Null hypothesis

Lore & Background

The null hypothesis is a statement about a population parameter, such as 'the mean change in blood pressure is zero.' It is compared against an alternative hypothesis (H1), which is its negation. The test computes a test statistic from sample data and evaluates the probability (p-value) of observing a result at least as extreme, assuming the null hypothesis is true. If this p-value is less than a predetermined significance level (α), the null hypothesis is rejected.

Reader's Guide

The null hypothesis is central to statistical hypothesis testing, providing a default position that the data must contradict to establish an effect. It is typically a statement of 'no effect' or 'no difference,' and the test is designed to assess the strength of evidence against it. The null hypothesis and alternative hypothesis are mutually exclusive. The test does not conclude that the null hypothesis is false, only that the data are inconsistent with it at a given significance level. Errors can occur: a Type I error rejects a true null hypothesis, with probability α, while a Type II error fails to reject a false null hypothesis, with probability β. The concept is used across many fields, including medical trials, where a null hypothesis might state that a drug has no effect. The null hypothesis can be simple (specifying the population distribution completely) or composite (not specifying it completely). Its use adds mathematical rigor and philosophical consistency to statistical inference.

Did You Know?

• The null hypothesis is typically a statement of 'no effect' or 'no difference'.
• If the p-value is less than the significance level α, the null hypothesis is rejected.
• A Type I error occurs when the null hypothesis is rejected despite being true.
• The null hypothesis and alternative hypothesis are mutually exclusive statements.