Hypothesis Testing

Question

Hypothesis Testing

A government drug regulator believes that the toxicity level in a new drug is above the industry

standard and is therefore unsafe for consumers. As the final arbitrator, you are the person who has

reviewed both the manufacture’s information and the government’s claim.

You have the final authority to approve or deny this consumer drug ….

Explain what would be a Type I and Type II error in this case.

Which error would be more serious?

Explain how both of these errors could be minimized simultaneously.

Answer 1

FOR YOUR QUESTION

A more complete overview of Type I/II errors is below. As it relates to your question, it would be easiest to consider it in terms of False Positive and Negative Results.

The statement indicates that a new drug is toxic and therefore unsafe for consumer use.

To decide between the two, just think of what it would actually mean to be wrong in each scenario.

1. False Positive (Type I) - The drug is not sold, but no one gets hurt

1. False Negative (Type II) - People take the drug and are severely harmed

(definitely the bad one)

Review of Type I vs. Type II Error

Type I Error = False Positive = False Rejection of Null Hypothesis

Type II Error = False Negative = False Acceptance of Null

Type I and Type II errors can be really confusing. The best way I have found to remember and differentiate them is through the (relatively common) pregnancy test example. With this mnemonic image, all you have to remember is that the test has to be wrong & everything else will fall into place.

Case 1.

1. Sex - Single Male
2. Test Result: Positive
3. Null Hypothesis: Rejected Incorrectly

Case 2.

1. Sex - Pregnant Female
2. Test Result - Negative
3. Null Hypothesis - Accepted Incorrectly

In Case 1, there is a single male, representing 1 patient (Type I error) being tested while in Case 2., the pregnant female represents 2 patients (type 2 error). You would not normally expect the male patient to have a positive pregnancy test which should help you remember that Type I errors are caused by False Positives. On the flip side, you would expect a pregnant person to have a positive test, so the error in that case is a False Negative.

The null hypothesis simply says there is no difference in two things. So in this example a Null Hypothesis could state, "There is no difference in the patient's current hormone levels compared to a normal non-pregnant person." If a difference is detected, then the Null Hypotheses is rejected (as seen in Type I Error). If there's no difference, then the test will be negative and the Null will be accepted.