Blocking

Blocking is a decision made before the randomization: sort the experimental units so that units inside a group are alike on a variable you expect to affect the response, then randomize the treatments separately within each group. The variable is picked for its effect on the response, not because it is interesting on its own. What blocking buys is precision, and only precision. It does not replace random assignment and it licenses no causal claim by itself.

Eighteen plots are to be split among three fertilizers. Yields across all eighteen have a standard deviation near 8 bushels, most of it drainage rather than fertilizer. Sort the plots into 6 blocks of 3 by drainage, so that within a block yields vary by more like 3 bushels, then randomize the three fertilizers inside each block. The fertilizer comparison now rests on the within-block spread of 3 instead of the overall spread of 8. That is the whole mechanism.

It is paid for in degrees of freedom. On those eighteen plots a completely randomized design leaves $18 - 3 = 15$ degrees of freedom for error, while the block design spends 5 of them on the six blocks and leaves 10. If drainage turns out to have nothing to do with yield, the error estimate is no smaller and the 95 percent critical value has risen from 2.131 to 2.228, so the interval comes out about 4.5 percent wider in exchange for nothing. Block on a variable you have a reason to believe matters.

The sentence to avoid is "blocking reduces bias." It does not. Blocking reduces the variability of the treatment comparison, and random assignment is what deals with systematic differences between the groups.

Blocking is the experimental counterpart of stratifying a population, and the two are set side by side in blocking vs stratifying. Topic 1.13 covers it as part of experimental design.