Table 5

Main methodological issues and solutions to answer the question "Do innovative cropping systems perform better than the control systems in the production situations under consideration?”.

Methodological issues Solutions Actions
Should we use data collected at the plot level or at the block level? In order to control, as well as possible, for possible sources of bias in the comparison of the two cropping systems, it is advisable to use the smallest unit. We choose the plot here because the difference between plots will be found in the random variation, whereas with the blocks it could be confused with the effect of crops and not necessarily be found in the random variation evaluated between blocks.

How to compare cropping systems? Given the complexity of cropping systems, the first step is to verify that there are no elements that could distort the comparison by confounding effects or by increasing random variation.
If it is a cross-cutting analysis, the different levels of spatial scale must be controlled.
A mixed model is the most suitable statistical model for this question, provided that its conditions of application are respected.
Check that items that could increase random variation cannot be controlled even if they were not included in the experimental design.
Use of mixed models to control the site and block effects
Lattice graphs are well-suited for visualizing all the effects that apply to the dependent variable.

How to write a model to compare systems without bias? A good knowledge of the experimental layout to identify the relevant point. Design of the conceptual scheme of the experiment; identification of statistical units, random effect variables, fixed effect variables, the way modalities intersect or interlock.

In the context of an experimental network, can we compare innovative systems with control systems if they do not have the same number of systems in each block? It is necessary that the modalities of the fixed effect variables are balanced between blocks. If not, it is advised to retain only common modalities for carrying out analyses. The Béarn platform tests three cropping systems (one control and two innovative) whereas other platforms only consider two. To overcome this agronomic issue, we considered only one of the innovative systems of this platform. The choice was made for the most promising system (I2, Tab. 2).

How to implement temporal variables in statistical models? If one of the objectives is to study trajectories of cropping systems’ effects, time is to be considered here as a fixed factor, whose effects are to be evaluated.
When this is not the case, time can be considered as a random effect factor, allowing repetitions within the experiment.
One of the objectives of the Syppre experimental network is to study trajectories of the effects of cropping systems. Time was therefore considered here as a fixed factor to be evaluated. A mixed model was implemented where time was considered at the interaction ‘platform x cropping system’ level.

How to compare cropping systems with different rotations, possibly with different durations? If crop diversity is not a lever and crops should not bias the comparison, the crop variable can be considered as a random variable and controlled in a mixed model.
If diversification is considered as a lever, and that one system is more diversified than another, the “crop effect” should not be controlled in the model, as this would affect the comparison of systems
Duration should be a controlled factor. Its impact can be estimated at any time, but with specific interpretations at the end of each cropping sequence.
Implement mixed models without the “crop variable” being controlled.
Our analyses only show the effect of time during the sequences because no system has yet completed its crop rotation.

How to deal with heteroscedasticity, notably caused by heterogeneity of crops with regard to variability, for comparison of cropping systems? It is necessary to use models whose heteroscedasticity is corrected by a mathematical transformation of the dependent variable.
This is not always satisfactory.
Scaling transformation for dependent variables when necessary. Use of logarithm, square root and inverse functions, alone or in combination.

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