Related papers: Comparing three groups
Factor analysis is over a century old, but it is still problematic to choose the number of factors for a given data set. The scree test is popular but subjective. The best performing objective methods are recommended on the basis of…
In this expository paper we describe four primality tests. The first test is very efficient, but is only capable of proving that a given number is either composite or 'very probably' prime. The second test is a deterministic polynomial time…
Conjoint analysis is a popular experimental design used to measure multidimensional preferences. Researchers examine how varying a factor of interest, while controlling for other relevant factors, influences decision-making. Currently,…
Orthogonalization is one of few mathematical methods conforming to mathematical standards for approximation. Finding a consistent PC matrix of a given an inconsistent PC matrix is the main goal of a pairwise comparisons method. We introduce…
We consider sequential hypothesis testing based on observations which are received in groups of random size. The observations are assumed to be independent both within and between the groups. We assume that the group sizes are independent…
There are many priority deriving methods for pairwise comparison matrices. It is known that when these matrices are consistent all these methods result in the same priority vector. However, when they are inconsistent, the results may vary.…
We consider a new group testing model wherein each item is a binary random variable defined by an a priori probability of being defective. We assume that each probability is small and that items are independent, but not necessarily…
Factorial designs are frequently used in different fields of science, e.g. psychological, medical or biometric studies. Standard approaches, as the ANOVA $F$-test, make different assumptions on the distribution of the error terms, the…
In real life situations often paired comparisons involving alternatives of either full or partial profiles to mitigate cognitive burden are presented. For this situation the problem of finding optimal designs is considered in the presence…
We consider the problem of evaluating preferences for criteria used by university students when selecting a hotel for accommodation during a professional development program in a foreign country. Input data for analysis come from a survey…
Empirical studies on formal methods and tools are rare. In this paper, we provide guidelines for such studies. We mention their main ingredients and then define nine different study strategies (laboratory experiments with software and human…
Pairwise comparisons based on human judgements are an effective method for determining rankings of items or individuals. However, as human biases perpetuate from pairwise comparisons to recovered rankings, they affect algorithmic decision…
We propose a test of fairness in score-based ranking systems called matched pair calibration. Our approach constructs a set of matched item pairs with minimal confounding differences between subgroups before computing an appropriate measure…
The standard paradigm for confirmatory clinical trials is to compare experimental treatments with a control, for example the standard of care or a placebo. However, it is not always the case that a suitable control exists. Efficient…
We consider the problem of constructing matched groups such that the resulting groups are statistically similar with respect to their average values for multiple covariates. This group-matching problem arises in many cases, including…
Genome-wide association analysis has generated much discussion about how to preserve power to detect signals despite the detrimental effect of multiple testing on power. We develop a weighted multiple testing procedure that facilitates the…
The task of ranking individuals or teams, based on a set of comparisons between pairs, arises in various contexts, including sporting competitions and the analysis of dominance hierarchies among animals and humans. Given data on which…
Recommender systems are one of the most pervasive applications of machine learning in industry, with many services using them to match users to products or information. As such it is important to ask: what are the possible fairness risks,…
We consider problems of rating alternatives based on their pairwise comparison under various assumptions, including constraints on the final scores of alternatives. The problems are formulated in the framework of tropical mathematics to…
This paper compares three approaches to the problem of selecting among probability models to fit data (1) use of statistical criteria such as Akaike's information criterion and Schwarz's "Bayesian information criterion," (2) maximization of…