In
statistics
Statistics (from German language, German: ''wikt:Statistik#German, Statistik'', "description of a State (polity), state, a country") is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of ...
, the size of a
test
Test(s), testing, or TEST may refer to:
* Test (assessment), an educational assessment intended to measure the respondents' knowledge or other abilities
Arts and entertainment
* ''Test'' (2013 film), an American film
* ''Test'' (2014 film), ...
is the probability of
falsely rejecting the
null hypothesis
In scientific research, the null hypothesis (often denoted ''H''0) is the claim that no difference or relationship exists between two sets of data or variables being analyzed. The null hypothesis is that any experimentally observed difference is d ...
. That is, it is the probability of making a
type I error
In statistical hypothesis testing, a type I error is the mistaken rejection of an actually true null hypothesis (also known as a "false positive" finding or conclusion; example: "an innocent person is convicted"), while a type II error is the fa ...
. It is denoted by the Greek letter α (alpha).
For a
simple hypothesis
A statistical hypothesis test is a method of statistical inference used to decide whether the data at hand sufficiently support a particular hypothesis.
Hypothesis testing allows us to make probabilistic statements about population parameters.
...
,
:
In the case of a
composite null hypothesis, the size is the supremum over all data generating processes that satisfy the null hypotheses.
:
A test is said to have
significance level if its size is less than or equal to
.
In many cases the size and level of a test are equal.
References
Davidson, Russell, and James G. MacKinnon. Econometric theory and methods. Vol. 5. New York: Oxford University Press, 2004.
Statistical hypothesis testing
{{statistics-stub