In: Statistics and Probability
What could you do if you wanted to reduce your chances of Type I Error?
The probability of type 1 error is just exactly equal to the
significance level (call it alpha as usual). So we can manipulate
it easily as we like. If one feels like, for just any reason suits,
to take a higher risk of committing it, he/she just simply choose
alpha equal to 10%. If he/she doesn't feel like it, just decreases
the choice to 1% or even lower.
But this's not that easy in case of type 2 error.
The probability of type 2 error (call it beta as usual) will
increase if we decrease alpha, and vice versa. But by how much? It
depends on what is the true answer of the unknown parameter you're
testing. In other words, beta is a function of the unknown
parameter.
If we know the equation of this function as well as the true answer
of the unknown parameter, we surely can calculate the exact answer
of beta. But this is rarely the case in reality. And this means we
don't know how much risk we're taking when talking about the
possibility of committing a type 2 error.
That's why people tend to say "not reject the null hypothesis" but
not "accept the null hypothesis".
If you accept it, you will immediately expose to the risk of
committing type 2 error, and people don't like to take this risk
because they don't know the probability of the risk.
But if you're just not rejecting it, you can make some excuse
saying "not rejecting it doesn't mean accepting it", something like
that. Then you can even further say "we need further investigation
in order to determine whether we should really accept it or not".
This is a game of language.
But in some cases, people just gotta really accept the null
hypothesis, especially when they gotta make a decision and take an
action upon it (if you're asking me what's the reason, well, I
don't know either). One word, "just do it!"
In this case, either they pay some money or time or resources or
any other costs to make "further investigation in order to
determine...", or they can only "just do it!"