Hello Everyone I'm started afield experiment 3 treatments and 4 replicates What is the optimal statistics analysis design for my experiment ?
The way this works best is to develop a question or set of questions. Figure out what kind of analysis will work best. Then using knowledge about the system plan a sample size that will provide enough power to make the methodology work. After all of that planning, start the experiment.
What was the question?
Why is four replicates per treatment sufficient, or how did you arrive at having 4 replicates?
What will you do if you have to discard 2 or 3 replicates from one treatment?
How will you define (or identify) the optimal statistical method?
Do you have one treatment at three levels, or three treatments each at several levels? I apply nitrogen at 30, 90, and 270 kg/ha (this is one treatment at three levels). I apply nitrogen, potassium, and phosphorus and nitrogen is at 20, 40, 80 kg/ha, potassium is at 8, 16, and 32 kg/ha, and phosphorus is also at 8, 16, and 32 kg/ha (three treatments each at three levels)?
How many variables are you measuring? One variable (total biomass) or many: yield, time to harvest, disease, root and shoot nutrient levels (N, P, K, Ca, Mg, Cu, Zn, B, and Mn), SPAD, number of aphids, and 20 other variables.
one treatment control + 2 levels and i will measure many nutrients such as N,P,K, and some micro nutrients in shoot and root so i want to know the optimal statistical method I distribute the replicates and the levels randomly
One approach to analysis is to take each nutrient (N,P,K,+micros) for each location (root, shoot) and do an ANOVA with a multiple comparison procedure like Tukey.
A different approach would be to argue that this experiment is a treatment at three levels (0, 1, and 2) and do a regression analysis using a mixed model with nutrient and location.
A different approach would be to ask how far apart are the treatments where there are now six treatments shoot (0, 1, 2) and root (0, 1, 2) labeled something like S0, R0, S1, R1, S2, R2 and you now use the nutrient measures as independent variables in something like a discriminant analysis and you calculate a Mahalanobis distance as part of the analysis. For this analysis your sample size must be larger than the number of variables in order to do the calculations. I have seen suggestions of 25 times (or more) the number of samples as there are variables.
There are many other types of analyses. Do the roots and shoots have the same response? Is there a relationship between N and B or any other pair of nutrients? Are you interested in DRIS? see: https://www.srs.fs.usda.gov/pubs/ja/ja_coleman010.pdf
If you do not have some idea about the size of the response you will get from the treatments and you have no idea of the variability in this system, then you and RG will have to take some guesses or forge an alternate path forward.
1) Look at the literature. What is the sample size in studies that have also looked at nutrient analysis of roots and shoots?
2) Look at your budget. What is the largest number of samples you can afford to process? That is money if samples are sent off to another lab, or time if you process all samples.
3) Look at greenhouse or field sites. Is there greenhouse space to do the experiment, is there a way to haul the samples back from the field?
4) If reduced to guessing then I would consider this a project with six treatments, and I would strive for 20 replicates in each treatment where each replicate would have its own tissue analysis (you cannot pool samples). Make sure that each treatment will provide sufficient material to conduct the tissue analysis.
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