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.