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I designed my experiment in a way that I thought would present me with options for analysis, but I'm starting to wonder if one of the options would be considered pseudoreplication.

The experiment was like this:

I work with 2 mussel species (Z and Q).

I put 4 of each species in a pipe in the river (each of the four got their own little chamber inside).

Each pipe had a baffle on the front and back to change water flow into and out of the pipe

I made four baffle types (A, B, C, D), with the intent that each one would allow faster/more water flow than the previous (ie A

I grouped one of each pipe type together to make a replicate (right?) and attached these replicates to a cinderblock

There were 10 cinderblocks total

I put these underwater, cleaned them every two weeks, and took pre- and post- measurements of mussel body size, and also got attachment strength.

The pipes looked like this So, option 1 is:

I could just analyze the data as a 4x2 ANOVA, with the pipe type (A, B, C, D) vs. species (Z vs Q) with something like body length as the response variable (I have others), and Cinderblocks as a random blocking factor.

BUT! in each pipe, I also included a hard plaster block that dissolved over time under water, ostensibly with higher dissolution due to increased water flow. I checked to see if the pipe baffle had any effect with a one way ANOVA (response variable = amount dissolved; four pipe types) and I found that the baffles basically did what I wanted them to (A

Therefore option 2 is:

I could do a regression/ANCOVA using these plaster blocks, with species as the factor, plaster mass lost as the covariate, and body length as the response variable, with cinderblocks again acting as a random blocking factor.

My questions are:

1) is the second option pseudoreplication, because there is only one measure of flow per pipe, but 4 mussels of each species per pipe?.

2) if it's not pseudoreplication, how do I tell if I should go with the ANOVA or ANCOVA?

I'm using JMP for the analysis, which can't do GLMM unfortunately. Any help would be appreciated.

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    $\begingroup$ Define what you mean by pseudoreplication? $\endgroup$ – Richard Border Apr 12 '18 at 14:19
  • $\begingroup$ Imagine you have two fish tanks with the same species of fish. In one tank you feed food type A, in the other tank, food type B. If you try to compare these two, your replicates within the tank are pseudoreplicated and unreliable because what if tank A had a higher salinity than tank B, or what if the lab tech only cleaned tank A, etc etc. I ask because I worried my pipes might be like the fish tanks, but they were close together in the same river. I included the random blocking factor, so hopefully that would make the design more reliable, but I wanted to ask what others thought. $\endgroup$ – Nathan Haag Apr 12 '18 at 14:32

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