Simulates confidence interval coverage probability for a standardized mean difference in a paired-samples design

Source: R/statpsych1.R

Performs a computer simulation of confidence interval performance for two types of standardized mean differences in a paired-samples design (see ci.stdmean.ps). Sample data for the two levels of the within-subjects factor can be generated from five different population distributions. All distributions are scaled to have standard deviations of 1.0 at level 1.

sim.ci.stdmean.ps(alpha, n, sd.ratio, cor, dist1, dist2, d, rep)

Arguments

alpha

alpha level for 1-alpha confidence

n

sample size

sd.ratio

ratio of population standard deviations (sd2/sd1)

cor

correlation between paired measurements

dist1

type of distribution at level 1 (1, 2, 3, 4, or 5)

dist2

type of distribution at level 2 (1, 2, 3, 4, or 5)

  • 1 = Gaussian (skewness = 0 and excess kurtosis = 0)

  • 2 = platykurtic (skewness = 0 and excess kurtosis = -1.2)

  • 3 = leptokurtic (skewness = 0 and excess kurtosis = 6)

  • 4 = moderate skew (skewness = 1 and excess kurtosis = 1.5)

  • 5 = large skew (skewness = 2 and excess kurtosis = 6)

d

population standardized mean difference

rep

number of Monte Carlo samples

Value

Returns a 1-row matrix. The columns are:

  • Coverage - Probability of confidence interval including population std mean difference

  • Lower Error - Probability of lower limit greater than population std mean difference

  • Upper Error - Probability of upper limit less than population std mean difference

  • Ave CI Width - Average confidence interval width

Examples

sim.ci.stdmean.ps(.05, 20, 1.5, .8, 4, 4, .5, 2000)
#>                         Coverage Lower Error Upper Error Ave CI Width   Ave Est
#> Unweighted Standardizer   0.8905       0.069      0.0405    0.7371796 0.5318356
#> Level 1 Standardizer      0.9310       0.043      0.0260    0.9285844 0.5182281

# Should return (within sampling error):
#                         Coverage Lower Error Upper Error Ave CI Width   Ave Est
# Unweighted Standardizer   0.9095      0.0555       0.035    0.7354865 0.5186796
# Level 1 Standardizer      0.9525      0.0255       0.022    0.9330036 0.5058198