# 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 (\omega^2) for between-subject fixed-effects ANOVA and ANCOVA designs (and partial omega-squared \omega^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 \omega^2 (or partial \omega^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 (\omega^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 Oct. 26, 2023, 9:07 a.m.