Statistical test

Definition

A statistical test, $T$, is characterised by two (a pair) of probabilities:

• $T\eq(u,v)$, where:
  • $u$ is the probability of the test yielding a true-positive result
  • $v$ 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, $s$, we say the outcome of the test is:

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

Power and Significance

The power of the test is

Explanation

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