Practical Tests of 2 × 2 Contingency Tables

Liddell, Douglas

doi:10.2307/2988087

Cited by 76 publications

(50 citation statements)

References 10 publications

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“…However, the test is computationally involved, and enormous computation is needed for power calculation (see Section 3). Another approach, due to Liddell (1978) and later followed by Storer and Kim (1990), is to reject the null hypothesis if an estimated p value is less than ¬ . If we use this latter approach, then a natural estimate of (7) is given by and [x] denotes the integer part of x.…”

Section: E Testmentioning

confidence: 99%

Hypothesis Testing About Proportions in Two Finite Populations

Krishnamoorthy

Thomson

2002

The American Statistician

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The problem of hypothesis testing about proportions in twonite populationsis addressed. The usual test based on the normal approximation (Z test) and a test based on estimated p values (E test) are considered. The exact properties of the tests are evaluated numerically. Numerical studies indicate that the E test is very satisfactory even for small samples and can be recommended for practical use. Power computation for a given level and sample size is also outlined for both tests. The testing methods are illustrated using an example.

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Section: E Testmentioning

confidence: 99%

Hypothesis Testing About Proportions in Two Finite Populations

Krishnamoorthy

Thomson

2002

The American Statistician

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“…Sous l'hypothèse nulle, on doit poser π 1 = π 2 = π; cependant, cette valeur unique de π n'est pas connue. Liddell (1978) propose l'estimateur du maximum de vraisemblance basé sur les données, soit la proportion La somme des 28 probabilités associées aux coupleś enumérés donne 0,05383; en doublant cette valeur pour un test bilatéral, nous obtenons la probabilité globale de 0,108.…”

Section: La Proposition Kendall-stuart Etunclassified

“…Notre test exact, correspondantà l'expression (14), a pour mérite d'exploiter le principe d'analyse proposé par Kendall et Stuart (1977),à l'instar de Liddell (1978); de ne faire intervenir aucune approximation, ni comme modèle de probabilité ni pour l'estimation de la probabilité de référence π 0 , et enfin de fournir une vraisemblance de l'hypothèse d'égalité: π 1 = π 2 , basée réalistement sur les proportions observées x 1 /n 1 et x 2 /n 2 . Nous retenons ici ce test commeétalon dans l'examen comparatif des autres tests.…”

Section: Répertoire Des Testsà Comparerunclassified

Le test binomial exact de la différence entre deux proportions et ses approximations [The exact binomial test between two proportions and its approximations]

Laurencelle¹

2017

TQMP

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Though it is a commonplace and quite frequent operation, the comparison of two independent proportions remains a problematic and ill understood issue in textbooks on applied statistics and for researchers. On the one hand, the comparison may be arrayed as a 2 × 2 contingency table and be referred to chi-square type calculations; on the other hand, it can be viewed as the difference between means based on 0 / 1 data, this perspective leading to alternative normal-type treatments. The main known solutions for deciding upon the difference between two proportions are reviewed and briefly discussed. An original, theoretically deduced solution that we deem 'exact' is then proposed. We conclude with a short numerical study that endorses two well-known approximate solutions. Résumé Situation statistique banale, voire quotidiennement rencontrée, la comparaison de deux proportions indépendantes demeure une opération problématique dans les ouvrages de statistique appliquée comme dans la pratique. D'un côté, cette comparaison peutêtre présentée dans le format d'un tableau de contingence 2 × 2, ce qui l'associe aux statistiques habituelles d'un tel tableau; d'un autre côté, la différence entre deux proportionséquivautà la différence entre deux moyennes indépendantes, en considérant que les valeurs moyennées sont des « 0 » et des « 1 », ce cas admettant un autre type de traitement. Nous revoyons ici les principales solutions proposées pour l'étude de la différence entre deux proportions, et nousélaborons par déduction notre propre solution, que nous croyons exacte. Dans une courteétude numérique, nousétablissons enfin les vertus de deux approximations déjà connues.

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“…The three well known tests for this purpose are respectively (a) Pearson chisquared test for large samples, (b) Chi-square test with Yates' continuity correction for intermediate sized samples (Yates, 1984) and (c) the Fisher's exact test for small samples. A considerable body of research have done a comparative analysis of these tests with respect to various characteristics and have concluded that Fisher's exact test and the Yates correction to Pearson's test are both extremely conservative (Berkson, 1978;Conover, 1974;Liddell, 1976;Grizzle, 1967;Kempthorne, 1979;Upton, 1982). An extensive study comparing the above two tests with 22 other alternative tests of independence corroborated the same (D 'Agostino, 1988).…”

Section: Conservativeness Of Fisher's Testmentioning

confidence: 99%

Tests of Independence for a $2 \times 2$ Contingency Table with Random Margins

Yu¹,

Bhadra²,

Nandram³

2017

IJSP

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Fisher's exact test is commonly used for testing the hypothesis of independence between the row and column variables in a r × c contingency table. It is a "small-sample" test since it is used when the sample size is not large enough for the Pearsonian chi-square test to be valid. Fisher's exact test conditions on both margins of a 2 × 2 table leading to a hypergeometric distribution of the cell counts under independence. Moreover, it is conservative in the sense that its actual significance level falls short of the nominal level. In this paper, we modify Fisher's exact test by lifting the restriction of fixed margins and allow the margins to be random. In doing so, we propose two new tests -a likelihood ratio test in a frequentist framework and a Bayes factor test in a Bayesian framework, both of which are based on a new multinomial distributional framework. We apply the three tests on data from the Worcester Heart Attack study and compare their power functions in assessing gender difference in the therapeutic management of patients with acute myocardial infarction (AMI).

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Practical Tests of 2 × 2 Contingency Tables

Cited by 76 publications

References 10 publications

Hypothesis Testing About Proportions in Two Finite Populations

Hypothesis Testing About Proportions in Two Finite Populations

Le test binomial exact de la différence entre deux proportions et ses approximations [The exact binomial test between two proportions and its approximations]

Tests of Independence for a $2 \times 2$ Contingency Table with Random Margins

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