Statistical test

Definition

A statistical test, [ilmath]T[/ilmath], is characterised by two (a pair) of probabilities:

• [ilmath]T\eq(u,v)[/ilmath], where:
  • [ilmath]u[/ilmath] is the probability of the test yielding a true-positive result
  • [ilmath]v[/ilmath] is the probability of the test yielding a true-negative result

Tests are usually asymmetric, see: below and asymmetry of statistical tests for more info.

Notation and Terminology

For a test subject, [ilmath]s[/ilmath], we say the outcome of the test is:

1. Positive: [ilmath][T(s)\eq 1][/ilmath], [ilmath][T(s)\eq\text{P}][/ilmath], or possibly either of these without the [ilmath][\ ][/ilmath]
2. Negative: [ilmath][T(s)\eq 0][/ilmath], [ilmath][T(s)\eq\text{N}][/ilmath], or possibly either of these without the [ilmath][\ ][/ilmath]

Power and Significance

The power of the test is

Explanation

Let [ilmath]R[/ilmath] denote the result of the test, here this will be [ilmath]1[/ilmath] or [ilmath]0[/ilmath], and let [ilmath]P[/ilmath] be whether or not the subject actually has the property being tested for. As claimed above the test is characterised by two probabilities