Search Results for “size (statistics)”

Source: Size (statistics)

In statistics, the size of a test is the probability of falsely rejecting the null hypothesis. That is, it is the probability of making a type I error. It is denoted by the Greek letter α (alpha).
For a simple hypothesis,

α
=
P
(

test rejects

H

0

∣

H

0

)
.

{\displaystyle \alpha =P({\text{test rejects }}H_{0}\mid H_{0}).}

In the case of a composite null hypothesis, the size is the supremum over all data generating processes that satisfy the null hypotheses.

α
=

sup

h
∈

H

0

P
(

test rejects

H

0

∣
h
)
.

{\displaystyle \alpha =\sup _{h\in H_{0}}P({\text{test rejects }}H_{0}\mid h).}

A test is said to have significance level

α

{\displaystyle \alpha }

if its size is less than or equal to

α

{\displaystyle \alpha }

.
In many cases the size and level of a test are equal.