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)

sample size

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.

Examples

Run this code

# NOT RUN {
signal.to.noise.R2(R.Square=.5, N=50, p=2)
signal.to.noise.R2(R.Square=.5, N=50, p=5)
signal.to.noise.R2(R.Square=.5, N=100, p=2)
signal.to.noise.R2(R.Square=.5, N=100, p=5)
# }

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