XLSTAT - Comparison of k proportions

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Principles of the comparison of k proportions

This type of parametric test is used to determine k (k>2) proportions can be considered as equal (null hypothesis H0) or if at least two proportions are significantly different (alternative hypothesis Ha).

Tests use for the comparison of k proportions

XLSTAT offers three different approaches to compare k proportions.

Chi-square test

This test is identical to that used for the contingency tables.

Monte Carlo method

The Monte Carlo method is used to calculate a distribution of the Chi² distance based on simulations with the constraint of complying with the total number of observations for the k groups. This results in an empirical distribution which gives a more reliable critical value (on condition that the number of simulations is large) than that given by the Chi-square theoretical distribution which corresponds to the asymptotic case.

Marascuilo procedure

It is advised to use the Marascuilo procedure only if the Chi-square test or the equivalent test based on Monte Carlo simulations reject H0. The Marascuilo procedure compares all pairs of proportions, which enables the proportions possibly responsible for rejecting H₀ to be identified.