Confidence Interval for the Signal-To-Noise Ratio

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Description

Function to obtain the exact confidence interval for the signal-to-noise ratio (i.e., the variance of the specific factor over the error variance).

Usage

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ci.snr(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).

This function uses the confidence interval transformation principle (Steiger, 2004) to transform the confidence limits for the noncentality parameter to the confidence limits for the population's signal-to-noise ratio. The confidence interval for noncentral F parameter can be obtained from the conf.limits.ncf function in MBESS, which is used internally within this function.

Value

Returns the confidence limits for the signal-to-noise ratio.

Lower.Limit.Signal.to.Noise.Ratio

lower limit for signal to noise ratio

Upper.Limit.Signal.to.Noise.Ratio

upper limit for signal to noise ratio

Note

The signal to noise ratio is defined as the variance due to the particular factor over the error variance (i.e., the mean square error).

Author(s)

Ken Kelley (University of Notre Dame; KKelley@ND.Edu)

References

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

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

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.srsnr, conf.limits.ncf

Examples

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## 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 example was 
## used in Venables (1975),  Fleishman (1980), and Steiger (2004). If one wants to calculate 
## the exact confidence interval for the signal-to-noise ratio of that example, this
## function can be used.

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

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

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

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