Difference between revisions of "Statistical test"
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==Definition== | ==Definition== | ||
− | + | A ''statistical test'', {{M|T}}, is characterised by two (a [[ordered pair|pair]]) of [[probability (object)|probabilities]]: | |
− | + | * {{M|T\eq(u,v)}}, where: | |
+ | ** {{M|u}} is the probability of the test yielding a ''[[true-positive]]'' result | ||
+ | ** {{M|v}} is the probability of the test yielding a ''[[true-negative]]'' result | ||
− | + | Tests are usually ''asymmetric'', see: [[#Explanation|below]] and ''[[asymmetry of statistical tests]]'' for more info. | |
− | + | ===Notation and Terminology=== | |
− | + | For a test subject, {{M|s}}, we say the outcome of the test is: | |
− | + | # '''Positive: ''' {{M|[T(s)\eq 1]}}, {{M|[T(s)\eq\text{P}]}}, or possibly either of these without the {{M|[\ ]}} | |
− | + | # '''Negative: ''' {{M|[T(s)\eq 0]}}, {{M|[T(s)\eq\text{N}]}}, or possibly either of these without the {{M|[\ ]}} | |
− | + | ====Power and Significance==== | |
− | == | + | The ''power'' of the test is |
− | + | ==Explanation== | |
+ | Let {{M|R}} denote the result of the test, here this will be {{M|1}} or {{M|0}}, and let {{M|P}} be whether or not the subject actually has the property being tested for. | ||
+ | As claimed above the test is characterised by two probabilities |
Revision as of 17:05, 4 October 2017
Contents
[hide]Definition
A statistical test, T, is characterised by two (a pair) of probabilities:
- T=(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:
- Positive: [T(s)=1], [T(s)=P], or possibly either of these without the [ ]
- Negative: [T(s)=0], [T(s)=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