tau3scen2new {chi2x3way}R Documentation

Marcortchino's index for three-way contingency tables under Scenario 2. Revised formulation.

Description

It provides the partition of the Marcotorchino' index as well of the $C_M$-statistic revised formula, under the Scenario 2, when probabilities are equal to the observed marginal frequencies. The constant in the computation of the $C_M$-statistic is different, it does not consider the denominator of the index and is equal to $(n-1)I$ where $n$ is the total individual number and $I$ the row category number.

Usage

tau3scen2new(X, digits = 3)

Arguments

X

The three-way contingency table.

digits

The minimum number of decimal places, digits, used for displaying the numerical summaries of the analysis. By default, digits = 3.

Value

z

The Marcotorchino's index partition under Scenario 2, we get five terms of the chi-square partition, three bivariate terms and a trivariate one. The output is in a matrix, the six rows of this matrix indicate the tau index numerator, the tau index, the percentage of explained inertia, the revised $C_M$-statistic, the degree of freedom, the p-value, respectively.

Note

This function belongs to the class chi3class.

Author(s)

Lombardo R, Takane Y and Beh EJ

References

Beh EJ and Lombardo R (2014) Correspondence Analysis: Theory, Practice and New Strategies. John Wiley & Sons. Lancaster H O (1951) Complex contingency tables treated by the partition of the chi-square. Journal of Royal Statistical Society, Series B, 13, 242-249.
Lombardo R Carlier A D'Ambra L (1996). Nonsymmetric correspondence analysis for three-way contingency tables. Methodologica, 4, 59-80.
Loisel S and Takane Y (2015) Partitions of Pearson's chi-square statistic for frequency tables: A comprehensive account. Computational Statistics, 31, 1429-1452.
Marcotorchino F (1985) Utilisation des comparaisons par paires en statistique des contingencies: Partie III. Etude du Centre Scientifique, IBM, France. No F 081

Examples

##---- Should be DIRECTLY executable !! ----
data(olive)
tau3scen2new(olive)

[Package chi2x3way version 1.1 Index]