Difference between revisions of "Statistical test"
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| − | {{ProbMacro}} | + | {{ProbMacro}}{{Stub page|grade=A*|msg=Include [[hypothesis testing]] of which are an instance of statistical tests. Link to [[true/false positive/negative]] and create pages for [[false positive]] and such that redirect to an anchor on that page. Don't forget the {{link|power function|statistics}} - [[User:Alec|Alec]] ([[User talk:Alec|talk]]) 13:32, 14 December 2017 (UTC)}} |
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==Definition== | ==Definition== | ||
Latest revision as of 13:32, 14 December 2017
Contents
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
If we write [ilmath][T\eq 1][/ilmath] for the test coming back positive, [ilmath][T\eq 0][/ilmath] for negative and let [ilmath]P[/ilmath] denote the actual correct outcome (which may be unknowable), denoting [ilmath][P\eq 1][/ilmath] if the thing being tested for is, in truth, present and [ilmath][P\eq 0][/ilmath] if absent, then:
| Outcomes: | Truly present [ilmath][P\eq 1][/ilmath] |
Truly absent [ilmath][P\eq 0][/ilmath] |
|---|---|---|
| Test positive [ilmath][T\eq 1][/ilmath] |
[ilmath]\Pcond{T\eq 1}{P\eq 1}\eq u[/ilmath] | [ilmath]\Pcond{T\eq 1}{P\eq 0}\eq 1-v[/ilmath] |
| Test negative [ilmath][T\eq 0][/ilmath] |
[ilmath]\Pcond{T\eq 0}{P\eq 1}\eq 1-u[/ilmath] |
[ilmath]\Pcond{T\eq 0}{P\eq 0}\eq v[/ilmath] |
OLD PAGE
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:
- Positive: [ilmath][T(s)\eq 1][/ilmath], [ilmath][T(s)\eq\text{P}][/ilmath], or possibly either of these without the [ilmath][\ ][/ilmath]
- 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
