signal.to.noise.R2 {MBESS}

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

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.

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

Author(s)

Ken Kelley (University of Notre Dame; [e-mail])

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.

See Also

ci.R2, ss.aipe.R2

Examples

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)