CT_Distribution {ConcordanceTest}

Probability Distribution of the Concordance Coefficient and the Kruskal-Wallis Statistic

Description

This function computes the probability distribution tables of the Concordance coefficient and Kruskal-Wallis statistic. Probability distribution tables can be obtained exactly or by simulation (default option).

Usage

CT_Distribution(Sample_Sizes, Num_Sim = 10000, H = 0, verbose = TRUE)

Arguments

Sample_Sizes

Numeric vector (n1,...,nk) containing the number of repetitions of each element, i.e., the size of each sample in the experiment.

Num_Sim

Number of simulations in order to obtain the probability distribution of the statistics. The default is 10000. If set to 0, the probability distribution tables are obtained exactly. Otherwise they are obtained by simulation.

H

0 by default. If set to 1, the probability distribution table of the Kruskal-Wallis statistic is also calculated and returned.

verbose

A logical indicating if some "progress report" of the simulations should be given. The default is TRUE.

Value

The function returns a list with the following elements:

1. C_freq: Matrix with the probability distribution of the Concordance coefficient. Each row in the matrix contains the disorder, the value of the coefficient, the frequency and its probability.

2. H_freq: Matrix with the probability distribution of the Kruskal-Wallis statistic. Each row in the matrix contains the value of the statistic, the frequency and its probability (only if H = 1).

Warning

The computational time in exact calculations increases exponentially with the number of elements and with the number of sets.

Examples

Sample_Sizes <- c(5,4)
CT_Distribution(Sample_Sizes, Num_Sim = 0)
CT_Distribution(Sample_Sizes, Num_Sim = 0, H = 1)

CT_Distribution(Sample_Sizes, Num_Sim = 1000)
CT_Distribution(Sample_Sizes, Num_Sim = 1000, H = 1)