Question

One of the tree planters on your team is a law student. You've been talking to her (from a safe distance) about how the hypothesis testing process works in psychology and, in particular, about the idea of setting an alpha level to .05 (1 in 20). She is appalled and responds: ``If I made an error one time in twenty there would be so many innocent people in jail it would be a major tragedy. You psychologists need to clean up your act and set your alpha level to something like one in 100,000 or one in a million''. Explain to your law student teammate why what she's suggesting would be a bad idea.

Answer 1

While performing a hypothesis testing, two type of error arise. One is type 1 error and another one is type 2 error . Usually it is desirable to have a test procedure which having minimum probabilities of these errors , that is we want to find such tests whiche minimises type 1 error probability and type 2 error probability simultaneously.but for a sample of fixed size w can't minimise both error probabilities simultaneously .that's why here we just give a bound to the type 1 error probabilities by alpha and then find such a test which is having minimum type 2 error probability.

Here if we minimise alpha by one by one million then type 1 error probability that is the probability of selecting an innocent one in jail is really minimise as a result type 2 error is maximized which is probability that the original harmful person is set to free.it is not the desired purpose of our testing. Here the type 2 error seems to be more serious than type 1 error that's why we can't really minimise the probability of type 1 error so that the probability of type 2 error get maximize too much .