Related papers: Comparing three groups
Methods for quantifying the similarity of datasets are relevant in applications where two or more datasets, or their underlying distributions, need to be compared, ranging from two- and k-sample testing to applications in machine learning…
This paper examines the constricted use of group theory in the studies of pairwise comparisons. The presented approach is based on the application of the famous Levi Theorems of 1942 and 1943 for orderable groups. The theoretical foundation…
We consider statistical procedures for hypothesis testing of real valued functionals of matched pairs with missing values. In order to improve the accuracy of existing methods, we propose a novel multiplication combination procedure.…
The pairwise comparisons method is a convenient tool used when the relative order among different concepts (alternatives) needs to be determined. One popular implementation of the method is based on solving an eigenvalue problem for the…
Comparison and contrast are the basic means to unveil causation and learn which treatments work. To build good comparison groups, randomized experimentation is key, yet often infeasible. In such non-experimental settings, we illustrate and…
The complexity of biological systems, and the increasingly large amount of associated experimental data, necessitates that we develop mathematical models to further our understanding of these systems. As biological systems are generally not…
Method comparisons are essential to provide recommendations and guidance for applied researchers, who often have to choose from a plethora of available approaches. While many comparisons exist in the literature, these are often not neutral…
We study the ranking of individuals, teams, or objects, based on pairwise comparisons between them, using the Bradley-Terry model. Estimates of rankings within this model are commonly made using a simple iterative algorithm first introduced…
The paper considers the problem of finding the number of dominant voters in two-level voting procedures. At the first stage, voting is conducted among local groups of voters, and at the second stage, the results are aggregated to form a…
Statistical tests that compare classification algorithms are univariate and use a single performance measure, e.g., misclassification error, $F$ measure, AUC, and so on. In multivariate tests, comparison is done using multiple measures…
Evaluation in NLP is usually done by comparing the scores of competing systems independently averaged over a common set of test instances. In this work, we question the use of averages for aggregating evaluation scores into a final number…
Chess championships are often organised as a Swiss-system tournament, causing great challenges in ranking the participants due to the different strength of schedules and possible circular triads. The paper suggests that pairwise comparison…
Owing to the advancement of deep learning, artificial systems are now rival to humans in several pattern recognition tasks, such as visual recognition of object categories. However, this is only the case with the tasks for which correct…
One of the major challenges for collective intelligence is inconsistency, which is unavoidable whenever subjective assessments are involved. Pairwise comparisons allow one to represent such subjective assessments and to process them by…
This paper describes a generalizable model evaluation method that can be adapted to evaluate AI/ML models across multiple criteria including core scientific principles and more practical outcomes. Emerging from prediction competitions in…
We consider a simple model of imprecise comparisons: there exists some $\delta>0$ such that when a subject is given two elements to compare, if the values of those elements (as perceived by the subject) differ by at least $\delta$, then the…
The development of rigorous quality assessment model relies on the collection of reliable subjective data, where the perceived quality of visual multimedia is rated by the human observers. Different subjective assessment protocols can be…
In this paper, paired comparison models with stochastic background are investigated. We focus on the models that allow three options for choice. We estimate all parameters, the strength of the objects and the boundaries of equal decision,…
In this paper, we present a mathematical model to capture various factors which may influence the accuracy of a competitive group recommendation system. We apply this model to peer review systems, i.e., conference or research grants review,…
In the social sciences we are often interested in comparing models specified by parametric equality or inequality constraints. For instance, when examining three group means $\{ \mu_1, \mu_2, \mu_3\}$ through an analysis of variance…