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

Source: R/ss_aipe_sc.R
ss_aipe_sc.Rd

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,
  ...
)

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

Value

necessary_n_per_group

Necessary sample size per group

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

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. 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, conf_limits_nct, 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.

Author

Ken Kelley kkelley@nd.edu

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)
#>  term                  value
#>  necessary_n_per_group 102  
#> 
#> Confidence level: 95%

# 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)
#>  term                  value
#>  necessary_n_per_group 108