ci.R: Confidence interval for the multiple correlation coefficient

In MBESS: The MBESS R Package

Confidence interval for the multiple correlation coefficient

Description

A function to obtain the confidence interval for the population multiple correlation coefficient when predictors are random (the default) or fixed.

Usage

ci.R(R = NULL, df.1 = NULL, df.2 = NULL, conf.level = 0.95, 
Random.Predictors = TRUE, Random.Regressors, F.value = NULL, 
N = NULL, K=NULL, alpha.lower = NULL, alpha.upper = NULL, ...)

Arguments

R	multiple correlation coefficient
df.1	numerator degrees of freedom
df.2	denominator degrees of freedom
conf.level	confidence interval coverage (i.e., 1- Type I error rate); default is .95
Random.Predictors	whether or not the predictor variables are random or fixed (random is default)
Random.Regressors	an alias for Random.Predictors; Random.Regressors overrides Random.Predictors
F.value	obtained F-value
N	sample size
K	number of predictors
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

This function is based on the function ci.R2 in MBESS package.

This function can be used with random predictor variables (Random.Predictors=TRUE) or when predictor variables are fixed (Random.Predictors=FALSE). In many applications in the behavioral, educational, and social sciences, predictor variables are random, which is the default for this function.

For random predictors, the function implements the procedure of Lee (1971), which was implemented by Algina and Olejnik (2000; specifically in their ci.smcc.bisec.sas SAS script). When Random.Predictors=TRUE, the function implements code that is in part based on the Alginia and Olejnik (2000) SAS script.

When Random.Predictors=FALSE, and thus the predictors are planned and thus fixed in hypothetical replications of the study, the confidence limits are based on a noncentral F-distribution (see conf.limits.ncf).

Value

Lower.Conf.Limit.R	lower limit of the confidence interval around the population multiple correlation coefficient
Prob.Less.Lower	proportion of the distribution less than Lower.Conf.Limit.R
Upper.Conf.Limit.R	upper limit of the confidence interval around the population multiple correlation coefficient
Prob.Greater.Upper	proportion of the distribution greater than Upper.Conf.Limit.R

Author(s)

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

References

Algina, J. & Olejnik, S. (2000). Determining sample size for accurate estimation of the squared multiple correlation coefficient. Multivariate Behavioral Research, 35, 119–136.

Lee, Y. S. (1971). Some results on the sampling distribution of the multiple correlation coefficient. Journal of the Royal Statistical Society, B, 33, 117–130.

Smithson, M. (2003). Confidence intervals. New York, NY: Sage Publications.

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.

Steiger, J. H. & Fouladi, R. T. (1992). R2: A computer program for interval estimation, power calculation, and hypothesis testing for the squared multiple correlation. Behavior research methods, instruments and computers, 4, 581–582.

See Also

ci.R2, ss.aipe.R2, conf.limits.nct

MBESS documentation built on Oct. 26, 2023, 9:07 a.m.