Interpret errors, power and p-values

A Type I error rejects a true H0; its probability is controlled at α by the procedure. A Type II error fails to reject H0 at a specified false parameter value; its probability is β. Power=1-β. A p-value is the probability, under H0 and the model, of a test result at least as extreme as observed in the direction(s) being tested. Reject when p≤α. Otherwise fail to reject; this does not prove equality or no effect.