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I am currently studying Random Complete Block Designs (RCBD) and I would like to ask a question.

I cam across an example where we were able to conclude with the RCBD as significant, but regular ANOVA (done incorrectly) failed to identify the significance.

As I read the text it says that one can INCORRECTLY do the regular ANOVA without realizing that one has to block the data, things like this could happen.

Can someone explain to me when we are supposed to block the data?

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One blocks the design and the analysis for added precision. This will in effect reduce standard errors, and increase the chances of obtaining a significant finding (provided the experiment does actually produce a measureable effect). In other words, it increases power.

The reason why is that there is preliminary data or a belief that there is some variability in response between blocks. Blocking decreases the chance of a probabilistic imbalance in randomization, and it also stratifies the response so that comparisons between randomized groups are more precise. For instance a blood pressure medication might be studied in two analysis sets: young adults with healthy blood pressure, and older adults with a prior diagnosis of hypertension. A 10mmHg drop in blood pressure will be less precise if we pool those two types of participants in the same comparison groups.

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  • $\begingroup$ Thank you for the response. I see that the error by the blocks are taken away so that the error by the treatment goes down, but if that is the case would we not want to ALWAYS block the data? $\endgroup$ – hyg17 Mar 8 '19 at 23:57
  • $\begingroup$ @hyg17 two reasons: 1) incomplete randomization permutations and 2) overadjustment. For 1) this happens when you don't expect to even recruit at least 2 of each type for each block, you must have at least 2-per-cluster to permute randomization, and if you don't you can't block anyway (has the net-effect of dropping the observation). For 2) overadjustment reduces DF and creates bias, though you can use a paired design. $\endgroup$ – AdamO Mar 9 '19 at 0:02

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