Probability theory MOC

Statistical hypothesis

A statistical hypothesis is a statement to be verified of the value of a parameter of a probability model, such as the Expectation or variance.

Often we speak of two hypotheses

• The null hypothesis represents the status quo — the state of affairs we expect, i.e. the real distribution's parameters match our own. We continue to believe this state of affairs unless we have strong data for the contrary.
• The alternate hypothesis is a different state of affairs we need strong evidence to support.

Testing

Statistical hypothesis testing involves using an Estimator to determine which of two hypotheses (see above) should be rejected. This itself means reconciling an observed estimate with an assumed estimate. Common methods include

• -value hypothesis test
• Critical value hypothesis test

Summary table

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