Type I error mistakenly rejects the true null. The Type II error mistakenly accepts a false null. Significance, α, is the desired Prob[Type I error]. Power is 1 - β = 1 - Prob[Type II error] but is more difficult to compute because, while there is only one true null, there can be many false nulls.
David's XLS: http://trtl.bz/2GldhxM
David's XLS: http://trtl.bz/2GldhxM