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hbiostat.org | ||
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fharrell.com
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| | | | | In this article I provide much more extensive simulations showing the near perfect agreement between the odds ratio (OR) from a proportional odds (PO) model, and the Wilcoxon two-sample test statistic. The agreement is studied by degree of violation of the PO assumption and by the sample size. A refinement in the conversion formula between the OR and the Wilcoxon statistic scaled to 0-1 (corcordance probability) is provided. | |
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fharrell.com
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| | | | | Since the Wilcoxon test is a special case of the proportional odds (PO) model, if one likes the Wilcoxon test, one must like the PO model. This is made more convincing by showing examples of how one may accurately compute the Wilcoxon statistic from the PO model's odds ratio. | |
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fharrell.com
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| | | | | This article briefly discusses why the rank difference test is better than the Wilcoxon signed-rank test for paired data, then shows how to generalize the rank difference test using the proportional odds ordinal logistic semiparametric regression model. To make the regression model work for non-independent (paired) measurements, the robust cluster sandwich covariance estimator is used for the log odds ratio. Power and type I assertion \alpha probabilities are compared with the paired t-test for n=25. The ordinal model yields \alpha=0.05 under the null and has power that is virtually as good as the optimum paired t-test. For non-normal data the ordinal model power exceeds that of the parametric test. | |
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djalil.chafai.net
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| | | Convergence in law to a constant. Let \( {{(X_n)}_{n\geq1}} \) be a sequence of random variables defined on a common probability space \( {(\Omega,\mathcal{A},\mathbb{P})} \), and taking their values in a metric space \( {(E,d)} \) equipped with its Borel sigma-field. It is well known that if \( {{(X_n)}_{n\geq1}} \) converges in law as \( {n\rightarrow\infty} \) to some Dirac... | ||
