You want to conduct a study to determine if a dietary protein supplement, Supple

Question

You want to conduct a study to determine if a dietary protein supplement, SupplementA, is effective at increasing strength. You find a group of 40 people, 20 of whom use SupplementA on a regular basis, and 20 of whom do not. Other than the supplement, their diets and training regimens are comparable. You run an independent samples t-test, and find a statistically significant difference; on average, people who take SupplementA on a regular basis are indeed stronger. While reviewing the data, you find that the group that was on the supplement consisted of 17 men and 3 women, while the group that was not on the supplement consisted of 16 women and 4 men. Do you see anything wrong with the design of this study? Can you think of any way to correct it? You do not have to do any calculation for this question.  

(Please explain with as much detail as posisble to help further my understanding in linear regression. Thank you.)

Explanation / Answer

Yes there is a sampling bias in the data. If we see the first sample, it consists of 17 men and 3 women i.e. 85% of the sample units are male in the first sample. Now if we see the second sample, it consists of 16 women and 4 men i.e. 80% of the sampling units are female. Since men are generally stronger than women, most of the times the difference in the values of group taking supplement A and group taking supplement B will be significanct but it may not necessarily be because of the effect of supplement A. This difference would be because of bias while taking samples.

The way to correct this is to take random sample such that men and women would be equally distributed in both the groups. A completely random sample would be most likely providing such a sample in which men and women are evenly distributed.

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