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

Source: R/ss_aipe_sm.R
ss_aipe_sm.Rd

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, ...)

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

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)

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. 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. 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. 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. 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

conf_limits_nct, 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.

Author

Ken Kelley kkelley@nd.edu

Examples

# 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)
#> Warning: During the iterative sample size search, conf_limits_nct() reported a noncentrality parameter exceeding 37.62 in magnitude in 254 intermediate evaluations, the limit at which R's pt()/qt() can return accurate noncentral t probabilities. The returned sample size may be affected; see ?conf_limits_nct.
#>  term        value
#>  necessary_N 150  
#> 
#> Confidence level: 95%