ci.omega2: Confidence Interval for omega-squared (omega^2) for...

View source: R/ci.omega2.R

ci.omega2R 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)


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.


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



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.)


numerator degrees of freedom


denominator degrees of freedom


total sample size (i.e., the number of individual entities in the data)


confidence interval coverage (i.e., 1-Type I error rate), default is .95


Type I error for the lower confidence limit


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). 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.


Returns the confidence limits for (partial) omega-sqaured.


lower limit for omega-squared


upper limit for omega-squared


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


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.

See Also

ci.srsnr, ci.snr, conf.limits.ncf


## 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.