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Pour la différence entre deux proportions jumelées, un nouveau test, plus valide et plus puissant [A new standard normal-based test for the difference between paired proportions to supersede obsolete McNemar-like and other indirect procedures]

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Doi: 10.20982/tqmp.19.3.p254

Laurencelle, Louis
Keywords: McNemar , difference between paired proportions , alternative test
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Contrarily to the 6-faced dice or the head/tail coin with their a priori fixed probability values, proportions used in applied research are generally based on heterogeneous and inconstant sources, the mathematical binomial model suiting them only as a first approximation. Moreover, the shape of their distributions is strongly tied to each proportion's mean value, a fact that rules out a direct binomial calculation for comparing them and assessing their difference. When the compared proportions are paired, i.e. based on the same sources, the awkwardness of the binomial solution simply jumps skyward, their proposed implementations being doubtful and their exegeses warped and indirect. Quinn McNemar's 1947 chi-squared solution, simple and straightforward, has long won users' adhesion, however it is based on the sole subset of option changing data pairs, putting aside all stable ones. We hereby describe a new, fully documented procedure for testing the difference between two paired proportions. It is anchored on the normal probability model and uses the Fisher-Zubin-Anscombe binomial-to-normal transformation. It is shown to be more precise and more powerful than the previous indirect and convoluted approaches, and it links empirical proportions to the full set of linear variables qualified for standard normal-based analyses, including ANOVA.

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