# ci.omega2: Confidence Interval for omega-squared (omega^2) for... In MBESS: The MBESS R Package

 ci.omega2 R Documentation

## Confidence Interval for omega-squared (ω^2) for between-subject fixed-effects ANOVA and ANCOVA designs (and partial omega-squared ω^2_p for between-subject multifactor ANOVA and ANCOVA designs)

### Description

Function to obtain the exact confidence interval using the non-central \$F\$ distribution for omega-squared or partial omega-squared in between-subject fixed-effects ANOVA and ANCOVA designs.

### Usage

```ci.omega2(F.value = NULL, df.1 = NULL, df.2 = NULL, N = NULL, conf.level = 0.95,
alpha.lower = NULL, alpha.upper = NULL, ...)
```

### Arguments

 `F.value` The value of the \$F\$-statistic for the analysis of (co)variace model (ANOVA) or, in the case of a multifactor ANOVA, the \$F\$-statistic for the particular factor.) `df.1` numerator degrees of freedom `df.2` denominator degrees of freedom `N` total sample size (i.e., the number of individual entities in the data) `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 value returned is the confidence interval limits for the population ω^2 (or partial ω^2).

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 (partial) omega-squared (ω^2). The confidence interval for the 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 (partial) omega-sqaured.

 `lower_Limit_omega2` lower limit for omega-squared `lower_Limit_omega2` upper limit for omega-squared

### Author(s)

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

### 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.

`ci.srsnr`, `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 omega-squared of that example, this function can be used.

ci.omega2(F.value=11.221, df.1=4, df.2=50, N=55)

ci.omega2(F.value=11.221, df.1=4, df.2=50, N=55, conf.level=.90)

```

MBESS documentation built on Sept. 19, 2022, 5:05 p.m.