empirical_quantile_one_way {LRTesteR}

Test the equality of a quantile from an unknown distribution.

Description

Test the equality of a quantile from an unknown distribution.

Usage

empirical_quantile_one_way(x, Q, fctr, conf.level = 0.95)

Arguments

x

a numeric vector.

Q

The quantile. A single numeric number. (.50 is median.)

fctr

a factor vector indicating groups.

conf.level

overall confidence level of the likelihood intervals. Uses Bonferroni correction.

Details

• Null: Quantiles are equal. (Q1 = Q2 ... Qk).

• Alternative: At least one quantile is not equal.

Value

An S3 class containing the test statistic, p value, list of likelihood based confidence intervals, overall confidence level, individual confidence level of each interval and alternative hypothesis.

Source

• Yudi Pawitan. In All Likelihood. Oxford University Press.

• Owen. Empirical Likelihood. Chapman & Hall/CRC.

Examples

library(LRTesteR)

# Null is true
set.seed(1)
x <- rnorm(75, 1, 1)
fctr <- c(rep(1, 25), rep(2, 25), rep(3, 25))
fctr <- factor(fctr, levels = c("1", "2", "3"))
empirical_quantile_one_way(x, .50, fctr, .95)

# Null is false
set.seed(1)
x <- c(rnorm(25, 1, 1), rnorm(25, 2, 1), rnorm(25, 3, 1))
fctr <- c(rep(1, 25), rep(2, 25), rep(3, 25))
fctr <- factor(fctr, levels = c("1", "2", "3"))
empirical_quantile_one_way(x, .50, fctr, .95)