I gave three treatments A,B,C, to my aquatic animal (each treatment have 10 animals), and measured the total length of the studied animal every 3 days. At the end of the culture I had data of the total length at 10 time points. I want to use ANOVA to compare whether or not there are difference among the three treatment in the total length of the animal.
Since the length was measured at different time point, which ANOVA i need to use？ obviously， one-way ANOVA is not applicable.
here some solutions amongst others :
1 - the simplest : neglect all the sizes but the last - obviously the final size is the issue - you may then perform a simple one-way anova.
2 - still simple : the same as before but with the "baseline" (size at t=0) as a covariate to take into account a possible/probable heterogeneity of sizes at t=0. The ancova is the the good method, the test is still comparison of the treatments.
3 - more elaborate : keep all the observations, perform an ancova with the time as covariate. Your treatment comparisons will be performed via test(s) of the interaction treatment:time. You must be aware that a proper modelling of the growth may be critical and that a simple linear trend might be grossly inaccurate - an eye-check on a scatter plot may be informative enough.
4 - the same as 3 but with animals as random factor in a Mixed Models. Test and modelling the same as above.
I think you can use both (ANOVA and MANOVA).
MANOVA to see the combination between two factors (treatment and time).
One-way ANOVA to see the effect of each factor at fixed level of the other.
mixed model factorial repeated ANOVS is best, rest other method affects alpha (increase type I error).
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