Probability of type 1/type 2 errors and distribution of p-values

[humantripod]

Hi,

I had a statistics exam today and there were three questions about which I felt a little uneasy.

The questions which felt too easy involved finding the probability of type 1 and type 2 errors. The scenario was that a lie detector test was given to 1000 people. Of those 1000 people, 500 lied and 500 told the truth. The lie detector incorrectly reported that 185 of the people who were truthtellers were actually lying and that 120 of the liars were telling the truth.

I calculated the P(Type 1 error) by simply doing 185/500 = 0.37
I calculated the P(Type 2 error) by simply doing 120/500 = 0.24

The other question asked me to give the distribution of p-values. I don't recall the question giving any details about whether it was under the assumption that H0 is true or Ha is true, just simply asking for the distribution. I said N(0,1).

What do you think guys? Any mistakes/fundamental flaws in my working out?

 

[scottdave]

If P(Type I) = 37% and P(Type II) = 24%, what is the probability that there is no error? What should these sum up to?

Think about what your choice of denominator tells about what assumptions you make.
You may find reading this, helpful https://nflinjuryanalyticscom.files.wordpress.com/2020/04/diagnostic_testing_characteristics.pdf

So they don't specifically use the terminology Type I and II, but use False Positive and False Negative. As far as the p-values, you can look it up, but I think it is the probability that the Null-Hypothesis is correct.

Again, you should look this up, but I think a "Negative" would mean the detector did not detect anything (so it thinks the person told Truth)a "Positive" would mean the detector detected a lie.

Somebody else may chime in with more insight.