ss.aipe.sm: Sample size planning for Accuracy in Parameter Estimation (AIPE) of the standardized mean

Description

A function to calculate the appropriate sample size for the standardized mean such that the width of the confidence interval is sufficiently narrow.

Usage

ss.aipe.sm(sm, width, conf.level = 0.95, assurance = NULL, certainty=NULL, ...)

Arguments

the population standardized mean

width

the desired full width of the obtained confidence interval

conf.level

the desired confidence interval coverage, (i.e., 1 - Type I error rate)

assurance

parameter to ensure that the obtained confidence interval width is narrower than the desired width with a specified degree of certainty (must be NULL or between zero and unity)

certainty

an alias for assurance

…

allows one to potentially include parameter values for inner functions

Value

the necessary sample size in order to achieve the desired degree of accuracy (i.e., the sufficiently narrow confidence interval)

References

Cumming, G. & Finch, S. (2001). A primer on the understanding, use, and calculation of confidence intervals that are based on central and noncentral distributions, Educational and Psychological Measurement, 61, 532--574.

Hedges, L. V. (1981). Distribution theory for Glass's Estimator of effect size and related estimators. Journal of Educational Statistics, 2, 107--128.

Kelley, K. (2005). The effects of nonnormal distributions on confidence intervals around the standardized mean difference: Bootstrap and parametric confidence intervals, Educational and Psychological Measurement, 65, 51--69.

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

Kelley, K., & Rausch, J. R. (2006). Sample size planning for the standardized mean difference: Accuracy in Parameter Estimation via narrow confidence intervals. Psychological Methods, 11(4), 363--385.

Steiger, J. H., & Fouladi, R. T. (1997). Noncentrality interval estimation and the evaluation of statistical methods. In L. L. Harlow, S. A. Mulaik,& J.H. Steiger (Eds.), What if there were no significance tests? (pp. 221--257). Mahwah, NJ: Lawrence Erlbaum.

Examples

Run this code

# NOT RUN {
# Suppose the population mean is believed to be 20, and the population
# standard deviation is believed to be 2; thus the population standardized
# mean is believed to be 10. To determine the necessary sample size for a 
# study so that the full width of the 95 percent confidence interval 
# obtained in the study will be, with 90% assurance, no wider than 2.5, 
# the function should be specified as follows. 

# ss.aipe.sm(sm=10, width=2.5, conf.level=.95, assurance=.90)
# }