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Im trying to determine the correct analysis for paired data with a grouping variable.

I have 3 fish in each of 4 treatments, so 12 fish in total. Treatments are that the fish are fed at one of four different time points: 24h, 48h, 72h, 120h. However, it suits my study better to consider Time as a factor, so lets call Time = A, B, C and D.

From each individual fish I have repeated sampling: Nitrogen in blood is sampled at the beginning of the experiment (T=0) and then again 3 hours after their feeding treatment time (T= A,B,C,D).

I would like to know 1) if any of the time treatments causes a signifcant change in blood Nitrogen, and 2) which treatments have blood Nitrogen significantly different from one another (A vs B vs C vs D).

If I take the difference in Nitrogen between the two time points within each fish, and then run a one-way anova between treatments, presumably this only tells me if means of treatments are different, but I dont think this tells me if any of the differences in Nitrogen between time points within a fish (within each treatment) are signifcantly different from zero?

What would be the appropriate way to analyse this data to test my two questions?

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You should include a repeated-measures (or within-subject) factor (pre- vs. post-delay).

This results in a mixed ANOVA with two factors, and you can test both factors using the same model.

Note: 3 fish per condition seems to be very small number. Are you serious about the research question?

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  • $\begingroup$ Thanks Jank. 3 fish should be enough as preliminary tests suggest between fish variation is small and treatment effects large. $\endgroup$ – user2890989 Feb 21 '15 at 16:17

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