MBESS (version 4.9.3)

ss.aipe.sm.sensitivity: 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, ...)

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

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

Author

Ken Kelley (University of Notre Dame; ); 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