Sample Size Planning for Accuracy in Parameter Estimation for the multiple correlation coefficient.

Description

Determines necessary sample size for the multiple correlation coefficient so that the confidence interval for 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 desired.

Usage

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ss.aipe.R2(Population.R2 = NULL, conf.level = 0.95, width = NULL, 
Random.Predictors = TRUE, Random.Regressors, which.width = "Full", p = NULL, 
K, degree.of.certainty = NULL, assurance=NULL, 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

K

an alias for p; K overrides p

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.e.g, .80, .90, .95)

assurance

an alias for degree.of.certainty

certainty

an alias for degree.of.certainty

verify.ss

evaluates numerically via an internal Monte Carlo simulation the exact sample size given the specifications

Tol

the tolerance of the iterative function conf.limits.nct for convergence

...

for modifying the parameters of functions this function calls upon

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) 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 on the type of regressors. The default methods are approximate but can be made exact with the specification of verify.ss=TRUE, which performs an a priori Monte Carlo simulation study. Kelley (2007) and Kelley & Maxwell (2008) 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 implied 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.

Note

This function without verify.SS=FALSE can be slow to converge when verify.SS=TRUE, the function can take some time to converge (e.g., 15 minutes). Most times this will not be the case, but it is possible in some situations.

Author(s)

Ken Kelley (University of Notre Dame; KKelley@ND.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. (2007). 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. (2008). 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.), Handbook of Social Research Methods (pp. 166–192). Newbury Park, CA: Sage.

See Also

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

Examples

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## Not run: 
# Returned sample size should be considered approximate; exact sample
# size is obtained by specifying the argument 'verify.ss=TRUE' (see below).
# ss.aipe.R2(Population.R2=.50, conf.level=.95, width=.10, which.width="Full",
# p=5, Random.Predictors=TRUE)
# Uncomment to run in order to get exact sample size.
# ss.aipe.R2(Population.R2=.50, conf.level=.95, width=.10, which.width="Full",
# p=5, Random.Predictors=TRUE, verify.ss=TRUE)


# Same as above, except the predictor variables are considered fixed.
# Returned sample size should be considered approximate; exact sample
# size is obtained by specifying the argument 'verify.ss=TRUE'.
# ss.aipe.R2(Population.R2=.50, conf.level=.95, width=.10, which.width="Full",
# p=5, Random.Predictors=FALSE)
# Uncomment to run in order to get exact sample size.
#ss.aipe.R2(Population.R2=.50, conf.level=.95, width=.10, which.width="Full",
#p=5, Random.Predictors=FALSE, verify.ss=TRUE)


# Returned sample size should be considered approximate; exact sample
# size is obtained by specifying the argument 'verify.ss=TRUE'.
# ss.aipe.R2(Population.R2=.50, conf.level=.95, width=.10, which.width="Full",
# p=5, degree.of.certainty=.85, Random.Predictors=TRUE)
# Uncomment to run in order to get exact sample size.
#ss.aipe.R2(Population.R2=.50, conf.level=.95, width=.10, which.width="Full",
#p=5, degree.of.certainty=.85, Random.Predictors=TRUE, verify.ss=TRUE)


# Same as above, except the predictor variables are considered fixed.
# Returned sample size should be considered approximate; exact sample
# size is obtained by specifying the argument 'verify.ss=TRUE'.
# ss.aipe.R2(Population.R2=.50, conf.level=.95, width=.10, which.width="Full",
# p=5, degree.of.certainty=.85, Random.Predictors=FALSE)
# Uncomment to run in order to get exact sample size.
#ss.aipe.R2(Population.R2=.50, conf.level=.95, width=.10, which.width="Full",
#p=5, degree.of.certainty=.85, Random.Predictors=FALSE, verify.ss=TRUE)

## End(Not run)

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