Statistical Hypothesis

statistical hypothesis

[stə′tis·tə·kəl hī′päth·ə·səs] (statistics) A statement about the way a random variable is distributed.

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.