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DMAR (version 1.0.0)

ss_aipe_sm: Sample Size Planning for Accuracy in Parameter Estimation (AIPE) of the Standardized Mean

Description

Plans the sample size needed for a sufficiently narrow confidence interval for the population standardized mean, the mean divided by the standard deviation, from the accuracy in parameter estimation (AIPE) perspective.

Usage

ss_aipe_sm(sm, width, conf_level = 0.95, assurance = NULL, ...)

Value

A 1-row data.frame with columns term and value:

necessary_N

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

Arguments

sm

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)

...

Allows one to potentially include parameter values for inner functions

Author

Ken Kelley [email protected]

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(4), 532--574. tools:::Rd_expr_doi("10.1177/0013164401614002")

Hedges, L. V. (1981). Distribution theory for Glass's Estimator of effect size and related estimators. Journal of Educational Statistics, 6(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. tools:::Rd_expr_doi("10.1177/0013164404264850")

Kelley, K. (2007). Confidence intervals for standardized effect sizes: Theory, application, and implementation. Journal of Statistical Software, 20(8), 1--24. tools:::Rd_expr_doi("10.18637/jss.v020.i08")

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. tools:::Rd_expr_doi("10.1037/1082-989X.11.4.363")

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.

See Also

ci_nc_t, ci_sm

design_consequences for what a chosen design delivers: power, the Type S (sign) and Type M (exaggeration) errors of the significance filter, and the expected confidence interval width.

Examples

Run this code
# 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)

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