Comments on “Two‐tailed significance tests for 2 × 2 contingency tables: What is the alternative?” by Robin J Prescott <i>Statistics in Medicine</i> 2019;38:4264‐4269

Andrés, Antonio Martín; Tejedor, I. Herranz; Moreno, Francisco Gayá

doi:10.1002/sim.8432

Cited by 1 publication

(4 citation statements)

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“…As stated previously in the third paragraph of the Section 1, Mantel (1974) explained how to determine the p ‐value of the two‐tailed test based on the statistic

{\chi}_{Y(i)}^2

and from the perspective of conditional inference. Martín Andrés et al (2020) extended the idea to the statistic

{\chi}_{OR- XY}^2

. Here we also generalize it to the case of the other statistics and the other parameters.…”

Section: Proposed Inference Methodsmentioning

confidence: 93%

“…Something similar occurs with the XC , ZY , and ZC statistics. However, this approach makes the test very conservative (see e.g., Martín Andrés et al, 2020 in the

{\chi}_{OR- XY}^2

statistic). The inference methods that are obtained by “doubling the p ‐value” will be denominated in a general way by adding letter D : methods XYD , XCD , ZYD and ZCD .…”

Section: Proposed Inference Methodsmentioning

confidence: 99%

“…Nevertheless, the version with cc by Conover has not been defined in them, nor has the performance been assessed for the data from Model II, with or without the precaution of Mantel, and finally their definitions have not been modified in order to obtain coherent values. The only exception to what is stated previously is that in the case of the OR parameter, since recently Martín Andrés et al (2020) proposed the application of the Mantel method to the Yates statistic. Moreover, when the maximum likelihood estimators of the unknown parameters are obtained under the null hypothesis, the z statistic from the score test is equivalent to the chi‐square statistic; but this does not happen in another case.…”

Section: Introductionmentioning

confidence: 90%

“…The independence test in 2 × 2 tables has a long, controversial and complicated history (Martín Andrés, 1998; Martín Andrés, Herranz Tejedor, & Gayá Moreno, 2020), and this applies both to the exact test and the asymptotic test. In both cases, the test to be used depends on whether or not the researcher is in favor of the conditional method (Fisher, 1935) or the unconditional method (Barnard, 1947).…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

The Yates, Conover, and Mantel statistics in 2 × 2 tables revisited (and extended)

Martín Andrés,

Hernández,

Gayá Moreno

2023

Statistica Neerlandica

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Asymptotic inferences about the difference, ratio or odds‐ratio of two independent proportions are very common in diverse fields. This article defines for each parameter eight conditional inference methods. These methods depend on: (1) using a chi‐squared type statistic or a z type one; (2) using the classic Yates continuity correction or the less well‐known Conover one; and (3) whether the p‐value of the test is determined by doubling the one‐tailed p‐value or by the Mantel method (asymmetrical approach). In all cases, the conclusions are: (i) the methods based on the chi‐squared statistic should not be used, as they are too liberal; (ii) for those in favour of using the criterion of doubling the p‐value, the best method is using the z statistic with Conover continuity correction; and (iii) for those in favour of the asymmetrical approach, the best method is based on the z statistic with Conover continuity correction and the Mantel p‐value.This article is protected by copyright. All rights reserved.

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“…As stated previously in the third paragraph of the Section 1, Mantel (1974) explained how to determine the p ‐value of the two‐tailed test based on the statistic

{\chi}_{Y(i)}^2

and from the perspective of conditional inference. Martín Andrés et al (2020) extended the idea to the statistic

{\chi}_{OR- XY}^2

. Here we also generalize it to the case of the other statistics and the other parameters.…”

Section: Proposed Inference Methodsmentioning

confidence: 93%

“…Something similar occurs with the XC , ZY , and ZC statistics. However, this approach makes the test very conservative (see e.g., Martín Andrés et al, 2020 in the

{\chi}_{OR- XY}^2

statistic). The inference methods that are obtained by “doubling the p ‐value” will be denominated in a general way by adding letter D : methods XYD , XCD , ZYD and ZCD .…”

Section: Proposed Inference Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 90%