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 .01, .005, or .001.

When we calculate the goodness 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_max = g(p₀); beta is 1 minus the value of this function at the value set in the alternate hypothesis, i.e. β = 1 - g(p₁).

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

*I hope this is the correct English term, in German it is "Gütefunktion"