[R] correlation between categorical data

[Marc Schwartz]

On Jun 20, 2009, at 2:05 PM, Jason Morgan wrote:

> On 2009.06.19 14:04:59, Michael wrote:
>> Hi all,
>>
>> In a data-frame, I have two columns of data that are categorical.
>>
>> How do I form some sort of measure of correlation between these two  
>> columns?
>>
>> For numerical data, I just need to regress one to the other, or do
>> some pairs plot.
>>
>> But for categorical data, how do I find and/or visualize correlation
>> between the two columns of data?
>
> As Dylan mentioned, using crosstabs may be the easiest way. Also, a
> simple correlation between the two variables may be informative. If
> each variable is ordinal, you can use Kendall's tau-b (square table)
> or tau-c (rectangular table). The former you can calculate with ?cor
> (set method="kendall"), the latter you may have to hack something
> together yourself, there is code on the Internet to do this. If the
> data are nominal, then a simple chi-squared test (large-n) or Fisher's
> exact test (small-n) may be more appropriate. There are rules about
> which to use when one variable is ordinal and one is nominal, but I
> don't have my notes in front of me. Maybe someone else can provide
> more assistance (and correct me if I'm wrong :).



I would be cautious in recommending the Fisher Exact Test based upon  
small samples sizes, as the FET has been shown to be overly  
conservative. This also applies to the use of the continuity  
correction for the chi-square test (which replicates the behavior of  
the FET).

For more information see:
Chi-squared and Fisher-Irwin tests of two-by-two tables with small  
sample recommendations
Ian Campbell
Stat in Med 26:3661-3675; 2007
http://www3.interscience.wiley.com/journal/114125487/abstract
and:
How conservative is Fisher's exact test?
A quantitative evaluation of the two-sample comparative binomial trial
Gerald G. Crans, Jonathan J. Shuster
Stat Med. 2008 Aug 15;27(18):3598-611.
http://www3.interscience.wiley.com/journal/117929459/abstract


Frank also has some comments here (bottom of the page):

http://biostat.mc.vanderbilt.edu/wiki/Main/DataAnalysisDisc#Some_Important_Points_about_Cont


More generally, Agresti's Categorical Data Analysis is typically the  
first reference in this domain to reach for. There is also a document  
written by Laura Thompson which provides for a nice R companion to  
Agresti. It is available from:

https://home.comcast.net/~lthompson221/Splusdiscrete2.pdf


HTH,

Marc Schwartz