qad (version 0.1.2)

cci: Conditional confidence interval

Description

Conditioned on the sample size n, approximated confidence intervals of the dependence measure qad(x,y) for independent random variables are computed. cci() can be used to test two random variables for independence.

Usage

cci(n, alternative = c("one.sided", "two.sided"))

Arguments

n

an integer indicating the sample size.

alternative

character string specifying the type of the confidence interval; must be one of "one.sided" (default) or "two.sided".

Value

a named vector indicating the lower and upper boundary of the confidence interval.

Details

alternative = "one.sided" provides a one-sided confidence interval, which can be interpreted that in 95 of 100 realizations of two independet random variables X and Y the calculated dependence measure qad(x,y) is less than the upper interval boundary. If alternative = "two.sided" 95 of 100 realizations lie in between the interval boundaries.

Examples

# NOT RUN {
set.seed(31415)
n <- 100
x <- runif(n, -2, 2)
y <- x^2 + rnorm(n, 0, 1)
sample <- data.frame(x, y)
plot(sample)
mod <- qad(sample, print = FALSE)

#Test for H0: independence
cci(n, alternative = "one.sided")
coef(mod, select = c('q(x1,x2)'))
if(coef(mod, select = c('q(x1,x2)')) > cci(n, alternative = "one.sided")[2]){
  print('Reject H0')
}else{
  print('Accept H0')
}
# }