MBESS (version 4.9.3)

ci.omega2: 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, ...)

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

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

Author

Ken Kelley (University of Notre Dame; )

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.

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.

See Also

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)