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

Source: R/statpsych1.R

Performs a computer simulation of confidence interval performance for a population median difference in a paired-samples design. Sample data for the two levels of the within-subjects factor can be generated from bivariate population distributions with five different marginal distributions. All distributions are scaled to have standard deviations of 1.0 at level 1. Bivariate random data with specified marginal skewness and kurtosis are generated using the unonr function in the mnonr package.

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

Arguments

alpha

alpha level for 1-alpha confidence

n

sample size

sd.ratio

ratio of population standard deviations

cor

population correlation of paired observations

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)

rep

number of Monte Carlo samples

Value

Returns a 1-row matrix. The columns are:

  • Coverage - probability of confidence interval including population median difference

  • Lower Error - probability of lower limit greater than population median difference

  • Upper Error - probability of upper limit less than population median difference

  • Ave CI Width - average confidence interval width

Examples

sim.ci.median.ps(.05, 30, 1.5, .7, 4, 3, 1000)
#>  Coverage Lower Error Upper Error Ave CI Width
#>     0.963       0.029       0.008    0.9587446

# Should return (within sampling error):
# Coverage Lower Error Upper Error Ave CI Width
#    0.961       0.026       0.013    0.9435462