I am going through the first part of the Duke statistics course on Coursera, and the concept of blocking in experimental design comes up. If I understand correctly, blocking refers to separating subjects into groups based on some variable that might affect the outcome.

However, if we are already performing random assignment, shouldn't all "values" of the blocking variable be equally represented in the different treatment groups? If so, why do we bother with blocking?

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    $\begingroup$ Every random sample is essentially a draw from a random variable. In expectation, the distribution of data in the sample is the same as in the population. But only in expectation. $\endgroup$ – shadowtalker Sep 3 '16 at 22:52

Well, if you have small number of experimental runs, then the random assignment could well make some variable poorly balanced between the experimental and control groups. By using blocking you avoid that.

Another idea with blocking is that it makes it possible to on purpose use inhomogeneous experimental material, because the blocking assures that it is balanced between the groups. That makes for a better basis for generalization from the experiments, as conclusion from experiment is valid for a greater range of conditions.

  • $\begingroup$ What if I use a fair coin to determine the destiny (i.e., whether go to treatment group or control group) for each subject. Then in this case, whether you first do blocking, i.e., divide your sample based on their attributes into several cohort, then within each cohort, you use each people's coin to assign treatment; or you just use people's coin to assign treatment initially, without blocking, will give you exactly the same person in the treatment or control group. In this case, blocking does not make any difference. Because in the data analysis, you always run a linear model with attribute $\endgroup$ – KevinKim Dec 13 '16 at 2:43
  • $\begingroup$ This just got downvoted. I would really like to hear what is seen as wrong with this answer!, as I cannot imageine what it is---apart from being to short on details? $\endgroup$ – kjetil b halvorsen Dec 13 '16 at 14:58
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    $\begingroup$ Say you have 4 men 6 women in your sample. Each one flip a fair coin, H to treatment, T to control. If you do a completely randomize design, you could end up with (1 men, 5 women) in Treatment, (3 men, 1 women) in Control based on their own coin. Now if you first block the gender, so you have 4 men in M cohort and 6 women in W cohort, then within cohort, you let them flip their coin, you will end up with same probability of getting (1 men, 5 women) in Treatment, (3 men,1 women) in Control. Isn't it? $\endgroup$ – KevinKim Dec 13 '16 at 15:27

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