## Table 7

Main methodological issues and solutions to answer the question “Do diversification and the cultivation of oilseed and protein crops result in improved cropping system performance?”.

Methodological issues Solutions Actions
Should we use data collected at the plot level or at the block level? The statistical unit is the block since the question requires consideration of crop diversity in the crop sequence. We used a data frame presenting the mean per block in a row.
How to summarize performance indicators by block? The method should be adapted to each experimental situation.
In particular, we can use the median, which is not sensitive to outliers, the mean if outliers make sense in the summary, the sum if one does not want a value that is weighted by statistical individuals. If blocks do not have the same number of plots, sums will be affected.
The control and innovative cropping systems were not implemented in the same number of plots. The choice of crop sequence is therefore important for the overall evaluation of the systems.
We chose the mean to summarize information since it takes into account the number of plots.
The value of an indicator for a block-year corresponds to the mean of its values in the plots of the block.
How to describe crop diversification, oilseed and protein crop rate when there are no specific indicators? Data extracted from the database do not always provide variables immediately relevant for answering specific questions. Need for manual input: creation of variables to describe oilseeds, protein crops and diversification (see below) from the names of cultivated species in the database. Calculate diversification, oilseed and protein crop rate in each block each year from the plot data table.
How to describe diversification? Use simple calculation of the ratio between the number of different crops and the number of crops in the crop sequence. Use of a diversification index (Keichinger et al., 2021).
What calculation should be used to describe the rates of oilseeds and protein crops? A simple relationship between the number of oilseed/protein/crops and the number of crops in the crop sequence.
Adaptation of a diversification index (Keichinger et al., 2021) to oilseeds and protein crops based on their proportion in the crop sequence.
What analysis should be conducted to measure the association between performance indicators, diversification and oilseed and protein crop rates? Analyze non causal relationships between many variables. Multifactor analysis conducted on selected variables/indicators is relevant to illustrate multidimensional performance. Diversification index, oilseed and protein crop rates are descriptive variables. A hierarchical ascending classification on the factorial coordinates is thereafter recommended. Principal Component Analysis (PCA) on a data table where a row is a block measured in a given year.
PCA performed on the result indicators.
Hierarchical clustering on the components of the PCA.
Description of the classes with all indicators, as well as diversification indices, oilseed rate and protein crop rates.

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