cauchy_scale_one_way {LRTesteR}

Test the equality of scale parameters of cauchy distributions.

Description

Test the equality of scale parameters of cauchy distributions.

Usage

cauchy_scale_one_way(x, fctr, conf.level = 0.95)

Arguments

x

a numeric vector of at least 50 data values per group.

fctr

a factor vector indicating groups.

conf.level

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

Details

• Null: All scales are equal. (scale_1 = scale_2 ... scale_k).

• Alternative: At least one scale 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

• https://en.wikipedia.org/wiki/Likelihood-ratio_test

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

• Hodd, McKean, and Craig. Introduction to Mathematical Statistics. Pearson.

Examples

library(LRTesteR)

# Null is true
set.seed(1)
x <- rcauchy(n = 150, 1, 2)
fctr <- c(rep(1, 50), rep(2, 50), rep(3, 50))
fctr <- factor(fctr, levels = c("1", "2", "3"))
cauchy_scale_one_way(x, fctr, .95)

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