en:statpqpl:porown2grpl:nparpl:fisher2x2pl

These tests are based on data collected in the form of a contingency table of 2 features (, ), each of which has possible categories and (look at the table(\ref{tab_kontyngencji_obser})).

**The Chi-square test with the Yate's correction for continuity**

The test with the Yate's correction (Frank Yates (1934)^{1)}) is a more conservative test than the Chi-square test (it rejects a null hypothesis more rarely than the test). The correction for continuity guarantees the possibility of taking in all the values of real numbers by a test statistic, according to the distribution assumption.

The test statistic is defined by:

**The Fisher test for (2×2) tables**

The Fisher test for tables is also called the Fisher exact test (R. A. Fisher (1934)^{2)}, (1935)^{3)}). This test enables you to calculate the exact probability of the occurrence of the particular number distribution in a table (knowing and defined marginal sums.

If you know each marginal sum, you can calculate the probability for various configurations of observed frequencies. The exact significance level is the sum of probabilities which are less or equal to the analysed probability.

The mid-p is the Fisher exact test correction. This modified p-value is recommended by many statisticians (Lancaster 1961^{4)}, Anscombe 1981^{5)}, Pratt and Gibbons 1981^{6)}, Plackett 1984^{7)}, Miettinen 1985^{8)} and Barnard 1989^{9)}, Rothman 2008^{10)}) as a method used in decreasing the Fisher exact test conservatism. As a result, using the mid-p the null hypothesis is rejected much more qucikly than by using the Fisher exact test. For large samples a p-value is calculated by using the test with the Yate's correction and the Fisher test gives quite similar results. But a p-value of the test without any correction corresponds with the mid-p.

The p-value of the mid-p is calculated by the transformation of the probability value for the Fisher exact test. The one-sided p-value is calculated by using the following formula:

where:

– one-sided p-value of mid-p,

– one-sided p-value of Fisher exact test,

and the two-sided p-value is defined as a doubled value of the smaller one-sided probability:

where:

– two-sided p-value of mid-p.

The settings window with the `chi-square test and its corrections`

can be opened in `Statistics`

menu → `NonParametric tests`

→`Chi-square, Fisher, OR/RR`

or in ''Wizard''.

Yates F. (1934), Contingency tables involving small numbers and the chi-square test. Journal of the Royal Statistical Society, 1,2 17-235

Fisher R.A. (1934), Statistical methods for research workers (5th ed.). Edinburgh: Oliver and Boyd.

Fisher R.A. (1935), The logic of inductive inference. Journal of the Royal Statistical Society, Series A, 98,39-54

Lancaster H.O. (1961), Significance tests in discrete distributions. Journal of the American Statistical Association 56:223-234

Anscombe F.J. (1981), Computing in Statistical Science through APL. Springer-Verlag, New York

Pratt J.W. and Gibbons J.D. (1981), Concepts of Nonparametric Theory. Springer-Verlag, New York

Plackett R.L. (1984), Discussion of Yates' „Tests of significance for 2×2 contingency tables”. Journal of Royal Statistical Society Series A 147:426-463

Miettinen O.S. (1985), Theoretical Epidemiology: Principles of Occurrence Research in Medicine. John Wiley and Sons, New York

Barnard G.A. (1989), On alleged gains in power from lower p-values. Statistics in Medicine 8:1469-1477

Rothman K.J., Greenland S., Lash T.L. (2008), Modern Epidemiology, 3rd ed. (Lippincott Williams and Wilkins) 221-225

en/statpqpl/porown2grpl/nparpl/fisher2x2pl.txt · ostatnio zmienione: 2022/02/12 12:49 przez admin

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