For example we apply a fertilization regime on two different cultivars of a same plant, in 3 different growing seasons. There are differences between each season in studied traits. I want to know what is the best method to show this differences and to test if they are significant or not?
Apply mixed design ANOVA with cultivar as group variable and growing season as repeated measures factor. Then inspect for significance Between-Subject and Within-Subject effects. And if significant, proceed with post-hoc tests.
I assume that you have replicates (Block/Plot design).
What you can do is mixed modeling in R (lme4).
Your measured traits (I assume they are weighted between cultivars) are your response variable. Cultivar and season are your fixed factors and your plots (replicates) are your random factror to account for pseudoreplication.
Hi
Combined analysis is the best method for this analysis. Sources of variation, is including the season and the cultivar. You can make the best way to isolate the source of the error.
Hi, Hamed, hi all,
I concur with Panagiotis Theodorou.
If you are not familiar with coding in R, there is a very user-friendly GUI in R called R2STATS that will allow you to carry out the analyses as Panagiotis Theodorou suggests.
There are two fields in the R2STATS "models" tab, one for the dependent variable (DV), and one for the independent variables (IV), be they fixed effects or random effect(s). Fixed effects are to be put in as they are (e.g., if your fixed-effects IVs are called "cultivar" and "season", you just write in the IV box cultivar+season (for a model that tests for the principal effect of each of these two variables, assuming there is no interaction) or cultivar*season (for a model that tests for both the principal effect of each of these two variables and for their interaction) ) and the random-effect variable is to be put in as (1|replicates) if "replicates" is your random-effect variable.
The nice thing about R2STATS is that it yields the BIC (Bayesian information criterion) associated with each model so if you test all possible models (which is easy to do given your design) you know then which model is the most probably true (i.e., the "good" one) for your data (the lower the BIC, the better the model, so the "best" model, if and only if you test them all, is the one with the lower BIC).
Given you design you would have to test the following models:
M1: DV~ (1|replicates)+cultivar*season
M2: DV~ (1|replicates)+cultivar+season
If M2 is better than M1, then you test M2 versus
M3: DV~ (1|replicates)+cultivar
and versus
M4: DV~ (1|replicates)+season
Otherwise, if M1 is the best model this means that the interactive effect of "cultivar" and "season" is what best explain your data. You then look at the "graphs" tab in R2STATS to understand that interactive effect.
HTH,
cheers,
SCM
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