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I'm conducting a two-way analysis of variance. I have one fixed treatment factor and one random block factor and I have $n=1$ for any combination.

The thing is that the random block factor is significant ($p<0.05$) and I don't know how to deal with it.

I read this nice answer: What is a block in experimental design? from which I concluded that my block factor belongs to the structure because "I don't care about the values of the associated parameters and don't care to compare them".

Knowing this, should I just ignore the fact that the factor is significant?

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A significant result simply means that in at least one of your blocks the mean response was substantially different compared to the other blocks and you can consider your blocking effective.

At the same time, a non-significant block variable doesn't necessarily mean that your blocking was ineffective -- it just wasn't significant. Given the nature of randomized complete block design, i.e. all factor levels are replicated randomly in each block, the blocking variable may still account for potential variation present in the experiment.

In your case, that is, the blocking variable is significant, you could also try to figure out what's so special about the blocks, which eventually may turn into a new study.

But generally, as @Dennis said in his example (in the link you provided)

Remember: the goal of blocking is to get rid of Run differences.

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  • $\begingroup$ Thanks Stefan, that's what I wanted to know. Of course I can figure out why is there at least one difference between my blocks but I mostly wanted to be sure that it doesn't imply anything about the study of my significant (or not) treatment factor. (I can't upvote the answer yet, my reputation is too low) $\endgroup$ – Sarahdata Dec 10 '15 at 6:24
  • $\begingroup$ @Sarahdata, did the significance of your other factor change when the blocking factor is removed? I'm just wondering. You could consider accepting this as an answer though if it helped you. $\endgroup$ – Stefan Dec 10 '15 at 6:48
  • $\begingroup$ The F value of the treatment factor went from 3.38 to 2.14 and MSerror from 0.029 to 0.044. It is significant (***). $\endgroup$ – Sarahdata Dec 10 '15 at 7:15
  • $\begingroup$ @Sarahdata so that supports your results that the blocking factor is important. I also edited my answer and made it a bit more specific. $\endgroup$ – Stefan Dec 10 '15 at 8:03

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