Simulates confidence interval coverage probability for a Pearson correlation

Source: R/statpsych2.R

Performs a computer simulation of confidence interval performance for a Pearson correlation. A bias adjustment is used to reduce the bias of the Fisher transformed Pearson correlation. Sample data can be generated from bivariate population distributions with five different marginal distributions. All distributions are scaled to have standard deviations of 1.0. Bivariate random data with specified marginal skewness and kurtosis are generated using the unonr function in the mnonr package.

sim.ci.cor(alpha, n, cor, dist1, dist2, rep)

Arguments

alpha

alpha level for 1-alpha confidence

n

sample size

cor

population Pearson correlation

dist1

type of distribution for variable 1 (1, 2, 3, 4, or 5)

dist2

type of distribution for variable 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 correlation

  • Lower Error - probability of lower limit greater than population correlation

  • Upper Error - probability of upper limit less than population correlation

  • Ave CI Width - average confidence interval width

Examples

sim.ci.cor(.05, 30, .7, 4, 5, 1000)
#>      Coverage Lower Error Upper Error Ave CI Width
#> [1,]    0.935       0.042       0.023    0.3887633

# Should return (within sampling error):
#      Coverage Lower Error Upper Error Ave CI Width
# [1,]  0.93815     0.05125      0.0106    0.7778518