In statistical hypothesis testing we decide on and set the acceptable probability of error or significance level 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 of two errors: the Type 1 error α (alpha) and the Type 2 error β (beta). In a graphical representation of this function, alpha is the value below the graph, beta is the value above the line: α = g(p) and β = 1 - g(p), with p being the parameter we are interested in.
Here is an example:
The red line is αmax for H0: p ≤ 0.4 and H1: 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?
Or am I just getting confused over two unrelated values having the same name (alpha)?