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

In MBESS: The MBESS R Package

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)

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

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).

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

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.

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)

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