ci.R: 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

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

sample size

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

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

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).

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.