Simulates confidence interval coverage probability for a mean

Source: R/statpsych1.R

Performs a computer simulation of the confidence interval performance for a population mean. Sample data can be generated from five different population distributions. All distributions are scaled to have standard deviations of 1.0.

sim.ci.mean(alpha, n, dist, rep)

Arguments

alpha

alpha level for 1-alpha confidence

n

sample size

dist

type of distribution (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 mean

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

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

  • Ave CI Width - average confidence interval width

Examples

sim.ci.mean(.05, 40, 4, 1000)
#>  Coverage Lower Error Upper Error Ave CI Width
#>     0.952       0.018        0.03    0.6341142

# Should return (within sampling error):
# Coverage Lower Error Upper Error Ave CI Width
#  0.94722     0.01738      0.0354    0.6333067