I have 36 fish tanks - 3 age levels (post larval, 1 & 2 year),12 tanks per level. I apply 2 treatments with two levels each treatment; temperature (cold, warm) and feeding frequency (1 x day, 3 x day; same amount overall). So N = 3. I take 7 repeat measurements over 12 months to see how temperature and feeding frequency affects growth response and survival. Should I use a split plot ANOVA and if so what are my degrees of freedom?
Dear Paula,
I see no split plot in your description.
Let us first assume that you can characterize the outcome of your experiment by a single response, to be concrete say the total growth over the year, per tank (experimental unit=tank). Then you have a 3x2x2 factorial experiment with 3 replicates per combination, that leaves 24 residual degrees of freedom. You may study main effects and interaction effects.
I do not know how you make measurements of growth. If you make individual measurements for a sample of fish you should probably just use their average as value per tank. However, treatment effects on the variation btw individuals could possibly also be of interest.
if you consider survival, do not assume a binomial distribution per treatment combination, because you are likely to have correlation btw individuals from the same tank (contagion etc).
Finally, if you want to use your 7 repeat measurements individually (per tank), you have a repeated measures design to consider. But again, the simplest way to deal with repeated measures is to construct one or a few aggregate response variables that answer the questions you have about what happens in the tanks.
Best wishes,
Rolf Sundberg
My Dear Paula
Answer of My collegue Rolf is very good and in this time I say also you can solve by:
1- Split plot in time (repeated measurment) as time factore
2- use Multivarite analysis is very good becuse time of measurment in period (i+1 ) not independent with period(i) and this effect in error of model
My research in Msc about this subject you can see my researchgate
I hope all success to all works.
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