Methods for exact small-sample analyses with categorical data have been increasingly well developed in recent years. A variety of exact methods exist, primarily using the approach that eliminates unknown parameters by conditioning on their sufficient statistics. In addition, a variety of algorithms now exist for implementing the methods. This paper briefly summarizes the exact approaches and describes recent developments. Controversy continues about the appropriateness of some exact methods, primarily relating to their conservative nature because of discreteness. This issue is examined for two simple problems in which discreteness can be severe--interval estimation of a proportion and the odds ratio. In general, adjusted exact methods based on the mid-P-value seem a reasonable way of reducing the severity of this problem.

Exact inference for categorical data: recent advances and continuing controversies

This paper considers confidence intervals for the difference of two binomial proportions. Some currently used approaches are discussed. A new approach is proposed. Under several generally used criteria, these approaches are thoroughly compared. The widely used Wald confidence interval (CI) is far from satisfactory, while the Newcombe's CI, new recentered CI and score CI have very good performance. Recommendations for which approach is applicable under different situations are given.

Confidence intervals for two sample binomial distribution

We experimentally investigate the determinants of judicial decisions in a setting resembling real-world judicial decision making. We gave US federal judges 55 minutes to adjudicate a real appeals case from an international tribunal, with minor modifications to accommodate the experimental treatments. The fictitious briefs focused on one easily understandable issue of law. Our 2 × 2 between-subject factorial design crossed a weak precedent and legally irrelevant defendant characteristics. In a survey, law professors predicted that the precedent would have a stronger effect than the defendant characteristics. In actuality, the precedent had no detectable effect on the judges’ decisions, whereas the two defendants’ affirmance rates differed by 45 percent. Judges’ written reasons, on the other hand, did not mention defendant characteristics, focusing instead on the precedent and other legalistic and policy considerations.

/pdf/justice-is-less-blind-and-less-legalistic-than-we-thought-13h8z5ms0r.pdf

Justice Is Less Blind, and Less Legalistic, than We Thought: Evidence from an Experiment with Real Judges

The mixture approach for simulating bivariate distributions introduced by Michael, J. R. and Schucany, W. R. (2002). The mixture approach for simulating bivariate distributions with specific correlations. The American Statistician, 56, 48–54, is generalized to generate pseudo-random numbers from multivariate distributions. The simulated joint distributions have identical marginals and equal positive pairwise correlations. The approach is illustrated for the p-dimensional families of beta and gamma distributions. For these families the formulas for the correlations have simple closed forms and the computations are quite simple.

Simulating multivariate distributions with specific correlations

Statistically sound pattern discovery harnesses the rigour of statistical hypothesis testing to overcome many of the issues that have hampered standard data mining approaches to pattern discovery. Most importantly, application of appropriate statistical tests allows precise control over the risk of false discoveries -- patterns that are found in the sample data but do not hold in the wider population from which the sample was drawn. Statistical tests can also be applied to filter out patterns that are unlikely to be useful, removing uninformative variations of the key patterns in the data. This tutorial introduces the key statistical and data mining theory and techniques that underpin this fast developing field. 
We concentrate on two general classes of patterns: dependency rules that express statistical dependencies between condition and consequent parts and dependency sets that express mutual dependence between set elements. We clarify alternative interpretations of statistical dependence and introduce appropriate tests for evaluating statistical significance of patterns in different situations. We also introduce special techniques for controlling the likelihood of spurious discoveries when multitudes of patterns are evaluated. 
The paper is aimed at a wide variety of audiences. It provides the necessary statistical background and summary of the state-of-the-art for any data mining researcher or practitioner wishing to enter or understand statistically sound pattern discovery research or practice. It can serve as a general introduction to the field of statistically sound pattern discovery for any reader with a general background in data sciences.

/pdf/a-tutorial-on-statistically-sound-pattern-discovery-48qhpqp4u5.pdf

A Tutorial on Statistically Sound Pattern Discovery

The $2\times2$ table is used as a vehicle for discussing different approaches to statistical inference. Several of these approaches (both classical and Bayesian) are compared, and difficulties with them are highlighted. More frequent use of one-sided tests is advocated. Given independent samples from two binomial distributions, and taking independent Jeffreys priors, we note that the posterior probability that the proportion of successes in the first population is larger than in the second can be estimated from the standard (uncorrected) chi-square significance level. An exact formula for this probability is derived. However, we argue that usually it will be more appropriate to use dependent priors, and we suggest a particular "standard prior" for the $2\times2$ table. For small numbers of observations this is more conservative than Fisher's exact test, but it is less conservative for larger sample sizes. Several examples are given.

/pdf/the-2-times2-table-a-discussion-from-a-bayesian-viewpoint-4t00qj37yn.pdf

The $2\times2$ table: a discussion from a Bayesian viewpoint

Handle everyday research tasks with reliable, citation-backed results

Your personal Research Agent to handle research tasks with citation-backed results

Popular Tasks used by Researchers

How can I help with your research?

Meet SciSpace

Get more enhanced response by uploading the PDFs you want me to reference.

No relevant PDFs in your library

SciSpace is the AI research assistant for academics. Run systematic literature reviews on 280M+ papers, and write papers with cited sources. Trusted by 1M+ students, PhDs & researchers.

SciSpace | AI for Research

Analyze PDFs

Code & Manuscripts

Funding & Grants

Literature & Patents

Medical & Clinical Data

Systematic Review

Visualize & Present

Web & Data

Build a Google Scholar-like website for your research.

Build a website

Create charts and images for your research

Create a Chart

Write a paper for submission to a journal

Draft a manuscript

Patent Search

Design eye-catching scientific posters in minutes.

Scientific Poster Generation

Systematic Literature Review

One task is running at the moment. Your messages will be shown right after.

Drag and drop or click here to browse

Loved by <highlight>1 million+</highlight> researchers

Extract a list of specific topics and their sources from unstructured text

Topics

Compare and analyze relevant papers that matches with your search

Papers

Get insights from PDFs and bookmarked papers from your library

My library

Recent searches

Try searching for:

Catch AI-generated content in scholarly and non-scholarly content

{ai} Detector

Ai Writer

Get PDF Summaries, highlighted text explanations 

Chat with PDF

Effortlessly create in-text citations and bibliographies in APA and 2,500 other formats

Citation generator

Get explanations, summaries, and answers on academic papers

Ease up your research workflow with {scispace}'s cohort of exciting AI tools

Elevate your academic writing skills and convey your ideas the way you want

Paraphraser

Explore our range of reading and writing tools

Your file is being prepared and should be ready in a few minutes. If it's a large file, it might take a bit longer. You can close this window, and we'll email you the file when it's done.

You have reached a maximum limit of <strong>{limit}</strong> columns in the table. Remove at least <strong>1</strong> column to add or create another one.

J. V. Howard

Author Tools

Chat about Author

Papers

The $2\times2$ table: a discussion from a Bayesian viewpoint