I am analysing physiological data (transpiration rate, biomass production, silica content…) coming from plants cultivated in an experimental field with the aim of understanding if (1) water-treatment; (2) species; (3) variety have an effect on the silica content of leaves samples.
I would like to know an extra opinion on some issues: (a) can the experimental design (explication below) be considered a split-split plot design? If yes, is it correct to consider the block as the one year-experiment, the pplot as the treatment, the splot as the species and the ssplot as the variety? Do you have some suggestion to implement this design in R considering I have available, so far, only the data coming from one replication (one year of experimental field)?
Each plant grew inside a lysimeter (a cylindric tube placed inside a concreate pit which allowed me to control the water regime and the transpiration rate while it simulated the real field conditions as for example the soil profile). I am investigating 3 crops: Sorghum (S), Pearl millet (PM) and Finger millet (FM), 10 varieties for each crop, and I tested 2 different water treatments for each crop: water-stress (WS) and the control well-watered (WW). For each treatment I tested the same 10 varieties with 5 pseudo-replicas for each variety. I organized the field (file attached) into 6 plots: 1. FM- WS, 2. PM-WS, 3. S-WS, 4. FM-WW, 5. PM-WW, 6. S-WW. Each plot was filled with 50 cylinders (10 varieties x 5 pseudo-replicas) divided into 10 rows. The 50 plant-samples have been randomize separately (each plot has its own randomization). Therefore, in each plot I tested simultaneously 3 variables: (1) treatment; (2) species; (3) variety: each plot is characterized by 1 treatment and 1 species and 10 randomized-placed varieties and treatments have not been mixed in the same plot.
Yes, the circumstantial description indicates more affinity towards split-split plot design. Treatment i.e. WW and WS is the main factor because of its nature, species are sub-factor and varieties are sub-sub factor. To me pseudo-replica seems to be considered as replications if it fulfills the principles of experimental design. Mixing of the treatments in a plot is exactly not required since each species is required to grow separately during their cultivation. Probably in this study, investigator wants to determine comparative physiological parameters across the treatments, species and varieties within the species.
Yes, split-split plot design is appropriate. WW & WS assigned as main plot, species as the subplot and varieties of each species are assigned as the sub-subplot. There are three level of precision, with the main-plot factor receiving the lowest degree of precision and the sub-subplot factor receiving the highest degree of precision.
Yes you can use Split-split plot design where WS and WW is the main plot. First you decide your replicates. Then each replicate should be divided to into two main plots and randomly assigned WS and WW to these two main plots within a replicate. Then each main plot is divided to 3 Sub plots ( to assign three varieties randomly) and assign three varieties randomly to one main plot and then go to the other main plot and assign three varieties randomly. Then each sub-plot is divided into sub-sub plots to apply spp randomly within each subplot.
Please use the strip plot design because you have the main boc (water treatment), sub bloc (species), and sub-sub boc (varieties).
In strip plot/split block design, each block is divided into as many column (vertical strip) as levels of factor 'A' and as many row (horizontal strip) as the levels of factor 'B'. Levels of factor 'A' are assigned randomly to vertical strips and levels of factor 'B' are assigned to horizontal strips randomly. So in each strip, vertical or horizontal, level of one factor remain same throughout the different levels of second factor. In case of split plot design, formation of main plot and randomization of treatments remain similar to strip plot design. However, different levels second factor are accommodated randomly in relatively smaller plots within the main plot. Thus randomization of second factor and plot size are different from those adopted for strip plot design. Similarly, third factor which requires relatively smaller plots are accommodated as sub-sub plots in each subplot of the main plot. Again here randomization does not remain similar to strip plot design. Experimental details also indicate about different levels of precision and plot sizes for different treatments. Thus, looking over the experimental layout provided in the post, split-split plot design seems to be more pertinent than the strip plot design.
I do not agree with the answer given by Jean Pierre as if you use Strip plot because for the strip plot you use two sizes of main plots. You do not have Sub-sub plots here. eg
Thank you all for your answers, they have been very helpful and I am apprichiating the discussion.
As Isee the dabate is still open, so I take advantage to ask 2 more things:
1. I'm using the R package agricolae, function: sp.plot(block, pplot, splot, Y) to implement the split split plot design. First, do you have any other package to suggest in this specific case?
Secondly, (a) do you suggest to use as block the all year experiment (so block = 1, and this is not possible) or (b) do you suggest to use the cylinders as replications (so blocks =300) , as you suggested Narendra, or (c) is better to randomly divide the field into 2 blocks and assign to each block 150 cylinders, as I think Nimalshanthi suggested?
2.My supervisor suggested me to abandon the split-split plot design and to consider the randomized complete block design. In this case I would use the varieties as replications (so the cylinders) , and the blocks as the treatments. In this way the species (which are strictly depended on the varieties), would be avoided as parameters. Do you think tha RCBD should work properly? I have my doubs about because this would increase the differences within the block that won't be uniform at all. The blocks would have a source of variation which I know but that I am not taking into account.
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