ss.aipe.sm.sensitivity {MBESS}R Documentation

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

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 where 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


[Package MBESS version 2.0.0 Index]