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).

1 2 |

`F.value` |
observed |

`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 |

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.

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 |

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).

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

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`

, `conf.limits.ncf`

1 2 3 4 5 6 7 8 9 10 11 | ```
## 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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