Additive main effect and multiplicative interaction analysis of N and K fertilizations to perennial ryegrass turf

Abstract

Additive main effect and multiplicative interaction (AMMI) analysis has been shown to be more effective than the conventional two‐way fixed effects model when targeting the interaction. Field studies accumulate noise in the interaction, and this reduces predictive accuracy. Statistics from the multivariate component of AMMI are useful for interpreting the multiplicative interaction compared to the additive model, the basis of analysis of variance (ANOVA). Previously published field studies (RCB with four replicates) were reanalyzed using AMMI. AMMI was used to investigate clipping yield, soil K and leaf tissue K responses to 15 fertilizers (F, various N and K combinations) repeated over 5 years (Y) in perennial ryegrass ( Lolium perenne L.) maintained as turfgrass. Noise in the F × Y interaction with 56 degrees of freedom (df) ranged from 22.2 (clipping yield) to 44.0% (leaf tissue K) of F × Y sum of squares before AMMI partitioning of 39 df as noise. AMMI‐1 statistical gain using 4 reps was equal to as many as 8.8 reps using AMMI‐F (full or cell means model). AMMI‐F raw means exhibited twice the crossovers of AMMI‐1 means. AMMI‐1 interaction scores (IAS‐1) for fertilizer and year correlated with soil pH and offered plausible interpretation of F × Y interactions in AMMI‐1 biplots. AMMI reduction of noise is underutilized in data analysis, especially in field studies where simple two‐way interactions are common and the interaction becomes quickly buried by noise when repeated in years.