Question

A team of researchers has developed a new drug to treat atopic dermatitis, also known as eczema. They want to know if this new drug produces better results than a commonly prescribed older drug. The side effects of the two drugs are equivalent. The new drug would be more expensive to produce compared to the older drug. To address their research question, they will randomly assign patients to either the new or old drug. Each patient will be examined by an independent physician (i.e., not a member of the research team) before and after 90 days of using their assigned drug. The physician will not know which patients are in each group. The physician will measure the change in symptoms using a quantitative measure that considers the area of skin affected and the severity of the condition.

1. Type I Error:  
   1. What does a Type I error mean in this situation?
   2. What are the consequences of making a Type I error here?

2. Type II Error:  
   1. What does a Type II error mean in this situation?
   2. What are the consequences of making a Type II error here?

3. In this scenario, is a Type I or Type II error more serious? Or, are they equally serious? Explain your reasoning.

4. If you were working with this research team, what alpha level would you use? Give a specific value for alpha. Explain your reasoning.

Answer 1

Solution

In this scenario, the hypotheses would be:

Null H₀: New drug is at best only as effective as the old drug.

Vs

Alternative: New drug is more effective than the old drug........................................................................... (1)

Back-up Theory

Type I Error is the error of rejecting a null hypothesis when it is true.........................................................(2)

Type II Error is the error of accepting a null hypothesis when it is not true, i.e., Alternative is true...........(3)

Significance level, α, of a test = P(Type I Error) ....................................................................................... (4)

Now, to work out the solution,

Part (a)

Vide (1) and (2),

Type I error in this situation would mean that the new drug is declared more effective when it is not effective. Answer 1

The consequences are evidently, passing of an ineffective drug as effective. This step, normally,is the first step towards marketing a new drug. Thus eventually, market would be flooded with an ineffective drug, which obviously is not desirable. Answer 2

Part (b)

Vide (1) and (3),

Type II error in this situation would mean that the new drug is declared ineffective when actually it is effective. Answer 3

The consequences are evidently, depriving an effective drug its due recognition. This step, being normally, the first step towards marketing a new drug, a potential drug is not available to the patients. Answer 4

Part (c)

Being a question of health of the public, in this scenario, Type I error is more serious. Answer 5

Part (d)

Going by the conclusion under Part (c), it is desirable to devise a test that has a very low probability of committing Type I error, i.e., vide (4), significance level should be very low, say may be 0.1%. Answer 6

DONE