In statistics, a null hypothesis is a hypothesis that is presumed true until statistical evidence in the form of a hypothesis test indicates otherwise. Often it is a statement about a parameter that is a property of a population, the whole population being unobservable, and the test being based on a random sample from the population. Such a parameter is often a mean or a standard deviation.

Not unusually, such a hypothesis states that the parameters, or mathematical characteristics, of two or more populationss are identical. For example, if we want to compare the test scores of two random sampless of men and women, the null hypothesis would be that the mean score in the male population from which the first sample was drawn was the same as the mean score in the female population from which the second sample was drawn:

H0 = the null hypothesis
μ1 = the mean of population 1, and
μ2 = the mean of population 2.

Alternatively, the null hypothesis can postulate that the two samples are drawn from the same population:

The value of the null hypothesis is that it can be rejected with high probability, while non-null hypotheses cannot be confirmed with high probability. If experimental observations contradict the prediction of the null hypothesis, it means that either the null hypothesis is false, or we have observed an event with very low probability. This gives us high confidence in the falsehood of the null hypothesis, which can be improved by increasing the number of trials. Confirmation of a non-null hypothesis confirms only a difference in parameters; it does not provide support for the theory or principles from which the hypothesis was derived, since the difference could be due to one or more of many possible factors.

Rejection of a null hypothesis (that, say, rates of symptom relief in a sample of patients who received a placebo and a sample who received a medicinal drug will be equal) allows us to make a non-null statement (that the rates differed). Null hypotheses form part of the model of scientific discovery formulated by Karl Popper and followed in several branches of empirical research.

Concerns regarding the high power of statistical tests to detect differences in large samples have led to suggestions for re-defining the null hypothesis, for example as a hypothesis that an effect falls within a range considered negligible.

In 2002, a group of psychologists launched a new journal dedicated to experimental studies in psychology which support the null hypothesis. The Journal of Articles in Support of the Null Hypothesis (JASNH) was founded to address a scientific publishing bias against such articles. [1] According to the editors,

"other journals and reviewers have exhibited a bias against articles that did not reject the null hypothesis. We plan to change that by offering an outlet for experiments that do not reach the traditional significance levels (p < 0.05). Thus, reducing the file drawer problem, and reducing the bias in psychological literature. Without such a resource researchers could be wasting their time examining empirical questions that have already been examined. We collect these articles and provide them to the scientific community free of cost."

See also: statistical hypothesis testing.