ci.sm: Confidence Interval for the Standardized Mean

In MBESS: The MBESS R Package

Confidence Interval for the Standardized Mean

Description

Function to obtain the exact confidence interval for the standardized mean.

Usage

ci.sm(sm = NULL, Mean = NULL, SD = NULL, ncp = NULL, N = NULL, 
conf.level = 0.95, alpha.lower = NULL, alpha.upper = NULL, ...)

Arguments

sm	standardized mean
Mean	mean
SD	standard deviation
ncp	noncentral parameter
N	sample size
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 user must specify the standardized mean in one and only one of the three ways: a) mean and standard deviation (Mean and SD), b) standardized mean (sm), and c) noncentral parameter (ncp). 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).

This function uses the exact confidence interval method based on noncentral t-distributions. The confidence interval for noncentral t-parameter can be obtained from the conf.limits.nct function in MBESS.

Value

Lower.Conf.Limit.Standardized.Mean	lower confidence limit of the standardized mean
Standardized.Mean	standardized mean
Upper.Conf.Limit.Standardized.Mean	upper confidence limit of the standardized mean

Note

The standardized mean is the mean divided by the standard deviation.

Author(s)

Ken Kelley (University of Notre Dame; [e-mail])

References

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., & Fouladi, R. T. (1997). Noncentrality interval estimation and the evaluation of statistical methods. In L. L. Harlow, S. A. Mulaik, & J.H. Steiger (Eds.), What if there were no significance tests? (pp. 221–257). Mahwah, NJ: Lawrence Erlbaum.

See Also

conf.limits.nct

Examples

ci.sm(sm=2.037905, N=13, conf.level=.95)
ci.sm(Mean=30, SD=14.721, N=13, conf.level=.95)
ci.sm(ncp=7.347771, N=13, conf.level=.95)
ci.sm(sm=2.037905, N=13, alpha.lower=.05, alpha.upper=0)
ci.sm(Mean=50, SD=10, N=25, conf.level=.95)

MBESS documentation built on Aug. 8, 2025, 7:24 p.m.