Fishers exact test

Lifetime exposure of rats to hexachloroethane resulted in renal carcinomas and adenomas in Fischer-344 male rats (NTP 1989). The incidence of adenomas was 1/50 for the controls, 2/50 for animals at a dose of 10 mg/kg/day, and 4/50 for animals at a dose of 20 mg/kg/day. In the animals from the high-dose group, there were also 3/50 renal carcinomas. The number of tumors (carcinomas and adenomas) was significantly greater in exposed rats than in both controls and historical controls using the Fisher Exact Test (NTP 1989). No tumors were seen in the female rats. 

A statistically significant increase in hepatocellular carcinomas was seen in male and female mice that were dosed with 590 and 1,179 mg/kg/day hexachloroethane in com oil by gavage for 78 continuous weeks (Weisburger 1977). The incidence of tumors in the exposed mice was greater than that in controls on the basis of both the Fisher Exact test and the Cochran-Armitage test. There were no hepatic tumors in male or female rats with chronic exposure to doses of 10-423 mg/kg/day (NTP 1977, 1989 Weisburger 1977). 

Significantly more pre-pubescent animals investigated the environment with chemosensory behaviors at Ndarakwai (53.5%) than at AENP (38.2%) (Fisher Exact Test, P = 0.04), but no such difference existed for post-pubescent elephants (57% and 62%, respectively, P = 0.46). The likelihood of performing chemosensory behaviors to urine or feces did not differ between the populations for pre-pubescent (P= 1.0) or post-pubescent elephants (P = 0.85). The same trends were evident if only the main trunk chemosensory behaviors (SCPF) were considered... 

Cancer. Increased incidences of relatively rare renal tubular cell adenomas and carcinomas were observed in male rats, but the increases were not statistically significant by the Fisher Exact test or the Cochran-Armitage test (NTP 1986). When adjusted for mortality, however, the increased incidences were significantly different from control in the high-dose males when analyzed by the Lifetable test and significant for dose-related trend by the Lifetable and the Incidental Tumor tests. 

As the kidney tumors were not fatal, the appropriateness of Lifetable test for the analysis of these tumors is questionable. The overall unadjusted incidences were significantly different from the historical control incidence by the Fisher Exact test. The kidney tumors were not observed in female rats or in male or female mice. 

In some instances, particularly with respect to occurrence of specific disorders, the total numbers of events were very small. For these comparisons, a Fisher exact test was used to generate the probability of observing the number of events actually reported by the respondents, given the numbers observed in each of the two comparison groups. For example, assume that 10 of the respondents reported a particular disability, including 4 exposed subjects and 6 who were not exposed. The exact test provides the probability that the 10 reported events would include 4 or more exposed subjects (an excess as great as or greater than that observed). 

Statistical significance is assessed by means of the Fisher-exact-test. 

Two different types of in silico analysis are relevant for in silica target deconvolution (i) correlation analysis between phenotypic screening results and the in vitro biochemical profile of the screened compounds and (ii) machine learning models to predict the targets for the hits in the phenotypic screening. Two independent studies have been published very recently where the Fisher exact test... 

Figure 4.5 The results from a Fisher exact test analysis to identify targets in a TNF i screen. For example, p-value (/-axis) plotted against the odds ratio (X-axis).

An example of the outcome of a Fisher exact test is shown in Figure 4.5. A set of MMoA-annotated compounds were screened for inhibition of TNF-a production in lipopolysaccharide-stimulated THP-1 cells. The TNF-a pathway is well characterized and many known protein nodes, such as IKBKB, were identified in the analysis. Target discovery was consistent with a pathway enrichment analysis and, for each protein, a contigency table was constructed with /i-value and odds ratio calculated. To make sure that the / -values identified were significant when testing many different targets, a Bonferroni correction term - a method used to counteract the problem of multiple comparisons, which occurs when a set of statistical inferences are considered simultaneously - was applied. 

After collecting the data, the same have been worked in the software Ergofellow 3.0, Microsoft Excel and IBM SPSS statistics software SPSS version 22.0. The test applied to this study was the Fisher exact test. 

Correlation coefficient Spearman s Rank Correlation Kendall Tau Coefficient gamma Chi square Phi coefficient Fisher exact test Kendall coefficient of concordance... 

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 ... 

Statistical analysis For statistical analysis of the behavioral tests an analysis of variance (two-way ANOVA) was used. For the symptomatology a Fisher exact probability test or an unpaired t-test with Welch s correction was used. In all tests p values <0.05 were considered significant. 

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. 

Multiple Pairwise Group Comparisons by Fisher-Irwin 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. 

TABLE 22.8. Average Number of Animals Needed to Detect a Significant Increase in the Incidence of an Event (tumors, anomalies, etc.) over the Background Incidence (control) at Several Expected Incidence Levels Using the Fisher Exact Probability Test (p = 0.05)... 

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