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I test the effect of a plant dose on the abundance of a specific microbe, cultured in glass tube in vitro. The treatment consist of 5 doses (0, 1, 2, 3, 4). Each culture tube receives one of the dose in 4 replications. The abundance of the microbe is observed after two times point: 12h and 24h. I would like to check how the plant dose affect the microbe abundance throughout the time. Is this a randomized complete design with two repeated measures, a randomized complete block design with time point considered as block? or a 4 X 2 factorial design? I am confused between those three experimental design.

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Tentatively, we could write a model for this experiment like $$ Y_{ijt}=\mu + \delta_i + \alpha_t + \epsilon_{ijt} $$ as a starting point, where a completion of the model need some distributional assumptions on the error term $\epsilon_{iijt}$. In addition you could include an interaction term $(\delta\alpha)_{it}$.

You have not told us about any blocking, so this is not a blocked experiment. I would say it is a repeated measures experiment. Also a factorial experiment, with two factors dose and time.

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