Sensitivity analysis for sample size given the Accuracy in Parameter Estimation approach for the standardized mean difference.

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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

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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 the 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 were no significance tests? (pp. 221–257). Mahwah, NJ: Lawrence Erlbaum.

See Also

ss.aipe.smd

Examples

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# 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

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