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I am reading the second edition of Crawley's Statistics: An Introduction Using R and in the Pseudoreplication section of chapter 1 (pg. 15), he provides the following experiment structure:

"There are 20 plots, 10 sprayed and 10 not sprayed. [...] In fact there are 10 replicates in this experiment. There are 10 sprayed plots and 10 unsprayed plots, and each plot will yield a datum to the response variable (the proportion of leaf area consumed by insects, for example). Thus, there are 9 degrees of freedom within each treatment, and 2x9=18 degrees of freedom for error in the experiment as a whole.

Isn't that actually 20 replicates? 10 for each field? Wouldn't there be 20 rows in this dataframe? Aren't the rows the replicates? I believe I understand the degrees of freedom concept.

I have no problem with math or programming and even have a little probability theory, but I am a rank neophyte in statistics, and I apologize if this is a silly question.

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    $\begingroup$ I think by "replicate" Crawley means a realization that can be assumed to be independent, and identically distributed. Obviously, the sprayed and unsprayed groups will not be identically distributed. I'm a bit confused by how he arrives at 18 though. The degrees of freedom depends on the test and the analysis performed. If we test the hypothesis the means are equal and assume the variance is equal, then yes df=18 $\endgroup$
    – AdamO
    Commented May 12, 2023 at 1:53
  • $\begingroup$ I was thinking that the sprayed and unsprayed groups would be identically distributed. Is it that each group is iid by itself, but taken as a whole, they are not? $\endgroup$
    – Omortis
    Commented May 12, 2023 at 3:01

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If you think about one experiment as one control and one treatment that you compare, and each replicate as running the experiment once, you have 10 replicates. I think this is what he means.

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  • $\begingroup$ Such a subtle, simple answer. Thanks for the clarification. I am new to experiment design and don't know if you are correct, but I like the answer. I will update here if I learn anything new about it while I work my way through the book. Thanks! $\endgroup$
    – Omortis
    Commented May 12, 2023 at 19:24

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