Question

Here's a quick and easy way to randomize. You hove 100 subjects, 50 women and 50 men. Toss a coin. If it's heads, assign the men to the treatment group and the women to the control group. If the coin comes up tails, assign the women to treatment and the men to control. This gives every individual subject a 50-50 chance of being assigned to treatment or control. Why isn't this a good way to randomly assign subjects to treatment groups?

A. The result of a coin toss is not really random.
B. The probability of a coin to fall on each side is not the same.
C. We can't be sure that the composition of two groups will be similar.
D. The coin might be lost.

Answer 1

C. We can't be sure that the composition of two groups will be similar.

Explanation:

This is not a good way to randomly assign subjects to treatment groups because it is not guaranteed to have 50 people assigned to one group and 50 people to other group.

Using a binomial probability calculator, with 100 trials with p = 0.50, we get that the probability that each group has 50 members is

P(X = 50) = 0.0796.

There is only a 7.96% probability of having exactly 50 heads and 50 tails.

So the correct answer is:

C. We can't be sure that the composition of two groups will be similar.