Let s = (s1, . . . , sm) and t = (t1, . . . , tn) be vectors of nonnegative integer-valued functions of m,n with equal sum S = ∑m i=1 si = ∑n j=1 tj. Let M(s, t) be the number of m × n matrices with nonnegative integer entries such that the ith row has row sum si and the jth column has column sum tj for all i, j. Such matrices occur in many different settings, an important example being the con...

Two visualization techniques for the independence problem in 2-way contingency tables—assocation and mosaic plots—are extended in two directions: 1. The visualization is enhanced by displaying the significance of an appropriate test for independence and by using improved color schemes. 2. The implementation in the R system is improved using a more modular design and allowing for more flexible s...

This paper 1 describes a series of statistical meta-tests for comparing independent contingency tables for different types of significant difference. Recognising when an experiment obtains a significantly different result and when it does not is frequently overlooked in research publication. Papers are frequently published citing ‘p values’ or test scores suggesting a ‘stronger effect’ substitu...

In this paper, we propose a new counting scheme for m× n contingency tables. Our scheme is a modification of Dyer and Greenhill’s scheme for two rowed contingency tables [5]. We can estimate not only the sizes of error, but also the sizes of the bias of the number of tables obtained by our scheme, on the assumption that we have an approximate sampler.

• If we have data that are measurable (eg. height, time, weight, age, test score, etc.) then we can use the coefficient of correlation (r) to measure the strength of the linear association between two sets of data. • If we have two sets of rankings, then we can use Spearman's Rank Order Correlation Coefficient to measure the strength of the association between them. • However, both of these tec...

This paper considers a method that combines ideas from Bayesian learning, Bayesian network inference, and classical hypothesis testing to produce a more reliable and robust test of independence for constraintbased (CB) learning of causal structure. Our method produces a smoothed contingency table NXY Z that can be used with any test of independence that relies on contingency table statistics. N...

Applied researchers often use tests based on contingency tables in preliminary data analysis and diagnostic testing. We show that many of such tests may be alternatively implemented by testing for coefficient restrictions in linear regression systems (as a rule, employing the Wald test). This unifies the theories of regression analysis and contingency tables, sheds more light on intuitive conte...

Over the past fewdecades correspondence analysis has gained an international reputation as a powerful statistical tool for the graphical analysis of contingency tables. This popularity stems from its development and application inmany European countries, especially France, and its use has spread to English speaking nations such as the United States and the United Kingdom. Its growing popularity...

Rapid research progress in genotyping techniques have allowed large genomewide disease association studies. Existing methods often focus on determining associations between single loci and the disease. However, most diseases involve complex relationships between multiple loci an the environment. Here we describe a method for finding interacting loci by combining the traditionally used single-lo...