# Math Help - Type 1 and Type 2 Errors

1. ## Type 1 and Type 2 Errors

Hello,

I was given the following handout:

Study design:

Alpha = 0.05
Effect size = 0.3
Sample size n = 40

From these figures we can compute that:

Beta = 0.40
Power = 0.60
I know how to get the power, because this is 1 - beta = 1 - .40 = .60. But I just don't get how beta was calculated using the above figures.

Plus, if I have the following problem:

A sample size of 102 will be sufficient to detect an effect size of 0.5 with 80% power at the 0.05 level of significance.

a) What are the type 1 and type 2 error rates?

To get the type 1 error do I look at the alpha, which in this case is 0.05? Therefore, the probability of a Type 1 error = 5% ?

To get the type 2 error is it 1 - Power?

I think that I need to know the value of beta to determine my type 2 error? But I just don't understand how to get beta.

I'd be ever so grateful if someone could explain to me how I'd manage to calculate my type 2 error.

2. With the three pieces of information, you can always determine one of the other two provided (though, really one piece of information. The power of the test just is 1 - beta). I suggest reading up on the power of a test (an important concept in study designs). Wikipedia is a good place to start.

As for the type of errors, look up what type 1 and type 2 errors mean and the definitions of $\alpha$ and $\beta$. You'll see a profound similarity