What would be the reply of a statistician?

Question

A generic drug is being tested to test its efficacy (effectiveness) at reducing blood pressure in patients with hypertension (a.k.a. high blood pressure). In a randomized, double-blind experiment with 200 patients, 100 are given the name-brand drug (control group) and 100 are given a generic version of the drug (treatment group). In the control group, the average reduction in blood pressure is 15.2 mmHG with a standard deviation of 11.5 mmHG. In the treatment group, there is an average reduction of 14.6 mmHG and a standard deviation of 12.5 mmHG. Neither group has any outliers. A researcher claims that this study shows the generic drug is not as effective as the name-brand drug. What would be the reply of a statistician?

a.

The point estimate for the generic drug is lower than that of the name-brand drug, which means the generic drug is less effective. The researcher is correct.

b.

Because the difference in sample means is under 1 mmHG, we can safely conclude the drugs are equally effective.

c.

While there is some uncertainty in the point estimates, the sample sizes for each group are large, indicating that the difference must be real.

d.

The standard deviations are quite large within each group relative to the size of the difference in point estimates. It is unclear if there is a real difference in the effectiveness of the two drugs or if the difference is just due to chance.

Answer 1

In this situation, it would be appropriate to conduct a 2-sample t-test in order to determine if there is a significant difference between the the mean reduction of blood pressure of the two drugs.

If you use Test statistic: (x₁ – x₂) / s_p(√1/n₁ + 1/n₂)

where s_p = sqrt( [(n₁-1)s₁² +  (n₂-1)s₂² ] / (n₁+n₂-2))

We end up with a t-statistic of .3567971948. Our degrees of freedom is determined by the two sample sizes (n₁ + n₂ + 2) which is 202. If you looked up this value in a t-table with the appropriate degrees of freedom, you would see that the p-value obtained is way over significance level of 0.1.

The real p-value is actually above 50% (it's hard to find a t-table that shows df=202 and t-value=.35679)

This means that the probability of obtaining the results we did by random chance alone is greater than 50%.

In this scenario we would not have enough evidence to conclude that the means differ significantly.

With this being said, option D seems to be the most likely. It even talks about the "difference in point estimates" which refers to the numerator of the two-sample t-test.