ci.srsnr {MBESS}

Confidence Interval for the Square Root of the Signal-To-Noise Ratio

Description

Function to calculate the exact confidence interval for the square root of the signal-to-noise ratio.

Usage

ci.srsnr(F.value = NULL, df.1 = NULL, df.2 = NULL, N = NULL, 
conf.level = 0.95, alpha.lower = NULL, alpha.upper = NULL, ...)

Arguments

F.value

observed F-value from the analysis of variance

df.1

numerator degrees of freedom

df.2

denominator degrees of freedom

N

sample size

conf.level

confidence interval coverage (i.e., 1 - Type I error rate); default is .95

alpha.lower

Type I error for the lower confidence limit

alpha.upper

Type I error for the upper confidence limit

...

allows one to potentially include parameter values for inner functions

Details

The confidence level must be specified in one of following two ways: using confidence interval coverage (conf.level), or lower and upper confidence limits (alpha.lower and alpha.upper).

The square root of the signal-to-noise ratio is defined as the standard deviation due to the particular factor over the standard deviation of the error (i.e., the square root of the mean square error). This function uses the confidence interval transformation principle (Steiger, 2004) to transform the confidence limits for the noncentality parameter to the confidence limits for square root of signal-to-noise ratio. The confidence interval for noncentral F parameter can be abtained from function conf.limits.ncf in MBESS.

Value

Returns the square root of the confidence limits for the signal to noise ratio.

Lower.Limit.of.the.Square.Root.of.the.Signal.to.Noise.Ratio

lower limit of the square root of the signal to noise ratio

Upper.Limit.of.the.Square.Root.of.the.Signal.to.Noise.Ratio

upper limit of the square root of the signal to noise ratio

Author(s)

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

References

Fleishman, A. I. (1980). Confidence intervals for correlation ratios. Educational and Psychological Measurement, 40, 659–670.

Kelley, K. (2007). Constructing confidence intervals for standardized effect sizes: Theory, application, and implementation. Journal of Statistical Software, 20 (8), 1–24.

Steiger, J. H. (2004). Beyond the F Test: Effect size confidence intervals and tests of close fit in the Analysis of Variance and Contrast Analysis. Psychological Methods, 9, 164–182.

See Also

ci.snr, conf.limits.ncf

Examples

## To illustrate the calculation of the confidence interval for noncentral 
## F parameter,Bargman (1970) gave an example in which a 5-group ANOVA with 
## 11 subjects in each group is conducted and the observed F value is 11.2213. 
## This exmaple continued to be used in Venables (1975),  Fleishman (1980), 
## and Steiger (2004). If one wants to calculate the exact confidence interval 
## for square root of the signal-to-noise ratio of that example, this 
## function can be used.

ci.srsnr(F.value=11.221, df.1=4, df.2=50, N=55)

ci.srsnr(F.value=11.221, df.1=4, df.2=50, N=55, conf.level=.90)

ci.srsnr(F.value=11.221, df.1=4, df.2=50, N=55,  alpha.lower=.02, alpha.upper=.03)