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Am I thinking about this correctly?

Blocking is something that is done on the experimental design level: If I'm not interested in the differences between school districts, I block by school district and randomly sample within each school district, right?

My question is what is the difference between this and then statistically controlling? Or why couldn't I take the data, group by school district and then take a random sample from within the larger sample?

Basically what is the difference between blocking initially or controlling afterward or resampling from the larger sample

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Blocking is used when you cannot control a factor. In your case, you're not interested in variation created by school district. By putting subjects in blocks of schools districts then you can focus on variation in the variable of interest without having to worry about the effects of blocking. The blocking effects can then be accounted for elsewhere.

It's not clear how you would "control later" or resample in a way that removes the effect of differing school districts.

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  • $\begingroup$ If I had a large sample that included let's say test scores and a variable for school district, could I take a random sub-sample from each school district? Of if I'm doing a linear model, couldn't I included school district as one of the factors? $\endgroup$
    – crock1255
    Jan 14, 2020 at 17:28
  • $\begingroup$ If you add school districts as a factor then you'll be measuring the effects of school districts (and whatever other factors you include) on test scores. You can analyze test scores WITHIN a school district by that sort of subsample, but if you want to compare variation test scores ACROSS school districts without including school district effects, then you need to block. I guess the question is, what exactly are you trying to analyze? $\endgroup$
    – Todd Burus
    Jan 14, 2020 at 20:37
  • $\begingroup$ Ah that helps clear it up. THank you $\endgroup$
    – crock1255
    Jan 14, 2020 at 21:09

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