| Expected.R2 {MBESS} | R Documentation |
Expected value of the squared multiple correlation coefficient
Description
Returns the expected value of the squared multiple correlation coefficient given the population squared multiple correlation coefficient, sample size, and the number of predictors
Usage
Expected.R2(Population.R2, N, p)
Arguments
Population.R2 |
population squared multiple correlation coefficient |
N |
sample size |
p |
the number of predictor variables |
Details
Uses the hypergeometric function as discussed in section 28 of Stuart, Ord, and Arnold (1999) in order to obtain the correct value for the squared multiple correlation coefficient. Many times an exact value is given that ignores the hypergeometric function. This function yields the correct value.
Value
Returns the expected value of the squared multiple correlation coefficient.
Note
Uses package gsl and its hyperg_2F1 function.
Author(s)
Ken Kelley (University of Notre Dame; KKelley@ND.Edu)
References
Olkin, I. & Pratt, J. W. (1958). Unbiased estimation of certain correlation coefficients. Annals of Mathematical statistics, 29, 201–211.
Stuart, A., Ord, J. K., & Arnold, S. (1999). Kendall's advanced theory of statistics: Classical inference and the linear model (Volume 2A, 2nd Edition). New York, NY: Oxford University Press.
See Also
ss.aipe.R2, ci.R2, Variance.R2
Examples
# library(gsl)
# Expected.R2(.5, 10, 5)
# Expected.R2(.5, 25, 5)
# Expected.R2(.5, 50, 5)
# Expected.R2(.5, 100, 5)
# Expected.R2(.5, 1000, 5)
# Expected.R2(.5, 10000, 5)