Fisher s exact test

Race is handled precisely as gender was, with the exception that Fisher s exact test is used for the therapy comparison between Active and Placebo. ... 

P-values Age = Wilcoxon rank-sum, Gender = Pearson s chi-square, Race = Fisher s exact test. 

If the normal approximation to the binomial distribution is not valid (that is, more than 20% of expected cell counts are less than 5) for drug therapy and symptom of headache, then you can use Fisher s exact test, which is a nonparametric test, to test for a difference in proportions. To get the p-value using Fisher s exact test, you run the following SAS code ... 

The test material, test cells, used, method of treatment, harvesting of cells, cytotoxicity assay, and so on, should be clearly stated as well as the statistical methods used. Richardson et al. (1989) recommend that comparison be made between the frequencies in control cells and at each dose level using Fisher s Exact Test. 

Fisher s exact test should be used to compare two sets of discontinuous, quantal (all or none) data. Small sets of such data can be checked by contingency data tables, such as those of Finney et al. (1963). Larger sets, however, require computation. These include frequency data such as incidences of mortality or certain histopatho-logical findings, and so on. Thus, the data can be expressed as ratios. These data do not fit on a continuous scale of measurement but usually involve numbers of responses classified as either negative or positive that is, contingency table situation (Sokal and Rohlf, 1994). 

Fisher s exact test must be used in preference to the chi-square test when there are small cell sizes. 

Though Fisher s Exact Test is preferable for analysis of most 2x2 contingency tables in toxicology, the chi square test is still widely used and is preferable in a few unusual situations (particularly if cell sizes are large yet only limited computational support is available). 

As in Fisher s exact test, the initial step is setting up a table (this time a RxC contingency table). This table would appear as follows ... 

Typically, comparison of incidences of any one type of lesion between controls and treated animals are made using the multiple 2x2 chi square test or Fisher s exact test with a modification of the numbers of animals as the denominators. Too often, experimenters exclude from consideration all those animals (in both groups) that died prior to the first animals being found with a lesion at that site. 

The test is repeated for all identifiable effects and for a number of different rates of exposure. Standard 2x2 contingency tables(2 ) are used to determine the odds of observing the bioassay outcome if the null hypothesis is true using Fisher s exact test. For all adverse effects, including cancer, the first rule of the strategy for deciding whether a substance is toxic is to ... 

The practical consequence from this is that in the study type under consideration, always the dam/litter rather than the individual fetus is the basic statistical unit (see Chapters 23, 33, 34 and 35). Six malformed fetuses from six different litters in a treated group of dams is much more likely to constitute a teratogenic effect of the test substance than ten malformed fetuses all from the same litter. It is, therefore, important to report all fetal observations in this context and to select appropriate statistical tests (e.g., Fisher s exact test with Bonferroni correction) based on litter frequency. For continuous data, a procedure to calculate the mean value over the litter means (e.g., ANOVA followed by Dunnet s test) is preferred. An increase in variance (e.g., standard deviation), even without a change in the mean, may indicate that some animals were more susceptible than others, and may indicate the onset of a critical effect. 

For statistical analysis, fetal abnormality values belong to two types those where at least 50% of litters have one or more fetuses affected, and those where most litters have no affected fetuses. For the first type, the incidences (percentage of affected fetuses within that litter) are analyzed by the Kruskal-Wallis test (13) for the second type, the number of litters with affected fetuses is compared with the number with no affected fetuses by Fisher s Exact test (14). 

Pearson s chi-square test is what we refer to as a large sample test this means that provided the sample sizes are fairly large then it works well. Unfortunately when the sample sizes in the treatment groups are not large there can be problems. Under these circumstances we have an alternative test, Fisher s exact test. 

CH04 TESTS FOR SIMPLE TREATMENT COMPARISONS Table 4.5 Data for fisher s exact test... 

The rule of thumb for the use of Fisher s exact test is based on the expected frequencies in the 2x2 contingency table each of these need to be at least five for the chi-square test to be used. In the example, the expected frequencies in each of the two cells corresponding to success are 3.5, signalling that Fisher s exact test should be used. 

In fact, Fisher s exact test could be used under all circumstances for the calculation of the p-value, even when the sample sizes are not small. Historically, however, we tend not to do this Fisher s test requires some fairly hefty combinatorial calculations in large samples to get the null probabilities and in the past this was just too difficult. For larger samples p-values calculated using either the chi-square test or Fisher s exact test will be very similar so we tend to reserve use of Fisher s exact test for only those cases where there is a problem and use the chi-square test outside of that. 

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