Confidence intervals for differences between independent R-squares

Model 1 Model 2
Observed R-square (R2):
Number of predictors (k):
Sample size (n):
Confidence interval (CI):
R-square difference:
Approximate confidence interval: to

Approximate confidence intervals for a difference in R-square values (proportion of explained variance) from multiple linear regression models in two independent samples, given the values of R-square, the number of predictors, and the total sample sizes.

For example: for two observed R-square values of 0.254 and 0.193 in samples 1 and 2, 4 predictors, and sample sizes of 654 and 761, respectively, the 95% confidence interval for the difference in R-square ranges from -0.015 to 0.137. Since this confidence interval includes zero, the difference between the R-square values is not significant at the α = 0.05 level.

Note: Confidence intervals are based on large sample theory. Provides adequate approximations for models with >60 degrees of freedom (nk – 1).

Olkin I, Finn JD. Correlations Redux. Psychol Bull. 1995;118(1):155–64.