How do I compare two squared correlation coefficients (R-squareds)?

Zou (2007) presents two methods of computing a confidence interval for the difference in R-squareds obtained from regressions on different data sets. If zero is not contained in the confidence interval then the two R-squareds do not differ statistically at the (two-tailed) input alpha level. Zou suggests for samples under 100 that a modified version of the traditional delta method be used to compute confidence intervals. Both methods may be computed using a [attachment:rsqdiff.xls spreadsheet.] Zou also gives formulae for obtaining confidence intervals and tests for comparing two correlations.

There is also [http://www.statpower.net/ downloadable] MS-DOS software to evaluate confidence intervals for a single R-squared and a [attachment:rsqci.xls spreadsheet] based on formulae from [http://psychology.anu.edu.au/people/smithson/details/CIstuff/CI.html Smithson.] SAS and SPSS syntax from Zou to compute confidence intervals for a single R-squared is also [http://www.apa.org/journals/supplemental/met_12_4_399/met_12_4_399_supp.html available.]

R-squared is the square of the semi-partial correlation and so the above tests are equivalent to comparing two semi-partial correlations. The proportion of the outcome variance which is accounted for by a particular predictor or set of predictors beyond that accounted for by other predictors.

Reference

Zou, GY (2007) Toward using confidence intervals to compare correlations. Psychological methods 12(4) 399-413. (available on [http://intranet.mrc-cbu.cam.ac.uk/CBU_Library/index.shtml ScienceDirect] for CBSU users).