Which ANOVA test to use in this experimental design?

Question

I have an experimental design as follows:

Three groups of cakes: treatment A, treatment B, control;

Three replicates per cake.

They are observed during 10 days for microbial growth.

My interest is in evaluate their resistance to microbial growth, that is, if they differ in the amount of microbial growth during the experiment.

My question is:

To evaluate that which statistical analysis strategy must I use? (and would you check my suggestions of R code as well for the given options?)

two-way ANOVA (cake treatment (means of replicates) vs. days); [equivalent in R: microbial_amount ~ treatment*days]
three-way ANOVA (cake replicate vs. cake treatment vs. days) or [equivalent in R: microbial_amount ~ treatment*days + replicate]
Another type of ANOVA (nested ANOVA, repeated measures ANOVA, I'm not sure yet...)

Peter Flom · Accepted Answer · 2017-03-10 14:47:45Z

1

I wouldn't use any kind of ANOVA. I would use a multilevel model or possibly generalized estimating equations.

If you, for some reason, have to use an ANOVA, then repeated measures is the only reasonable one, but it makes unrealistic assumptions.

answered Mar 10, 2017 at 14:47

Peter Flom

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$\begingroup$ Thanks for the quick reply, Peter! Would you please clarify why ANOVA is not the best option in this case? I never used multilevel models... What should I take into account if I am to choose between a multilevel model and generalized estimating equations? $\endgroup$
– Luís Muniz
Commented Mar 10, 2017 at 15:20
$\begingroup$ Regular ANOVA is wrong because it assumes that the errors are independent and yours will not be. RM ANOVA is not wrong, but it assumes sphericity, which is almost never there. GEE vs. MLM is complicated. See stats.stackexchange.com/questions/16390/… $\endgroup$
– Peter Flom
Commented Mar 10, 2017 at 18:05

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