Recommended tests for association in 2×2 tables

  title={Recommended tests for association in 2×2 tables},
  author={Stian Lydersen and Morten Wang Fagerland and Petter Laake},
  journal={Statistics in Medicine},
The asymptotic Pearson's chi‐squared test and Fisher's exact test have long been the most used for testing association in 2×2 tables. Unconditional tests preserve the significance level and generally are more powerful than Fisher's exact test for moderate to small samples, but previously were disadvantaged by being computationally demanding. This disadvantage is now moot, as software to facilitate unconditional tests has been available for years. Moreover, Fisher's exact test with mid‐p… 

Unconditional tests for association in 2 × 2 contingency tables in the total sum fixed design

The asymptotic approach and Fisher's exact approach have often been used for testing the association between two dichotomous variables. The asymptotic approach may be appropriate to use in large

The analysis of 2 × 2 contingency tables—yet again: Author's reply

We thank John Richardson for taking an interest in our recent article [1]. Richardson finds that we ought to have mentioned the ‘N −1’ chi-squared test as a recommended method for testing association

Good practice in testing for an association in contingency tables

Evidence that influential biostatistical textbooks give contradictory and incomplete advice on good practice in the analysis of contingency table data is presented and greater use of exact testing rather than tests which use an asymptotic chi-squared distribution is called for.

An exact, unconditional, nuisance-agnostic test for contingency tables

Exact tests greatly improve the analysis of contingency tables when marginals are low. For instance, researchers often use Fisher’s exact test, which is conditional, or Barnard’s test, which is

A New Test for Independence in 2×2 Contingency Tables

In statistical literature there exist many tests to reveal the independence of two qualitative variables in two‑way contingency tables (CTs), in particular in 2×2 CTs. In this paper four independence

Using Lancaster's mid-P correction to the Fisher's exact test for adverse impact analyses.

Lancaster's mid-P (LMP) test is reviewed, an adjustment to the FET that tends to have increased power while maintaining a Type I error rate close to the nominal level that was found to outperform theFET across a wide range of conditions typical of adverse impact analyses.

Power evaluation of asymptotic tests for comparing two binomial proportions to detect direct and indirect association in large-scale studies

Comparisons of the power functions of three popular asymptotic tests show that when the design is balanced between the two binomials, the three tests are equivalent in terms of power, but when theDesign is unbalanced, differences in power can be substantial and the choice of the most powerful test also depends on the value of the parameters of the two compared binomial.

How to analyze many contingency tables simultaneously in genetic association studies

Realized randomized p-values are proposed as a solution which is especially useful for data-adaptive (plug-in) procedures and allow to estimate the proportion of true null hypotheses much more accurately than their non-randomized counterparts.

The LMS for testing independence in two-way contingency tables

Three of the so-called “chi-squared tests”—the T3 test, BP test and |χ| test—were selected and compared with a logarithmic minimum test, which is the author’s proposal.

The McNemar test for binary matched-pairs data: mid-p and asymptotic are better than exact conditional

An easy-to-calculate mid-p version of the McNemar exact conditional test is examined for the analysis of paired binomial proportions and is an excellent alternative to the complex exact unconditional test.



Comparison of exact tests for association in unordered contingency tables using standard, mid-p, and randomized test versions

Pearson’s chi-square (Pe), likelihood ratio (LR), and Fisher (Fi)–Freeman–Halton test statistics are commonly used to test the association of an unordered r×c contingency table. Asymptotically, these

Power comparison of two‐sided exact tests for association in 2 × 2 contingency tables using standard, mid p and randomized test versions

The power and obtained significance level of the standard, mid p, and randomized versions of the Pearson's chi square, likelihood ratio, and Fisher's tests are compared for two-sided tests in 2 x 2 tables, using binomial and multinomial sampling.

Exact tests for 2×2 contingency tables

Abstract Fisher's exact test, difference in proportions, log odds ratio, Pearson's chi-squared, and likelihood ratio are compared as test statistics for testing independence of two dichotomous

Tests for the homogeneity of two binomial proportions in extremely unbalanced 2 × 2 contingency tables

The conditional exact test is more powerful than the unconditional exact test in extremely unbalanced cases whose sample ratio is greater than 20, and is compared with the Berger and Boos approach.

A Comparison of the Three Conditional Exact Tests in Two‐way Contingency Tables Using the Unconditional Exact Power

The conditional exact tests of homogeneity of two binomial proportions are often used in small samples, because the exact tests guarantee to keep the size under the nominal level. The Fisher's exact

Raised conditional level of significance for the 2 × 2‐table when testing the equality of two probabilities

In this paper it is to be shown that Fisher's non‐randomizing exact test for 2 × 2‐tables, which is a conditional test, can by simple means be changed into an unconditional test using raised levels

Exact Unconditional Sample Sizes for the 2 Times 2 Binomial Trial

SUMMARY Exact attained significance level and sample size methods are developed for use with the unconditional Z statistic in the 2 x 2 contingency table from two independent binomial samples of

A Cautionary Note on Exact Unconditional Inference for a Difference between Two Independent Binomial Proportions

Boschloo's test, in which the p-value from Fisher's test is used as the test statistic in an exact unconditional test, is uniformly more powerful than Fisher'sTest, and is also recommended.

A quasi-exact test for comparing two binomial proportions.

It is shown that the actual levels of significance of the mid-P-test tend to be closer to the nominal level as compared with various classical tests.

Tests of Significance for 2 × 2 Contingency Tables

Fisher's exact test, and the approximation to it by the continuity-corrected X 2 test, have repeatedly been attacked over the past 40 years, recently with the support of extensive computer exercises.