Ternary vs. Right-Angled Plots in Agricultural Research: An Assessment of Data Representation Efficiency and User Perception

Abstract

The results presented in the manuscript are meant to open a new avenue for research on the representation of compositional data. One of the conclusions is that a classical ternary plot is difficult to read; hence, an easier-to-read graphical tool might find its place in the practice of applied data visualization, for example, to represent soil features or to illustrate the relationships between various plant characteristics.

Visual representation of data can ease their understanding and interpretation, particularly when more variables are considered together. The ternary plot, based on a barycentric coordinate system and commonly used to represent compositional variables, may be difficult to interpret due to its structural complexity—stemming in part from the 60° axis projection and the need for indirect value estimation. This article presents its new alternative, the right-angled triangle plot, and compares the two plot types in the representation of a compositional variable of three components. According to a theoretical comparison, the right-angled plot has several technical advantages (e.g., larger plotting area, direct axis reading), resulting from its construction being based on the Cartesian coordinate system. To verify this hypothesis from an empirical point of view, a survey was conducted involving 441 researchers to assess the effectiveness in correctly interpreting the data presented on both plots. The bias was lower, and the precision was higher on the right-angled plot. Indeed, this study’s results, particularly the higher accuracy (more than 95% when a minimal tolerance was allowed) in determining the values of individual variables (X, Y, and Z), as well as the correctly identification of all three variables simultaneously in the right-angled plot compared with the ternary plot, suggest that the former may hold potential for improving the visualization of compositional data with three components. However, introducing this new type of plot would require familiarizing potential users with it, since the majority of respondents (63.2%) still considered the ternary plot easier to use, likely due to its long use and the novelty of the new plot type.