R: Confidence Interval for omega-squared (omega^2) for...

ci.omega2 {MBESS}

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.

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)

[Package MBESS version 4.9.3 Index]

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)