Statistical Hypothesis

statistical hypothesis

[stə′tis·tə·kəl hī′päth·ə·səs]

(statistics)

A statement about the way a random variable is distributed.

The following article is from The Great Soviet Encyclopedia (1979). It might be outdated or ideologically biased.

Statistical Hypothesis

an assumed statement on the probabilistic regularities obeyed by a phenomenon under study. A statistical hypothesis generally specifies the form of the probability distribution or the values of the parameters of the distribution.

A hypothesis that completely specifies the distribution is said to be simple. Any nonsimple hypothesis is said to be composite and can be represented as a class of simple hypotheses. An example of a composite hypothesis is the hypothesis that the probability distribution is a normal distribution with mathematical expectation a = a₀ and some unknown variance σ². The simple hypotheses here are a = a₀ and σ² = Statistical Hypothesis, where a₀ and Statistical Hypothesis are specified numbers.

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