Work with interactive mapping tools from across the Census Bureau.
Read briefs and reports from Census Bureau experts.
Watch Census Bureau vignettes, testimonials, and video files.
Read research analyses from Census Bureau experts.
Developer portal to access services and documentation for the Census Bureau's APIs.
Explore Census Bureau data on your mobile device with interactive tools.
Find a multitude of DVDs, CDs and publications in print by topic.
These external sites provide more data.
Download extraction tools to help you get the in-depth data you need.
Explore Census data with interactive visualizations covering a broad range of topics.
Information about the U.S. Census Bureau.
Information about what we do at the U.S. Census Bureau.
Learn about other opportunities to collaborate with us.
Explore the rich historical background of an organization with roots almost as old as the nation.
Explore prospective positions available at the U.S. Census Bureau.
Information about the current field vacancies available at the U.S. Census Bureau Regional Offices.
Discover the latest in Census Bureau data releases, reports, and events.
The Census Bureau's Director writes on how we measure America's people, places and economy.
Find interesting and quirky statistics regarding national celebrations and major events.
Find media toolkits, advisories, and all the latest Census news.
See what's coming up in releases and reports.
Chi-squared approximation, Edgeworth series, exact test, moment-matching approximation, nuisance parameter, power study, simulation.
There are multiple tests of homogeneity of binomial proportions in the statistics literature. However, when working with sparse data, most test procedures may fail to perform well. In this article we review nine classical and recent testing procedures, including the standard Pearson and likelihood ratio tests; exact conditional and unconditional tests; tests based on moment matching chi-squared approximations; a recently proposed test based on a normal approximation in an asymptotic framework for sparse data; and a recent test based on higher order moment corrections using an Edgeworth approximation. For each test we review its theoretical underpinning, and show how to calculate the P-value. Most of the P-values can be readily calculated in a statistical computing software package such as R. We compare type I error probability and power via simulation. As expected, none of the procedures uniformly outperforms the others in terms of type I error probability and power, but we can make some recommendations based on our empirical results. In particular, we indicate scenarios in which certain otherwise reasonable test procedures can perform inadequately.
Martin Klein and Peter Linton. (2013). On a Comparison of Tests of Homogeneity of Binomial Proportions. Center for Statistical Research & Methodology Research Report Series (Statistics #2013-03). U.S. Census Bureau. Available online at <http://www.census.gov/srd/papers/pdf/rrs2013-03.pdf>.
This symbol indicates a link to a non-government web site. Our linking to these sites does not constitute an endorsement of any products, services or the information found on them. Once you link to another site you are subject to the policies of the new site.