Some contributions to practice of 2 × 2 contingency tables
Piotr Sulewski · Journal of Applied Statistics · 2018
This paper focuses on 2×2 contingency tables (CTs) used to accept or reject 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 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.