MBESS (version 4.1.0)

ss.aipe.smd.sensitivity: Sensitivity analysis for sample size given the Accuracy in Parameter Estimation approach for the standardized mean difference.

Description

Performs sensitivity analysis for sample size determination for the standardized mean difference given a population and a standardized mean difference. Allows one to determine the effect of being wrong when estimating the population standardized mean difference in terms of the width of the obtained (two-sided) confidence intervals.

Usage

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

Arguments

true.delta

population standardized mean difference

estimated.delta

estimated standardized mean difference; can be true.delta to perform standard simulations

desired.width

describe full width for the confidence interval around the population standardized mean difference

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 confidence interval width with a specified degree of certainty (must be NULL or between zero and unity)

certainty

an alias for assurance

conf.level

the desired degree of confidence (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

...

for modifying parameters of functions this function calls

Value

Details

For sensitivity analysis when planning sample size given the desire to obtain narrow confidence intervals for the population standardized mean difference. Given a population value and an estimated value, one can determine the effects of incorrectly specifying the population standardized mean difference (true.delta) on the obtained widths of the confidence intervals. Also, one can evaluate the percent of the confidence intervals that are less than the desired width (especially when modifying the certainty parameter); see ss.aipe.smd)

Alternatively, one can specify selected.n to determine the results at a particular sample size (when doing this estimated.delta cannot be specified).

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.

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.smd

Examples

# Since 'true.delta' equals 'estimated.delta', this usage 
# returns the results of a correctly specified situation.
# Note that 'G' should be large (50 is used to make the example run easily)
# Res.1 <- ss.aipe.smd.sensitivity(true.delta=.5, estimated.delta=.5, 
# desired.width=.30, certainty=NULL, conf.level=.95, G=50,
# print.iter=FALSE)

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

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

#Extract d from the Results list of Res.1.
# d <- Res.1$Results$d 

# hist(d)

# Pull out summary measures
# Res.1$Summary

# True standardized mean difference is .4, but specified at .5.
# Change 'G' to some large number (e.g., G=5,000)
# Res.2 <- ss.aipe.smd.sensitivity(true.delta=.4, estimated.delta=.5, 
# desired.width=.30, certainty=NULL, conf.level=.95, G=50, 
# print.iter=FALSE)

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

# True standardized mean difference is .5, but specified at .4.
# Res.3 <- ss.aipe.smd.sensitivity(true.delta=.5, estimated.delta=.4, 
# desired.width=.30, certainty=NULL, conf.level=.95, G=50, 
# print.iter=FALSE)

# The effect of the misspecification on mean confidence intervals is:
# Res.3$Summary$mean.full.width