Analysis of defects in coffee beans compared to biplots for simultaneous tables

Abstract

The demand for high quality coffee has become a consolidated criterion to achieve the best prices. Currently,
cooperatives evaluate the coffee beans mainly through the particle size and the number of defects in the sample. This evaluation
type generates counting data that originates contingency tables from different periods or groups involving the same variables
in the row and column and there may be interest in knowing if two tables are related and how much are related. These
are the so-called combined tables. Statistical analysis techniques normally employed do not include categorical data in the
combined tables. The aim of this study was to evaluate the incidence of different types of defects in samples of large flat coffee
beans in two different harvests through the construction of biplots. The decomposition theory in single simultaneous values of
double entry contingency tables was used. The results of defect counting in beans of 24 coffee samples from southern Minas
Gerais, Brazil, were evaluated in the 2014 and 2015 harvests. Moreover, the association among defect types, considered within
different total defect proportions in the sample, was verified based on the percentage in 17/18 sieves. It was also evaluated the
relative sums of squares from the similarity and dissimilarity among the harvests. It is concluded that the simultaneous analysis
technique allows better visualizing the common behavior and alterations among different harvests, distinguishing the defect
types associated with each harvest and among different proportions of large flat beans.