Type I & Type II Errors

To reduce the error rate for a type one error we lower alpha, but this will increase the likelihood of committing a type II error. 

To reduce the error rate for both a type one error and a type two error, we need to increase the sample size.

To understand the two statements above consider a criminal trial, if a country decides to convict any person who ends up in court regardless of the evidence, they will not let any guilty people go free who end up in court, but as a result a lot of innocent people will end up in jail.  If you decide to let people off the hook for a crime unless the evidence is overwhelmingly against them, you will end up letting many guilty people go free.  This tug of war always exists we cannot reduce both kinds of errors at once, guarding against one will produce more of the other, unless we can find more evidence.  For us, this would mean taking a larger sample size.