## What is alpha?

The greek leter alpha (α) is most-often used to denote the pre-test significance threshold deemed acceptable for the test at hand.

In proper notation α = P(d(X) > c_{(&alpha)}; H_{0}) where H_{0} stands for the null hypothesis of interest, c_{(&alpha)} is the significance threshold and d(X) is a test statistic (**d**istance function).

In case the significance level after the test is complete is equal to α the two coincide. In case the observed significance (p) is different, the test can be interpreted as rejecting the null hypothesis at all levels α for which p < α.

The error rates alpha (α) and beta (β) are inversely related: increasing one decreases the other, assuming fixed variance, sample size and minimum effect of interest.