= A two group nonparametric effect size =

Field (2005) suggests an effect size associated with performing nonparametric group tests. This is analogous to Cohen's d for parametric group testing. In particular on pages 531-2 of his book Field suggests using the formula of Rosenthal (1991, p.19) to compute a correlation:

{{{
correlation = z /sqrt(N) 
}}}

where z is the z statistic that SPSS produces when you do the Mann-Whitney or Wilcoxon tests under analyze>nonparametrics and N is the size of the study. 

This is a correlation so can be compared to the rules of thumb suggested by Cohen with suggested thresholds of 0.1, 0.3 and 0.5 for small, medium and large magnitudes respectively. In fact the above statistic is equal to the Phi Coefficient (Howell, 1997,2001,2006) which is used to generate a correlation from 2x2 frequency tables and is of form

$$\sqrt{\chi_text{1}^text{2}/N}$$ = $$\sqrt{z^text{2}/N}$$ = z /sqrt(N) This effect size can be worked out for the Mann-Whitney test using this [attachment:phief.xls spreadsheet.] The input is the total number of subjects, group (coded as either 1 or 2) and the response.


__References__

Field A (2005) Discovering statistics using SPSS. Second Edition. Sage:London 

Howell (1997),(2001), (2006) Statistical methods for psychology. Furth, Fifth and Sixth Editions. Wadsworth:Belmont,CA.

Rosenthal R (1991) Meta-analytic procedures for social research (revised). Sage:Newbury Park,CA.