ci.R2 {MBESS} | R Documentation |
A function to calculate the exact confidence interval for the multiple correlation coefficient.
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)
R2 |
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 |
This function can be used with random predictor variables (Random.Predictors=TRUE
) or when predictor
variables are fixed (Random.Predictors=FALSE
). In most applications in the behavioral, educational,
and social sciences 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
).
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 Lower.Conf.Limit.R2 |
Ken Kelley (University of Notre Dame; KKelley@ND.Edu)
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. & 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.
ss.aipe.R2
, conf.limits.nct
# 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)