signal.to.noise.R2: Signal to noise using squared multiple correlation coefficient
Description
Function that calculates five different signal-to-noise ratios using the squared multiple correlation coefficient.
Usage
signal.to.noise.R2(R.Square, N, p)
Arguments
R.Square
usual estimate of the squared multiple correlation coefficient (with no adjustments)
N
sample size
p
number of predictors
Value
phi2.hat
Basic estimate of the signal-to-noise ratio using the usual estimate of the squared multiple correlation coefficient: phi2.hat=R.Square/(1-R.Square)
phi2.adj.hat
Estimate of the signal-to-noise ratio using the usual adjusted R Square in place of R-Square: phi2.hat=Adj.R2/(1-Adj.R2)
phi2.UMVUE
Muirhead's (1985) unique minimum variance unbiased estimate of the signal-to-noise ratio (Muirhead uses theta-U): see reference or code for formula
phi2.UMVUE.L
Muirhead's (1985) unique minimum variance unbiased linear estimate of the signal-to-noise ratio (Muirhead uses theta-L): see reference or code for formula
phi2.UMVUE.NL
Muirhead's (1985) unique minimum variance unbiased nonlinear estimate of the signal-to-noise ratio (Muirhead uses theta-NL); requires the number of predictors to be greater than five: see reference or code for formula
Details
The method of choice is phi2.UMVUE.NL, but it requires p of 5 or more. In situations where p < 5, it is suggested that phi2.UMVUE.L be used.
References
Cohen, J. (1988). Statistical power analysis for the behavioral sciences (2nd ed.). Hillsdale, NJ: Lawrence Erlbaum.
Muirhead, R. J. (1985). Estimating a particular function of the multiple correlation coefficient. Journal of the American Statistical Association, 80, 923--925.