In statistical hypothesis testing we decide on and *set* the acceptable **probability of error** α (alpha) to a value that fits our theory. Traditionally alpha is .1, .05, or .01.

When we *calculate* the power function g of the parameter we test for, we recieve the distribution of the probability two errors, the **Type 1 error** (alpha) and the Type 2 error (beta). The maximum value for alpha is the value of this function at the value of the parameter set in the null hypothesis, i.e. α<sub>max</sub> = g(p<sub>0</sub>); beta is 1 minus the value of this function at the value set in the alternate hypothesis, i.e. β = 1 - g(p<sub>1</sub>).

Here is an example:

![sample power function][1]

The red line is α<sub>max</sub> for H<sub>0</sub>: p ≤ 0.4 and H<sub>1</sub>: p > 0.4; the blue line is β for a sample p̂ = 0.5

**How do the probability of error (alpha) and the Type 1 error (alpha) relate to each other?**


  [1]: https://i.sstatic.net/dNGUU.png