Determines the per-group sample size needed for a two-independent-groups
design so that the (expected) confidence interval for Cohen's
d, the population standardized mean difference, denoted
\(\delta\), is no wider than a user-specified value. This is the
Accuracy in Parameter Estimation (AIPE) framework of Kelley and Rausch
(2006), the standardized-mean-difference companion to power-based
planning via ss_power_smd. Optionally, supplying
assurance returns the larger sample size needed so that the
realized interval will be at or below the target width with that
probability rather than just on average.
ss_aipe_smd(delta, conf_level = 0.95, width, assurance = NULL)A data.frame with columns term and value. The first
row, necessary_n_per_group, is the necessary per-group sample size
N; the remaining rows echo the user-supplied planning inputs
supposed_smd and width (and assurance when supplied), so
the assumptions the sample size was planned under travel with the result. The
supposed_smd row is the supposed effect the plan is built on: a value
the researcher posits, either a minimally important effect or a value
believed to be true in the population, never a sample estimate. The
confidence level is reported in the printed footer.
The supposed value of the population standardized mean
difference \(\delta\) the sample size is planned against: a value the
researcher posits, either a minimally important effect or a value believed
to be true in the population, never a sample estimate. Echoed in the
returned table as the supposed_smd row.
Desired confidence level (i.e., \(1-\alpha\), where
\(\alpha\) is the Type I error rate). Default 0.95.
Desired (full) width of the two-sided confidence interval on \(\delta\).
Optional probability with which the realized
confidence interval is to be no wider than width. When
NULL (the default), the planning targets the
expected width; when supplied (e.g., 0.80, 0.90, 0.99), the
procedure returns the larger N that guarantees the desired
width with that assurance. Must be NULL or strictly between
0.50 and 1.
The returned value is the sample size per group.
Ken Kelley [email protected]
Anderson, S. F., & Kelley, K. (2024). Sample size planning for replication studies: The devil is in the design. Psychological Methods, 29(5), 844--867. tools:::Rd_expr_doi("10.1037/met0000520")
Anderson, S. F., Kelley, K., & Maxwell, S. E. (2017). Sample-size planning for more accurate statistical power: A method adjusting sample effect sizes for publication bias and uncertainty. Psychological Science, 28(11), 1547--1562. tools:::Rd_expr_doi("10.1177/0956797617723724")
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(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., Maxwell, S. E., & Rausch, J. R. (2003). Obtaining power or obtaining precision: Delineating methods of sample size planning. Evaluation and the Health Professions, 26(3), 258--287. tools:::Rd_expr_doi("10.1177/0163278703255242")
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")
Maxwell, S. E., Delaney, H. D., & Kelley, K. (2027). Designing experiments and analyzing data: A model comparison perspective (4th ed.). Routledge. (See Chapter 4 on individual comparisons and Chapter 3 on one-way ANOVA.)
Maxwell, S. E., Kelley, K., & Rausch, J. R. (2008). Sample size planning for statistical power and accuracy in parameter estimation. Annual Review of Psychology, 59, 537--563. tools:::Rd_expr_doi("10.1146/annurev.psych.59.103006.093735")
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.
smd, smd_c, ci_smd, ci_smd_c,
ci_nc_t, stats::power.t.test()
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.
ss_aipe_smd(delta = .5, conf_level = .95, width = .30)
ss_aipe_smd(delta = .5, conf_level = .95, width = .30, assurance = .8)
ss_aipe_smd(delta = .5, conf_level = .95, width = .30, assurance = .95)
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