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I want to test effect of 3 PH on larval development. I would like to know what is the best experimental design and statistical analysis.

We can only use 3 compartments of sea water, each one with a different ph. In each compartment, larvae will grow in 4 differents cylinder.

Each day, we will take off severals larvae in each cylinder, measured larvae and count proportion of dead larvae.

Can I then analyse proportion of dead larvae per day with a GLMM with cylinder as random factor (and LMM for larvae biometry) ?

Can I "use" different parents to produce larvae of cylinders and analyse a kind of genetic effect ? In this case, could I use mixed models with family nested in cylinder as random effect ?

experiment design

Thank you.

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I will not answer to your question related to genetic, as I do not have the expertise for it.

But here's some comment and answers on your design:

  • My first concern is about the sea water compartment. Can you change the PH and randomized the PH treatment between those ? This may seems of low importance, but let's say that one of the compartment is closer to a source of light that disrupt larvae. You would then end up with a systematic bias.

  • From what you describe, your experimental unit is the sea water compartment. Your cylinder are samples, and NOT independent replicates and should not be in your model. If you change larvae each day, your random term could rather be the day.

  • Finally, if you want to test larvae family, you should not put it in the random term.

I hope this will help, even though it isn't complete.

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    $\begingroup$ I agree with your first 2 dot points. But whether the genetic effect is random or not depends on the actual situation. If the parents picked are a random sample of the entire population of parents, then perhaps it is worthwhile treating its effect as random. Alternatively, if the picked ones are of special interested, then maybe it should be fixed. Of course, the choice between fixed and random is also a debatable one, which is why I have used terms like 'perhaps' and 'maybe'. $\endgroup$ – qoheleth Jul 31 '14 at 1:05
  • $\begingroup$ @qoheleth You are right. Actually, I wrote it that way because I tough steph is interested in the effect of genetic, but your point is important. $\endgroup$ – Emilie Jul 31 '14 at 12:52
  • $\begingroup$ Thank you for your answer. I will see if it is possible to change the PH and to transfer larvae. If I do that, I suppose that I can put sea water compartment as random term. I know that my cylinders are not independent but I thought that larva were my sample. So, how can I include motality and biometry in my model ? One mortality rate for each cylinder ? And for larval length, as if larvae were in sea water compartment without cylinder (or an average per day per cylinder) ? The parents picked will be a random sample of the entire population of parents. $\endgroup$ – steph Aug 5 '14 at 2:39
  • $\begingroup$ First question: you could do a mean, but it's also possible to adjust your random term to take into account the factr they are samples. I don't have examples right now, but I could look for them if you don't find any. I'm not sure I understand your question about larval length tought... $\endgroup$ – Emilie Aug 12 '14 at 12:31

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