Jmp version 13.0 statistical software

All the statistical analyses were performed by JMP Version 13.0 statistical software (SAS Institute Inc., Cary, NC, USA), and values of p < 0.05 were considered to be statistically significant in all cases. A Shapiro–Wilk test was used to check normal distribution. Average and standard deviations were calculated for all measurements. The Wilcoxon rank sum test and a two-sample t-test were used to test for differences in baseline characteristics between the groups. The Wilcoxon signed-rank test and paired t-test were used to test for changes from baseline in each training group before and after the six-week training period. To compare changes from baseline between the two training groups, the data analyzed were tested with a Wilcoxon rank sum test and two-sample t-test. Moreover, we calculated the effect size of Cohen’s d to determine the strength of association between interventions.

The screening of the data was necessitated because some data points were inconsistent and observed to have either soil or plant nutrient concentrations extremely above and below literature range. To address this, multivariate outliers (n = 219) from the experimental data were discarded first at **P < 0.05 using Mahalanobis distance in JMP version 13.0 statistical software (SAS Institute Inc., 2017 ). Then to understands the characteristics of the screened experimental data (n = 1371), analysis of variance was computed using the same JMP 13.0 statistical software. Nutrient application (NA), agro-ecological zone (AEZ) and variety group (VG) were used as main factors. Season was excluded in the ANOVA because different fields were used between the two seasons of the field experimentation. Mean values with significant differences were compared using Tukey's HSD (Honestly Significant Difference) test. Finally, the screened experimental data was randomly divided into 80% independent fields for parameterization (n = 1090) and the remaining 20% (n = 281) for validation of the QUEFTS model.

Univariate analysis of the differences between the groups was determined by log‐rank tests, and multivariate analysis by chi‐squared tests. All statistical analyses were performed using JMP version 13.0 statistical software (SAS Institute Inc). Two‐sided P values < .05 were considered significant.