ss.aipe.smd: Sample size planning for the standardized mean difference from the Accuracy in Parameter Estimation (AIPE) perspective

Description

A function to calculate the appropriate sample size for the standardized mean difference such that the expected value of the confidence interval is sufficiently narrow, optionally with a degree.of.certainty.

Usage

ss.aipe.smd(delta, conf.level, width, which.width="Full", 
degree.of.certainty=NULL, assurance=NULL, certainty=NULL, ...)

Arguments

delta

the population value of the standardized mean difference

conf.level

the desired degree of confidence (i.e., 1-Type I error rate)

width

desired width of the specified (i.e., Full, Lower, and Upper widths) region of the confidence interval

which.width

the width that the width argument refers identifies the width of interest (i.e., Full, Lower, and Upper widths)

degree.of.certainty

parameter to ensure confidence interval width with a specified degree of certainty

assurance

an alias for degree.of.certainty

certainty

an alias for degree.of.certainty

...

for modifying parameters of functions this function calls upon

Value

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

Warning

Finding sample size for lower and uppper confidence limits is approximate, but very close to being exact. The pt() function is limited to accurate values when the the noncentral parameter is less than 37.62.

References

Cohen, J. (1988). Statistical power analysis for the behavioral sciences (2nd ed.). Hillsdale, NJ: Lawrence Erlbaum.

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., Maxwell, S. E., & Rausch, J. R. (2003). Obtaining Power or Obtaining Precision: Delineating Methods of Sample-Size Planning, Evaluation and the Health Professions, 26, 258--287.

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 where no significance tests? (pp. 221-257). Mahwah, NJ: Lawrence Erlbaum.

Examples

Run this code

# ss.aipe.smd(delta=.5, conf.level=.95, width=.30)
# ss.aipe.smd(delta=.5, conf.level=.95, width=.30, degree.of.certainty=.8)
# ss.aipe.smd(delta=.5, conf.level=.95, width=.30, degree.of.certainty=.95)

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