In experiment, if you know before that an attribute $X$ may affect the treatment effect, so you could do stratify sampling from your target population, e.g., if $X$ is weight, then you could divide the target population into several buckets, then do stratify sampling first, then within the sample from each bucket, you run a completely randomized experiment. Note that the stratified sampling method completely eliminate the small chance that some minority bucket gets very low number of samples.

Now, if you didn't do stratify sampling, instead, you just did random sampling from your target population, then I think there is no point to do blocking in your sample, i.e., first split your sample into several cohorts based on the value of $X$, then within each cohort, do completely randomized experiment. I think there is no point of doing that. Because one could just run completely randomized design on your entire sample and then in the post data analysis, you just run a linear regression incorporating $X$.

So my question is: if you don't have stratify sampling first, then blocking is useless, I am not sure if this claim is correct.

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    $\begingroup$ The idea of stratified random sampling is to produce a better estimate compared to completely randomized sampling when the strata have very different variances. To get unbiased estimates you need to take a weighted average. If all the strata have the same variance there is nothing gained by stratifying. $\endgroup$ – Michael Chernick Dec 13 '16 at 2:57
  • $\begingroup$ @MichaelChernick I agree with that. So blocking in this case I described, i.e., with non-stratified sample from the population, does not do anything good comparing to completely randomized assignment over the current sample, is that correct? $\endgroup$ – KevinKim Dec 13 '16 at 3:18
  • $\begingroup$ I think so but I am wondering if the context is different for blocking. When used in agricultural experiments blocking is used to take into account for differences in the effect to treatments such as when growing plants on a plot, you may have taller plants growing in one region (block) when the soil is richer compared to another region. $\endgroup$ – Michael Chernick Dec 13 '16 at 3:28
  • $\begingroup$ This is really stupid of me, but wouldn't it make more sense to do blocking if you the sample wasn't stratified? If our goal is to control for confounding variables, then we can do that either in the sampling stage, via stratified sampling, or during the assignment stage (i.e. after having chosen a sample from the population) via blocking. If we neither use stratified sampling nor block, then we have no control for the possible confounding variable. And blocking after doing stratified sampling is redundant by definition. (But I'm not sure if I actually understand any of the definitions.) $\endgroup$ – Chill2Macht Jun 4 '17 at 21:12

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