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

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 an 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

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).

Value

Results list of the results in G-length vector form
Specifications specification of the function
Summary summary measures of some important descriptive statistics
d contained in Results list: vector of the observed d values
Full.Width contained in Results list: vector of
Width.from.d.Upper contained in Results list: vector of the observed upper widths of the confidence interval (upper limit minus observed standardized mean difference)
Width.from.d.Lower contained in Results list: vector of the observed lower widths of the confidence interval (standardized mean difference minus lower limit)
Type.I.Error.Upper contained in Results list: iterations where a Type I error occurred on the upper end of the confidence interval
Type.I.Error.Lower contained in Results list: iterations where a Type I error occurred on the lower end of the confidence interval
Type.I.Error contained in Results list: iterations where a Type I error occurred
Upper.Limit contained in Results list: vector of the obtained upper limits from the simulation
Low.Limit contained in Results list: vector of the obtained lower limits from the simulation
replications contained in Specifications list: number of generations (i.e., replication) of the simulation
true.delta contained in Specifications list: population value of the standardized mean difference
estimated.delta contained in Specifications list: value of the population (mis)specified for purposes of sample size planning
desired.width contained in Specifications list: desired full width of the confidence interval around the population standardized mean difference
certainty contained in Specifications list: desired degree of certainty that the obtained confidence interval width is less than the value specified
n.j contained in Specifications list: sample size per group given the specifications
mean.full.width contained in Summary list: mean width of the obtained confidence intervals
median.full.width contained in Summary list: median width of the obtained confidence intervals
sd.full.width contained in Summary list: standard deviation of the obtained confidence intervals
Pct.Less.Desired contained in Summary list: Percent of the confidence widths less than the width specified.
mean.Width.from.d.Lower contained in Summary list:mean width of the lower portion of the confidence interval (from d)
mean.Width.from.d.Upper contained in Summary list:mean width of the upper portion of the confidence interval (from d)
Type.I.Error.Upper contained in Summary list: Type I error rate from upper side
Type.I.Error.Lower contained in Summary list: Type I error rate from the lower side

Note

Returns three lists, where each list has multiple components.

Author(s)

Ken Kelley (University of Notre Dame; KKelley@ND.Edu)

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 where 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

[Package MBESS version 2.0.0 Index]