Definition:Invariance (Statistics)/Quantity
< Definition:Invariance (Statistics)(Redirected from Definition:Invariance (Statistical Quantity))
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Definition
An invariance is a quantity that is unchanged by a transformation.
Examples
$t$ Statistic in $t$-Test
The $t$ statistic used in the $t$-test is an example of an invariance.
It is unchanged by a linear transformation of the sample values, such as replacing $x_i$ with $3 x_i + 7$.
Also see
- Results about invariances in the context of statistical quantities can be found here.
Sources
- 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): invariance: 2.
- 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): invariance: 2.