Question

A randomized trial comparing the efficacy of two drugs showed a difference between the two with a p value of <0.005. In reality, however the two drugs do not differ. This therefore is an example of:

• A. Type I error (alpha error)
• B. Type II error (beta error)
• C. 1 - \(\alpha\) (alpha)
• D. 1 - \(\beta\) (beta)

Hint:

Claiming a difference exists when the treatments are truly equal is a false positive, which is a Type I or alpha error.

Answer 1

The Correct Option is A

This question is testing the four basic outcomes of a hypothesis test, so it helps to check what each option actually means before matching it to the scenario given.

1. Type I error (alpha error): This means rejecting a true null hypothesis, that is, declaring a difference when none truly exists, a false positive. The trial declared the drugs different by their p value, but the question says they are truly the same, so this fits exactly.
2. Type II error (beta error): This means failing to reject a false null hypothesis, that is, missing a real difference that does exist, a false negative. Here there was no real difference to miss, since the drugs are truly equal, so this does not fit.
3. 1 - alpha: This is the confidence level, the probability of correctly accepting a true null hypothesis when it is in fact true. The trial did the opposite, it rejected the true null, so this does not describe what happened.
4. 1 - beta: This is the power of the test, the probability of correctly picking up a real difference when one truly exists. Since no real difference exists here, this concept does not apply.

Matching the scenario, a significant p value pointing to a difference that is not actually there, only fits the first option, a false positive conclusion.

Let's summarize:

• False positive, wrongly finding a difference, is a Type I or alpha error.
• False negative, wrongly missing a real difference, is a Type II or beta error.

So this scenario is a Type I error, also called an alpha error.