Sensitivity analysis for sample size planning for the standardized ANOVA contrast from the Accuracy in Parameter Estimation (AIPE) Perspective

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Description

Performs a sensitivity analysis when planning sample size from the Accuracy in Parameter Estimation (AIPE) Perspective for the standardized ANOVA contrast.

Usage

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ss.aipe.sc.sensitivity(true.psi = NULL, estimated.psi = NULL, c.weights, 
desired.width = NULL, selected.n = NULL, assurance = NULL, certainty=NULL, 
conf.level = 0.95, G = 10000, print.iter = TRUE, detail = TRUE, ...)

Arguments

true.psi

population standardized contrast

estimated.psi

estimated standardized contrast

c.weights

the contrast weights

desired.width

the desired full width of the obtained confidence interval

selected.n

selected sample size to use in order to determine distributional properties of at a given value of sample size

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

conf.level

the desired confidence interval coverage, (i.e., 1 - Type I error rate)

G

number of generations (i.e., replications) of the simulation

print.iter

to print the current value of the iterations

detail

whether the user needs a detailed (TRUE) or brief (FALSE) report of the simulation results; the detailed report includes all the raw data in the simulations

...

allows one to potentially include parameter values for inner functions

Value

psi.obs

observed standardized contrast in each iteration

Full.Width

vector of the full confidence interval width

Width.from.psi.obs.Lower

vector of the lower confidence interval width

Width.from.psi.obs.Upper

vector of the upper confidence interval width

Type.I.Error.Upper

iterations where a Type I error occurred on the upper end of the confidence interval

Type.I.Error.Lower

iterations where a Type I error occurred on the lower end of the confidence interval

Type.I.Error

iterations where a Type I error happens

Lower.Limit

the lower limit of the obtained confidence interval

Upper.Limit

the upper limit of the obtained confidence interval

replications

number of replications of the simulation

True.psi

population standardized contrast

Estimated.psi

estimated standardized contrast

Desired.Width

the desired full width of the obtained confidence interval

assurance

the value assigned to the argument assurance

Sample.Size.per.Group

sample size per group

Number.of.Groups

number of groups

mean.full.width

mean width of the obtained full conficence intervals

median.full.width

median width of the obtained full confidence intervals

sd.full.width

standard deviation of the widths of the obtained full confidence intervals

Pct.Width.obs.NARROWER.than.desired

percentage of the obtained full confidence interval widths that are narrower than the desired width

mean.Width.from.psi.obs.Lower

mean lower width of the obtained confidence intervals

mean.Width.from.psi.obs.Upper

mean upper width of the obtained confidence intervals

Type.I.Error.Upper

Type I error rate from the upper side

Type.I.Error.Lower

Type I error rate from the lower side

Author(s)

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

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. (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 where no significance tests? (pp. 221–257). Mahwah, NJ: Lawrence Erlbaum.

See Also

ss.aipe.sc, ss.aipe.c, conf.limits.nct

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