
Le traitement statistique des proportions incluant l'analyse de variance, avec des exemples // The statistical handling of proportions including analysis of variance, with worked out examples
Full text PDF
Bibliographic information:
BibTEX format
RIS format
XML format
APA style
Cited references information:
BibTEX format
APA style
Doi:
10.20982/tqmp.17.3.p272
Laurencelle, Louis
272285
Keywords:
Proportions
, Transformation angulaire
, Proportions corrélées
, Analyse de variance
, Test de McNemar
, Angular transformation
, Correlated proportions
, Analysis of variance
, McNemar's test
(no sample data)
(Appendix)
The simple proportion, $p = x / n$, a pervasive statistical tool equally used in public and academic research areas, is in the literature still short of the necessary analytical implements needed for fullscale statistical treatments. This is partly ascribable to its discrete numerical character, but it proceeds mostly from its other distributional properties: its variance is tied up with its expectation, and its density shows a strong Ushaped asymmetry reactive to its $\pi $ parameter, the habitual normalbased analytical procedures thus being contraindicated. We here revive the FisherYates angular transformation of the proportion, $y\left ( {x,n} \right ) = si{n^{  1}}\sqrt x $, heralded for its $\pi $independent variance and smoothedout nonnormality, and put to trial three of its improved descendants (Anscombe 1948, Tukey \& Freeman 1950, Chanter 1975). Following a wouldbe thorough study of the three $y$ functions retained (bias, variance, precision, test accuracy, power), largely documented in Laurencelle's (2021a) investigation, we develop and illustrate the $z$ test of significance on one proportion, the $z$ test on the difference of two independent proportions, the analysis of variance of $k \ge 2$ independent proportions and finally the test of two and anova of $k$ correlated proportions. A critical appraisal of the McNemar test for the difference of two correlated proportions is also essayed.
