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 November 16th, 2014, 12:23 PM #1 Senior Member   Joined: Feb 2010 Posts: 135 Thanks: 0 Type 1 error - stats what is a "two-sided type I error" in a statistical test (e.g: research study)? thanks
November 16th, 2014, 11:27 PM   #2
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Quote:
 Originally Posted by jsmith613 what is a "two-sided type I error" in a statistical test (e.g: research study)? thanks
Type 1 error is rejecting the null hypothesis when it is in fact true.

Suppose our null hypothesis $H_0$ that the true value of the test statitic $t=t_0$ then a two sided test with a type 1 error probability $\varepsilon$ would be one for which we reject $H_0$ if $|t-t_0|>v_{crit}$ where $v_{crit}$ is chosen so that:
$$p(|t-t_0|>v_{crit}|H_0)=\varepsilon$$

This is a two sided test because it is a test that $-v_{crit}<t-t_0<v_{crit}$. That is it is a test for the size of the deviation from the null in either direction.

CB

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