DMAR (version 1.0.0)

ss_aipe_sc: Sample Size Planning for Accuracy in Parameter Estimation (AIPE) of the Standardized Contrast in ANOVA

Description

Plans the sample size per group so that the confidence interval for a standardized contrast of means in a fixed effects analysis of variance, the interval computed by ci_sc, is sufficiently narrow, an application of the accuracy in parameter estimation (AIPE) approach to the standardized contrast.

Usage

ss_aipe_sc(
  psi_standardized,
  c_weights,
  width,
  conf_level = 0.95,
  alpha_lower = NULL,
  alpha_upper = NULL,
  assurance = NULL,
  ...
)

Value

necessary_n_per_group

Necessary sample size per group

Arguments

psi_standardized

Population standardized contrast

c_weights

The contrast weights

width

The desired full width of the obtained confidence interval

conf_level

The desired confidence interval coverage (i.e., 1 - Type I error rate). Default is .95, which gives a symmetric two-sided interval. Specify either conf_level or both of alpha_lower and alpha_upper, not both.

alpha_lower

Lower-tail Type I error rate, used to plan an asymmetric confidence interval. When supplied together with alpha_upper, the planned interval has lower-tail probability alpha_lower and upper-tail probability alpha_upper. Set conf_level = NULL when supplying these.

alpha_upper

Upper-tail Type I error rate, used together with alpha_lower to plan an asymmetric confidence interval.

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")

Lai, K., & Kelley, K. (2012). Accuracy in parameter estimation for ANCOVA and ANOVA contrasts: Sample size planning via narrow confidence intervals. British Journal of Mathematical and Statistical Psychology, 65, 350--370. tools:::Rd_expr_doi("10.1111/j.2044-8317.2011.02029.x")

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_sc, ci_nc_t, ss_aipe_c

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

# Suppose the population standardized contrast is believed to be .6
# in some 5-group ANOVA model. The researcher is interested in comparing
# the average of means of group 1 and 2 with the average of group 3 and 4.

# To calculate the necessary sample size per group such that the width
# of 95 percent confidence interval of the standardized
# contrast is, with 90 percent assurance, no wider than .4:

ss_aipe_sc(psi_standardized=.6, c_weights=c(.5, .5, -.5, -.5, 0), width=.4, assurance=.90)

# Asymmetric confidence interval: most of the alpha goes in the upper tail
# (e.g., when a one-sided concern dominates). Pass alpha_lower and
# alpha_upper instead of conf_level.
ss_aipe_sc(psi_standardized = .6, c_weights = c(.5, .5, -.5, -.5, 0), width = .4,
           conf_level = NULL, alpha_lower = .01, alpha_upper = .04)