Tests non-parametriques de tendance sur les proportions

The problem of testing for a monotone trend in proportions has been frequently disccussed in the literature and in various applications. The popular Cochran-Armitage test has received much attention in the past. It is based on measuring the correlation between the proportions of observed success at any time point with a collection of monotone constants which mimic the time trend. Unfortunately the Cochran-Armitage is sensitive to the choice of these constants as well as to the sample sizes. In this thesis, we propose two nonparametric tests based on the ranks of the data. These tests rely on the notion of compatibility introduced by Alvo and Cabilio and required the specification of a distance function between permutations. We derive the statistics tests which correspond to the Spearman, Kendall and Hamming distances. It is shown that the Spearman and Kendall distances lead to the same test statistic. We show that the asymptotic null distributions of the Spearman and Hamming based test statistics are both normal. We study the non-null distributions through simulation under various scenarios. We conclude that the Spearman statistic has generally higher power and is therefore the recommended test. We also note that the modified Hamming based statistic yield a higher power than the Hamming statistic. Furthermore, in some cases the power of the modified Hamming statistic is very close to the power of the Spearman statistic.