
Fisher procedure demonstrated with an example
The Fisher's Exact TestFisher's exact test is particularly appropriate when dealing with small samples. This section only covers test on a 2 by 2 table. That is, there are two variables, each has two categories. Comparing to the contingency chisquare test, Fisher's exact test is to exaclty calculate the pvalue rather than being based on an asymptotic approximation. For Fisher's test, the Pvalue for the nondirectional test is NOT twice the pvalue for the directional test, as would be for a normal test. Analyzing the data with Fisher's testConsider the following example. Extracorporeal membrane oxygenation (ECMO) is a potentially lifesaving procedure that is used to treat newborn babies who suffer from severe respiratory failure. An experiment was conduted in which 29 babies were treated with EcMO and 10 babies were treated with conventional medical therapy (CMT). Among the 5 babies died, 4 were treated with CMT and among the 34 babies survided, 6 were treated with CMT. Data is available as "ecmo.csv". Open the data set from SAS. Or import with the following command. data ecmo; infile "H:\sas\data\ecmo.csv" dlm=',' firstobs=2; input subject treament $ result $; run; proc freq data=ecmo; title "Fish's exact test for small 2 by 2 tables"; tables treatment*result / chisq expected norow nocol nopercent; run; The control option "expected" asks for expected value for assumption checking. The other options such as "norow" eliminate unwanted outputs for clarity. The key output and intepretationFish's exact test for small 2 by 2 tables The FREQ Procedure Table of treatment by result treatment result Frequency Expected die live  Total  CMT  4  6  10  1.2821  8.7179   ECMO  1  28  29  3.7179  25.282   Total 5 34 39 Fisher's Exact Test  Cell (1,1) Frequency (F) 4 Leftsided Pr <= F 0.9996 Rightsided Pr >= F 0.0110 Table Probability (P) 0.0106 Twosided Pr <= P 0.0110 Sample Size = 39 The pvalue for the Fisher's exact test is 0.011 for a nondirectional test. So the epxeriment provided strong evidence that ECMO really is different from CMT. Furthermore, the Pvalue for a directional test (Ha: ECMO > CMT) is 0.011 (happen to the same as the nondirectional test), so we could also conclude that ECMO really is better than CMT.

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