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I used a two-way ANOVA to analyze data collected in a randomized complete block design:

Y~Treatment+Block, where blocks represented spatial units

Whereas Treatment had a significant effect on Y, block effects were insignificant.

Does this simply mean that all blocks were the same with respect to the response variable? If that is so, would you it be a good idea to use an ANCOVA to see how parameters collected to describe spatial units affect Y?

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This result does not mean that the different blocks are the same on the dependent variable, only that there is not sufficient evidence to reject the notion; more precisely, it says that, in a sample of this size, an effect of this size would have arisen more than 5 percent of the time if, in the population from which the sample was drawn, there really was no effect.

As to your second question, I think that using the characteristics of the blocks as IVs makes sense, regardless of whether block is significant. The results will tell you more about what is going on.

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  • $\begingroup$ Do you mean that I should use the following ANCOVA maximal model then: Y~Treatment+Block*Characteristic1*Characteristic2? $\endgroup$ – user1182741 May 19 '13 at 16:46
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    $\begingroup$ If * means include the interaction, I am not sure if you need them all. Deciding on the right model is complex (and discussed here a lot). But I do think including the characteristics in your model building is appropriate. $\endgroup$ – Peter Flom May 19 '13 at 16:49

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