ss.aipe.sm.sensitivity: Sensitivity analysis for sample size planning for the...

In MBESS: The MBESS R Package

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

Description

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

Usage

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

Arguments

true.sm	population standardized mean
estimated.sm	estimated standardized mean
desired.width	desired full width of the confidence interval for the population standardized mean
selected.n	selected sample size to use in order to determine distributional properties of 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

sm.obs	vector of the observed standardized mean
Full.Width	vector of the full confidence interval width
Width.from.sm.obs.Lower	vector of the lower confidence interval width
Width.from.sm.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.sm	the population standardized mean
Estimated.sm	the estimated standardized mean
Desired.Width	the desired full confidence interval width
assurance	parameter to ensure that the obtained confidence interval width is narrower than the desired width with a specified degree of certainty
Sample.Size	the sample size used in the simulation
mean.full.width	mean width of the obtained full confidence 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.sm.obs.Lower	mean lower width of the obtained confidence intervals
mean.Width.from.sm.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; [e-mail]); 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.

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

ss.aipe.sm

Examples

# Since 'true.sm' equals 'estimated.sm', this usage
# returns the results of a correctly specified situation.
# Note that 'G' should be large (10 is used to make the 
# example run easily)
# Res.1 <- ss.aipe.sm.sensitivity(true.sm=10, estimated.sm=10, 
# desired.width=.5, assurance=.95, conf.level=.95, G=10,
# print.iter=FALSE)

# Lists contained in Res.1.
# names(Res.1) 

#Objects contained in the 'Results' lists.
# names(Res.1$Results) 

#How many obtained full widths are narrower than the desired one?
# Res.1$Summary$Pct.Width.obs.NARROWER.than.desired

# True standardized mean difference is 10, but specified at 12.
# Change 'G' to some large number (e.g., G=20)
# Res.2 <- ss.aipe.sm.sensitivity(true.sm=10, estimated.sm=12, 
# desired.width=.5, assurance=NULL, conf.level=.95, G=20)

# The effect of the misspecification on mean confidence intervals is:
# Res.2$Summary$mean.full.width

MBESS documentation built on Oct. 26, 2023, 9:07 a.m.