What is "null hypothesis"

n. (context statistics English) A hypothesis set up to be nullified or refuted in order to support an alternative hypothesis. When used, the null hypothesis is presumed true until statistical evidence in the form of a hypothesis test indicates otherwise. Therefore, the null and the alternative hypothesis must be mutually exclusive and exhaustive. The use of the null hypothesis is controversial.

In inferential statistics, the term "null hypothesis" usually refers to a general statement or default position that there is no relationship between two measured phenomena, or no association among groups. Rejecting or disproving the null hypothesis—and thus concluding that there are grounds for believing that there is a relationship between two phenomena (e.g. that a potential treatment has a measurable effect)—is a central task in the modern practice of science, and gives a precise criterion for rejecting a hypothesis.

The null hypothesis is generally assumed to be true until evidence indicates otherwise. In statistics, it is often denoted H (read “H-naught”, "H-null", or "H-zero").

The concept of a null hypothesis is used differently in two approaches to statistical inference. In the significance testing approach of Ronald Fisher, a null hypothesis is rejected if the observed data is significantly unlikely if the null hypothesis were true. In this case the null hypothesis is rejected and an alternative hypothesis is accepted in its place. If the data are consistent with the null hypothesis, then the null hypothesis is not rejected (i.e., accepted). In neither case is the null hypothesis or its alternative proven; the null hypothesis is tested with data and a decision is made based on how likely or unlikely the data is. This is analogous to a criminal trial, in which the defendant is assumed to be innocent (null is not rejected) until proven guilty (null is rejected) beyond a reasonable doubt (to a statistically significant degree).

In the hypothesis testing approach of Jerzy Neyman and Egon Pearson, a null hypothesis is contrasted with an alternative hypothesis, and the two hypotheses are distinguished on the basis of data, with certain error rates.

Proponents of each approach criticize the other approach. Nowadays, though, a hybrid approach is widely practiced and presented in textbooks. The hybrid is in turn criticized as incorrect and incoherent—for details, see Statistical hypothesis testing.

Statistical inference can be done without a null hypothesis, thus avoiding the criticisms under debate. An approach to statistical inference that does not involve a null hypothesis is the following: for each candidate hypothesis, specify a statistical model that corresponds to the hypothesis; then, use model selection techniques to choose the most appropriate model. (The most common selection techniques are based on either Akaike information criterion or Bayes factor.)