# ci.snr: Confidence Interval for the Signal-To-Noise Ratio In MBESS: The MBESS R Package

 ci.snr R Documentation

## Confidence Interval for the Signal-To-Noise Ratio

### 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

``````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.

`ci.srsnr`, `ci.omega2` `conf.limits.ncf`

### Examples

``````
## 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)
``````

MBESS documentation built on Oct. 26, 2023, 9:07 a.m.