Fisher's exact test is a statistical test used to analyze categorical data, typically in a contingency table format, such as in clinical trials where the outcome variable is categorical, like the presence or absence of a disease or adverse event.

For example, let's consider a clinical trial testing the efficacy of a new drug for treating a specific condition. The trial randomly assigns patients to one of two treatment groups: Group A receiving the new drug and Group B receiving a placebo. The primary outcome measure is the proportion of patients in each group who experience a specific adverse event.

The data from the clinical trial can be presented in a contingency table, where the rows represent the treatment groups (Group A and Group B) and the columns represent the presence or absence of the adverse event (Yes and No). Fisher's exact test can be used to determine whether there is a significant difference in the proportion of patients experiencing the adverse event between the treatment groups.

The null hypothesis for Fisher's exact test is that there is no association between the treatment group and the occurrence of the adverse event. The alternative hypothesis is that there is a significant association.

Fisher's exact test works by calculating the probability of obtaining the observed data or more extreme data under the null hypothesis. This probability is determined using a hypergeometric distribution, which takes into account the total number of patients, the number of patients in each treatment group, and the number of patients in each group who experience the adverse event.

If the p-value from Fisher's exact test is less than the pre-specified alpha level (usually 0.05), then the null hypothesis is rejected, and it can be concluded that there is a significant association between the treatment group and the occurrence of the adverse event. Conversely, if the p-value is greater than the alpha level, then the null hypothesis is not rejected, and it can be concluded that there is not a significant association between the treatment group and the occurrence of the adverse event.

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