Some contributions to practice of 2 × 2 contingency tables

Piotr Sulewski

Journal of Applied Statistics, 2019, vol. 46, issue 8, 1438-1455

Abstract: This paper focuses on $ 2 \times 2 $ 2×2 contingency tables (CTs) used to accept or reject $ {H_0} $ H0 hypothesis that two categorical features are independent. This paper promotes a new view of the essence of CTs. Particular CTs are created as a result of phenomena governed by random factors. We put forward four simple scenarios under which CTs may be created. Further in the paper, a measure of untruthfulness of $ {H_0} $ H0, which also may serve as the test statistics, is defined. The paper recalls several CT-related test statistics. Each test statistics produces its own power-of-the-test (PoT) function. The PoTs were determined with the Monte Carlo method and then compared to each other. In order to ease such a PoT-to-PoT comparison, the measure named ‘average outgoing untruthfulness level’ is put forward. Derivation, properties and example how to apply the measure in practice are given in details.

Date: 2019
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DOI: 10.1080/02664763.2018.1552665

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