiting http://www.stata.com.
(error occurred while loading somersd.ado)

[Rich Goldstein]

I don't recall when the -esize- command was added (and I'm too lazy to look it up right now), but it only requires version 13 so if you have it you can use it; see

h esize

the "pbcorr" option is the relevant one

if that doesn't work for you, you might try sending an email to Roger Newson (author of -somersd-) to see if there is a version still available that will run on your version of Stata

or, you can use -findit somersd- to find the SJ version and install that (you might need to uninstall the SSC version first)