Nonparametric Predictive Inference For Reproducibility of One-Way Layout Tests

Abstract

The reproducibility of research findings is of main interest in many disciplines. Reproducibility of a statistical test means that, if the experiment were repeated under the same conditions, it would lead to the same conclusion with regard to rejection of the null hypothesis. The probability that the test conclusion for the repeated test would be the same as the original test is called reproducibility probability (RP). The concept of test reproducibility is inherently a predictive inference problem. This thesis investigates the reproducibility of statistical hypothesis tests for One-Way Layout tests using Nonparametric Predictive Inference (NPI). NPI is a predictive approach based on few modelling assumptions that considers multiple future observations that are exchangeable with the data observations which makes it suitable for inference about reproducibility. The uncertainty can be quantified in NPI reproducibility through lower and upper reproducibility probabilities. This thesis considers reproducibility of general alternatives tests, including the Kruskal Wallis test and the one-way ANOVA test, as well as the Jonckheere-Terpstra test for the ordered alternative hypothesis. This thesis also considers reproducibility probabilities for the umbrella alternatives tests, specifically the Mack-Wolfe test and the Esra-Fikri test, as well as for slippage tests, namely, the Mosteller test. Deriving the exact NPI lower and upper reproducibility probabilities is not trivial for some tests and computationally challenging for large sample sizes. To address these difficulties, two NPI-based approaches are implemented, namely, the NPI sampling of orderings and the NPI-bootstrap techniques. The NPI reproducibility is low when the test statistic is close to the threshold between rejecting and not rejecting the null hypothesis. If the test statistic is close to the rejection threshold for tests with directional alternatives, reproducibility tends to be lower for rejection of the null hypothesis than for nonrejection. This may be problematic, in particular as rejection of the null hypothesis is often the main goal of statistical experiments.