MBESS (version 4.9.3)

ci.R2: Confidence interval for the population squared multiple correlation coefficient

Description

A function to calculate the confidence interval for the population squared multiple correlation coefficient.

Usage

ci.R2(R2 = NULL, df.1 = NULL, df.2 = NULL, conf.level = .95, 
Random.Predictors=TRUE, Random.Regressors, F.value = NULL, N = NULL, 
p = NULL, K, alpha.lower = NULL, alpha.upper = NULL, tol = 1e-09)

Value

Lower.Conf.Limit.R2

upper limit of the confidence interval around the population multiple correlation coefficient

Prob.Less.Lower

proportion of the distribution less than Lower.Conf.Limit.R2

Upper.Conf.Limit.R2

upper limit of the confidence interval around the population multiple correlation coefficient

Prob.Greater.Upper

proportion of the distribution greater than Upper.Conf.Limit.R2

Arguments

R2

squared multiple correlation coefficient

df.1

numerator degrees of freedom

df.2

denominator degrees of freedom

conf.level

confidence interval coverage; 1-Type I error rate

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

p

number of predictors

K

alias for p, the number of predictors

alpha.lower

Type I error for the lower confidence limit

alpha.upper

Type I error for the upper confidence limit

tol

tolerance for iterative convergence

Author

Ken Kelley (University of Notre Dame; )

Details

This function can be used with random predictor variables (Random.Predictors=TRUE) or when predictor variables are fixed (Random.Predictors=FALSE). In many applications of multiple regression, predictor variables are random, which is the default in 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.

Kelley, K. (2007). Constructing confidence intervals for standardized effect sizes: Theory, application, and implementation. Journal of Statistical Software, 20 (8), 1--24.

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. & 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

ss.aipe.R2, conf.limits.ncf

Examples

# For random predictor variables.
# ci.R2(R2=.25, N=100, K=5, conf.level=.95, Random.Predictors=TRUE)

# ci.R2(F.value=6.266667, N=100, K=5, conf.level=.95, Random.Predictors=TRUE)

# For fixed predictor variables.
# ci.R2(R2=.25, N=100, K=5, conf.level=.95, Random.Predictors=TRUE)

# ci.R2(F.value=6.266667, N=100, K=5, conf.level=.95, Random.Predictors=TRUE)

# One sided confidence intervals when predictors are random.
# ci.R2(R2=.25, N=100, K=5, alpha.lower=.05, alpha.upper=0, conf.level=NULL,
# Random.Predictors=TRUE)

# ci.R2(R2=.25, N=100, K=5, alpha.lower=0, alpha.upper=.05, conf.level=NULL,
# Random.Predictors=TRUE)

# One sided confidence intervals when predictors are fixed.
# ci.R2(R2=.25, N=100, K=5, alpha.lower=.05, alpha.upper=0, conf.level=NULL,
# Random.Predictors=FALSE)

# ci.R2(R2=.25, N=100, K=5, alpha.lower=0, alpha.upper=.05, conf.level=NULL,
# Random.Predictors=FALSE)