Alternative hypothesis

In statistical hypothesis testing, the alternative hypothesis (or maintained hypothesis or research hypothesis) and the null hypothesis are the two rival hypotheses which are compared by a statistical hypothesis test.

In the domain of science two rival hypotheses can be compared by explanatory power and predictive power.

An example might be where water quality in a stream has been observed over many years; and a test is made of the null hypothesis that: "there is no change in quality between the first and second halves of the data", against the alternative hypothesis that "the quality is poorer in the second half of the record".

The concept of an alternative hypothesis in testing was devised by Jerzy Neyman and Egon Pearson, and it is used in the Neyman–Pearson lemma. It forms a major component in modern statistical hypothesis testing. However it was not part of Ronald Fisher's formulation of statistical hypothesis testing, and he opposed its use. In Fisher's approach to testing, the central idea is to assess whether the observed dataset could have resulted from chance if the null hypothesis were assumed to hold, notionally without preconceptions about what other model might hold. Modern statistical hypothesis testing accommodates this type of test since the alternative hypothesis can be just the negation of the null hypothesis.

In the case of a scalar parameter, there are four principal types of alternative hypothesis:

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