*2.4. Statistical Analysis*

Linear mixed models were used to evaluate the e ffect of rye and winter triticale on cover crop height and biomass, weed biomass (Date 1 and Date 2), soybean population, biomass at flowering and yield. "Cover crop species" was treated as a fixed e ffect. The six sites and eight plots per sites were treated as a random e ffect. The "site" factor refers to "location x year". The following model was used for analysis:

$$Yijk = Xi + Aj + Bk + Cjk + XEijk$$

where *X* is the fixed factor (cover crop species), A the first random e ffect (sites), *B* the second random effect (plots), C the interaction between both random e ffect factors, *XE* the error term, *i* a particular cover crop species, *j* a particular site (location × year) and k refer to a particular plot.

ANOVA per factor was also conducted for each site. Cover crop height, soybean height and yield met the assumptions for analysis of variance (ANOVA). Cover crop biomass, weed biomass at Date 1 and Date 2, as well as soybean density and biomass, were transformed as needed to meet the assumption for analysis of variance using square root transformation. We used the R software for every statistical analysis in R version 1.1.463 © RStudio, Inc, and more precisely the lme4 package for the linear mixed models [47]. Statistical significance of the results was evaluated at a *p*-value < 0.05 and treatment means were compared using Tukey's pairwise comparison.
