ss.aipe.R2 {MBESS}R Documentation

Sample Size Planning for Accuracy in Parameter Estimation (i.e., precision) for the multiple correlation coefficient.

Description

Determines necessary sample size for the multiple correlation coefficient so that the confidence interval around the population multiple correlation coefficient is sufficiently narrow. Optionally, there is a certainty parameter that allows one to be a specified percent certain that the observed interval will be no wider than specified.

Usage

ss.aipe.R2(Population.R2 = NULL, conf.level = .95, width = NULL, 
Random.Predictors=TRUE, Random.Regressors, which.width = "Full", p = NULL, 
degree.of.certainty = NULL, verify.ss=FALSE, Tol = 1e-09, ...)

Arguments

Population.R2 value of the population multiple correlation coefficient
conf.level confidence interval level (e.g., .95, .99, .90); 1-Type I error rate
width width of the confidence interval (see which.width)
Random.Predictors whether or not the predictor variables are random (set to TRUE) or are fixed (set to FALSE)
Random.Regressors an alias for Random.Predictors; Random.Regressors overrides Random.Predictors
which.width defines the width that width refers to
p the number of predictor variables
degree.of.certainty value with which confidence can be placed that describes the likelihood of obtaining a confidence interval less than the value specified (e.g., .80, .90, .95)
verify.ss evaluates numerically via an internal Monte Carlo simualtion the exact sample size given the specifications
Tol the tolerance of the iterative function conf.limits.nct for convergence
... for modifying parameters of functions this function calls

Details

This function determines a necessary sample size so that the expected confidence interval width for the squared multiple correlation coefficient is sufficiently narrow (when degree.of.certainty=NULL) or so that the obtained confidence interval is no larger than the value specified with some desired degree of certainty (i.e., a probability that the obtained width is less than the specified width). The method depends on whether or not the regressors are regarded as fixed or random. This is the case because the distribution theory for the two cases is different and thus the confidence interval procedure is conditional the type of regressors. Kelley (2006) and Kelley & Maxwell (In press) detail the methods used in the function, with the former focusing on random regressors and the latter on fixed regressors.

It is recommended that the option verify.ss should always be used! Doing so uses the method impled sample size as an estimate and then evaluates with an internal Monte Carlo simulation (i.e., via "brute-force" methods) the exact sample size given the goals specified. When verify.ss=TRUE, the default number of iterations is 10,000 but this can be changed by specifying G=5000 (or some other value; 10000 is the recommended) When verify.ss=TRUE is specified, an internal function verify.ss.aipe.R2 calls upon the ss.aipe.R2.sensitivity function for purposes of the internal Monte Carlo simulation study. See the verify.ss.aipe.R2 function for arguments that can be passed from ss.aipe.R2 to verify.ss.aipe.R2.

Value

Required.Sample.Size sample size that should be used given the conditions specified.

Warning

Only Full in which.width should be used at the present time. Sample size returned for Lower and Upper widths are only approxiamate. If these widths are of interest, try using the ss.aipe.R2.sensitivity function to determine sample size through brute force (trial and error) procedures.

Note

This function can be slow to converge (e.g., 1 minute convergence in some situations). This is because the function is written so that it handles (essentially) all values and is thus very general.

Author(s)

Ken Kelley (Indiana University; KKIII@Indiana.Edu)

References

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

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.

Kelley, K. Sample size planning for the squared multiple correlation coefficient: Accuracy in parameter estimation via narrow confidence intervals, manuscripted submitted for publication.

Kelley, K. & Maxwell, S. E. (In press) Power and accuracy for omnibus and targeted effects: Issues of sample size planning with applications to multiple regression. In P. Alasuuta, J. Brannen, & L. Bickman (Eds.), textit{Handbook of Social Research Methods}. Newbury Park, CA: Sage.

See Also

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

Examples

ss.aipe.R2(Population.R2=.50, conf.level=.95, width=.10, which.width="Full",
p=5, Random.Predictors=TRUE)

# Same as above, except the predictor variables are considered fixed.
ss.aipe.R2(Population.R2=.50, conf.level=.95, width=.10, which.width="Full",
p=5, Random.Predictors=FALSE)

ss.aipe.R2(Population.R2=.50, conf.level=.95, width=.10, which.width="Full",
p=5, degree.of.certainty=.85, Random.Predictors=TRUE)

ss.aipe.R2(Population.R2=.50, conf.level=.95, width=.10, which.width="Full",
p=5, degree.of.certainty=.85, Random.Predictors=FALSE)

[Package MBESS version 0.0.7 Index]