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

Step 1: Understanding the Question.
A trial found a statistically significant difference, with a small p value under 0.005, between two drugs, but the question tells us that in truth the two drugs are equally effective. We need to name the kind of statistical error this represents.

Step 2: Key Concept or Approach.
Every hypothesis test starts with a null hypothesis, here that the two drugs do not differ. A Type I or alpha error happens when we wrongly reject a true null hypothesis, in plain words, we claim a difference exists when it really does not, a false positive. A Type II or beta error happens the other way round, we fail to reject a false null hypothesis, meaning we miss a real difference that does exist, a false negative. The value 1 minus alpha is the confidence level, the chance of correctly keeping a true null hypothesis, and 1 minus beta is the power of the study, the chance of correctly detecting a real difference.

Step 3: Detailed Explanation.
Here the trial's low p value led the researchers to reject the null hypothesis and conclude the drugs differ. But the question states that the drugs truly do not differ, so the null hypothesis was actually true, and rejecting a true null hypothesis is, by definition, a Type I or alpha error. This is not a Type II error, because a Type II error would mean missing a real difference, and here there is no real difference to miss, in fact a difference was wrongly detected. It is not 1 minus alpha, since that describes correctly accepting a true null, which is the opposite of what happened. It is not 1 minus beta either, since that describes correctly detecting a real effect, and there was no real effect to detect.

Step 4: Final Answer.
Concluding a difference exists between two treatments when none truly exists is a false positive result, which is a Type I error, also called alpha error.