Sample size planning for Accuracy in Parameter Estimation (AIPE) of the standardized contrast in ANOVA

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Description

A function to calculate the appropriate sample size per group for the standardized contrast in ANOVA such that the width of the confidence interval is sufficiently narrow.

Usage

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ss.aipe.sc(psi, c.weights, width, conf.level = 0.95, 
assurance = NULL, certainty = NULL, ...)

Arguments

psi

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)

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)

certainty

an alias for assurance

...

allows one to potentially include parameter values for inner functions

Value

n

necessary sample size per group

Author(s)

Ken Kelley (University of Notre Dame; KKelley@ND.Edu); Keke Lai

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, 532–574.

Hedges, L. V. (1981). Distribution theory for Glass's Estimator of effect size and related estimators. Journal of Educational Statistics, 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.

Kelley, K. (2007). Constructing confidence intervals for standardized effect sizes: Theory, application, and implementation. Journal of Statistical Software, 20 (8), 1–24.

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.

Lai, K., & Kelley, K. (2007). Sample size planning for standardized ANCOVA and ANOVA contrasts: Obtaining narrow confidence intervals. Manuscript submitted for publication.

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

Examples

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# 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 gorup 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=.6, c.weights=c(.5, .5, -.5, -.5, 0), width=.4, assurance=.90) 

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