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To compare how different analytical methods explain crop yields from a long-term field experiment (LTFE), we analyzed the grain yield of winter wheat (WW) under different fertilizer applications in Müncheberg, Germany. An analysis of variance (ANOVA), linear mixed-effects model (LMM), and MP5 regression tree model were used to evaluate the grain yield response. All the methods identified fertilizer application and environmental factors as the main variables that explained 80% of the variance in grain yields. Mineral nitrogen fertilizer (NF) application was the major factor that influenced the grain yield in all methods. Farmyard manure slightly influenced the grain yield with no NF application in the ANOVA and M5P regression tree. While sources of environmental factors were unmeasured in the ANOVA test, they were quantified in detail in the LMM and M5P model. The LMM and M5P model identified the cumulative number of freezing days in December as the main climate-based determinant of the grain yield variation. Additionally, the temperature in October, the cumulative number of freezing days in February, the yield of the preceding crop, and the total nitrogen in the soil were determinants of the grain yield in both models. Apart from the common determinants that appeared in both models, the LMM additionally showed precipitation in June and the cumulative number of days in July with temperatures above 30 °C, while the M5P model showed soil organic carbon as an influencing factor of the grain yield. The ANOVA results provide only the main factors affecting the WW yield. The LMM had a better predictive performance compared to the M5P, with smaller root mean square and mean absolute errors. However, they were richer regressors than the ANOVA. The M5P model presented an intuitive visualization of important variables and their critical thresholds, and revealed other variables that were not captured by the LMM model. Hence, the use of different methods can strengthen the statement of the analysis, and thus, the co-use of the LMM and M5P model should be considered, especially in large databases involving multiple variables.

Statistical Analysis versus the M5P Machine Learning Algorithm to Analyze the Yield of Winter Wheat in a Long-Term Fertilizer Experiment