Mid P Value
- A mid P-value averages the two-sided P-value contributions from both tails of the test statistic’s distribution.
- It offers a balanced assessment of evidence against the null hypothesis by considering probabilities on both sides of the observed statistic.
- Used to report significance in hypothesis tests where two-sided extremeness is relevant.
Definition
Section titled “Definition”The mid P-value is a statistical concept used to evaluate the significance of a hypothesis test. It is calculated by taking the average of the two-sided P-value, which is the probability of obtaining a test statistic that is at least as extreme as the one observed, given that the null hypothesis is true.
Explanation
Section titled “Explanation”A two-sided P-value measures the probability of observing a test statistic at least as extreme as the observed value, under the assumption that the null hypothesis is true. The mid P-value is obtained by averaging the two-sided P-value contributions: the probability of obtaining a test statistic more extreme than the observed one and the probability of obtaining a test statistic less extreme than the observed one. This averaging yields a single value intended to reflect both directions of extremeness relative to the null hypothesis.
Examples
Section titled “Examples”Example: mean height test
Section titled “Example: mean height test”Suppose we test the hypothesis that the mean height of a population is 5 feet using a sample of 100 individuals. The sample mean is 5.1 feet. A statistical test gives a P-value, defined as the probability of obtaining a sample mean of 5.1 feet or greater, given that the population mean is 5 feet. The mid P-value for this hypothesis test is the average of the P-values for the two-sided hypothesis test: the probability of obtaining a sample mean that is either greater than or less than 5.1 feet, given that the population mean is 5 feet. In other words, the mid P-value is the average of the probabilities of obtaining a test statistic that is either more extreme than the observed one, or less extreme than the observed one.
Example: medical treatment
Section titled “Example: medical treatment”Suppose we test whether a new drug is effective in reducing the risk of heart attacks using a sample of patients with a history of heart disease. Patients are randomly divided into two groups: one group receives the new drug and the other group receives a placebo. We measure the number of heart attacks in each group over a certain period and compute the P-value, the probability of obtaining the observed difference in the number of heart attacks between the two groups, given that the new drug is not effective. The mid P-value for this test is the average of the P-values for the two-sided hypothesis test: the probability of obtaining a difference in the number of heart attacks between the two groups that is either greater than or less than the observed difference, given that the new drug is not effective. In other words, the mid P-value is the average of the probabilities of obtaining a test statistic that is either more extreme than the observed one, or less extreme than the observed one.
Use cases
Section titled “Use cases”- Provides a more balanced evaluation of the significance of a hypothesis test by taking into account both the likelihood of observing a test statistic more extreme than the observed one and the likelihood of observing one less extreme.
- Aids researchers in making informed decisions about the validity of conclusions drawn from hypothesis tests.
Related terms
Section titled “Related terms”- P-value
- Two-sided P-value
- Null hypothesis
- Test statistic