# Split Plot Design? lmer analysis

I need advice regarding the analysis of a project that I am working at the moment. Here the picture of the experiment:

We have an RCBD with four blocks. Within each block there are 5 plots. Each plot is managed in a different way (mono cropping conventional, mono cropping organic, agroforestry conventional, agroforestry organic and SAFS). Within each plot, 12 cocoa varieties are planted. For each varieties we have 4 plants. We are collecting data on phonological traits (eg. Number of flowers per plant). We would like to know if there are differences among varieties and systems.

The first question is if such a design can be considered a split-plot design, when the different production systems represents the main plot effect and the different varieties represents the sub-plot level. Would you consider the following model to be correct?

number_of_flowers  ~  production_systems*variety + (1|block/plot)


Then we would use a contrast statement to test differences among systems.

• Are the varieties planted at the plots in a random way? Or are all plants of a variety together on a subplot? Also, since you have count data, you should use glmer with an appropriate family (e.g., Poisson). Right now your model assumes that differences between production systems or varieties are constant over the blocks/plots. That seems like something that should be tested. E.g., I might try number_of_flowers ~ production_systems*variety + (production_systems|block) + (variety|block/plot). – Roland Apr 28 '15 at 14:18
• Thanks for your suggestions. Unluckily the varieties were not planted in a random way and the are not togheter into subplots. they are planted spread at constant distances in each plot. Their planting order is the same for all the plots within each block, but each block differs from each other. In case we find out that the differences between production systems or varieties are not constant (which I believe to be so), how would you suggest to proceed? Thanks! – PietroB Apr 28 '15 at 15:27
• So maybe you also need to check whether position inside the plot influences the result. If the differences are not constant over blocks and plots, model this variation as random effects like in the example I've showed you. – Roland Apr 28 '15 at 15:45