One very striking abuse of a levels is to choose them after seeing the data and to choose them in such a way as to force rejection (or acceptance) of a null hypothesis. To see what the true Type I and Type II Error probabilities of such a procedure are, calculate size and power of the following two trivial tests: 
(a) Always reject H0, no matter what data are obtained (equivalent to the practice of choosing the α level to force rejection of H0).
(b) Always accept H0, no matter what data are obtained (equivalent to the practice of choosing the α level to force acceptance of H0).