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15 - Multiple Proportions

from Part III - Elements of Statistical Inference

Published online by Cambridge University Press:  22 July 2022

Ery Arias-Castro
Affiliation:
University of California, San Diego
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Summary

When a die (with 3 or more faces) is rolled, the result of each trial can take one of as many possible values. The same is true in the context of an urn experiment, when the balls in the urn are of multiple different colors. Such models are broadly applicable. Indeed, even `yes/no’ polls almost always include at least one other option like `not sure’ or `no opinion’. Another situation where discrete variables arise is when two or more coins are compared in terms of their chances of landing heads, or more generally, when two or more (otherwise identical) dice are compared in terms of their chances of landing on a particular face. In terms of urn experiments, the analog is a situation where balls are drawn from multiple urns. This sort of experiments can be used to model clinical trials where several treatments are compared and the outcome is dichotomous. When the coins are tossed together, or when the dice are rolled together, we might want to test for independence. We thus introduce some classical tests for comparing multiple discrete distributions and for testing for the independence of two or more discrete variables that are observed together.

Type
Chapter
Information
Principles of Statistical Analysis
Learning from Randomized Experiments
, pp. 203 - 229
Publisher: Cambridge University Press
Print publication year: 2022

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  • Multiple Proportions
  • Ery Arias-Castro, University of California, San Diego
  • Book: Principles of Statistical Analysis
  • Online publication: 22 July 2022
  • Chapter DOI: https://doi.org/10.1017/9781108779197.020
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  • Multiple Proportions
  • Ery Arias-Castro, University of California, San Diego
  • Book: Principles of Statistical Analysis
  • Online publication: 22 July 2022
  • Chapter DOI: https://doi.org/10.1017/9781108779197.020
Available formats
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Save book to Google Drive

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Google Drive.

  • Multiple Proportions
  • Ery Arias-Castro, University of California, San Diego
  • Book: Principles of Statistical Analysis
  • Online publication: 22 July 2022
  • Chapter DOI: https://doi.org/10.1017/9781108779197.020
Available formats
×