# Exact p-value

## Definition of Exact p-value

Exact p-value: The Exact p-value is the probability of obtaining a test statistic at least as extreme as the one that was actually observed, assuming that the null hypothesis is true.

## What is Exact p-value used for?

Exact p-values are used to help assess the strength of evidence for a hypothesis test. They provide information about how likely it is that the observed result from a hypothesis test could have occurred due to chance alone. In essence, an exact p-value helps determine the degree of confidence one can assign to the results of a statistical analysis. The smaller the exact p-value, the less likely it is that the result could be attributed to random chance and thus provides more support for accepting or rejecting a particular hypothesis. Exact p-values can be computed using various specialized algorithms such as Fisher’s Exact Test and Monte Carlo simulations. These methods use probability distributions and data from samples taken from populations to calculate an estimate of what the true population parameter might be. The exact p-value is then obtained by comparing this estimated value with a significance level which represents an acceptable degree of risk associated with making a decision based on the findings of a hypothesis test. By taking into account both sample size and underlying population parameters, exact p-values provide more precise estimates than other methods such as t-tests or chi square tests that may not take these factors into account when computing their p-values. This makes them especially useful in situations where hypotheses pertaining to small sample sizes are being tested or where specific population characteristics need to be taken into consideration when carrying out statistical analyses.