A New Test for 2 × 2 Tables

  title={A New Test for 2 × 2 Tables},
  author={Rory A. Fisher},
  • R. Fisher
  • Published 1 September 1945
  • Psychology
  • Nature
UNDER this heading, G. A. Barnard1 puts forward a test which, in language adopted from Neyman and Pearson, “is more powerful than Fisher's”. This means in practice that the test advocated passes as significant certain classes of experimental result which, by the test I had put forward2, would have been judged insignificant; and that, as judged by Barnard's method, my test is thought to be too stringent. However one may choose to express it, the cause of the difference in these calculations is… 


SUMMARY THE attempt to reinterpret the common tests of significance used in scientific research as though they constituted some kind of acceptance procedure and led to "decisions" in Wald's sense,

Resolving the conflict over fisher's exact test†

Fisher's exact test for two-by-two contingency tables has repeatedly been criticized as being too conservative. These criticisms arise most frequently in the context of a planned experiment for which

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

“Repeated sampling from the same population?” A critique of Neyman and Pearson’s responses to Fisher

  • Mark Rubin
  • Psychology
    European Journal for Philosophy of Science
  • 2020
Fisher ( 1945a , 1945b , 1955 , 1956 , 1960 ) criticised the Neyman-Pearson approach to hypothesis testing by arguing that it relies on the assumption of “repeated sampling from the same population.”

The analysis of 2 × 1 and 2 × 2 contingency tables: an historical review

The historical development of analytic techniques for frequency data presented as 2 x 1 or 2 x 2 contingency tables is described and a single statistic approximating the chi-square distribution is used to test the hypothesis of an association between the two relevant variables.

Assessing the Global and Local Uncertainty of Scientific Evidence in the Presence of Model Misspecification

Non-parametric bootstrap methodologies for estimating the sampling distribution of the evidence estimator under model misspecification are developed, which allows us to determine how secure the authors are in their evidential statement.

Some empirical comparisons of exact, modified exact, and higher-order asymptotic tests of independence for ordered categorical variables

We present results of a simulation study investigating the behavior of some exact, modified exact,and asymptotic tests of independence for two-way contingency tables having ordinal row and column

Proportions: Inferences and Comparisons

This article selectively reviews asymptotic, exact, and Bayesian methods for inference about one proportion, or for comparing two proportions from separate samples. For a single proportion, interval

Analysis of 2 x 2 tables of frequencies: matching test to experimental design.

  • J. Ludbrook
  • Mathematics
    International journal of epidemiology
  • 2008
A review of published work, and the use of five different statistical procedures to analyse a 2 x 2 table, executed by StatXact, Testimate, Stata, SAS, SAS 9.1 and SPSS 16.0.

Exact inference for categorical data: recent advances and continuing controversies

Controversy continues about the appropriateness of some exact methods, primarily relating to their conservative nature because of discreteness, but adjusted exact methods based on the mid-P-value seem a reasonable way of reducing the severity of this problem.




In advocating the particular method he chooses for the interpretation of data of this important class he has, I believe, overlooked a difficulty which the approach based on, and giving the exact solution for, the classical view-point of x2 and the four-fold table was expressly devised to obviate.

On Contingency Tables.

  • E. B. Wilson
  • Mathematics
    Proceedings of the National Academy of Sciences of the United States of America
  • 1942
This worksheet focuses on constructing, understanding and using contingency tables.

A New Test for 2 × 2 Tables

IF an experiment yields results in the form of a 2 × 2 table: