categorical - Author(s): Kerby Shedden, Ph.D., 2010...

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Author(s): Kerby Shedden, Ph.D., 2010 License: Unless otherwise noted, this material is made available under the terms of the Creative Commons Attribution Share Alike 3.0 License: http://creativecommons.org/licenses/by-sa/3.0/ We have reviewed this material in accordance with U.S. Copyright Law and have tried to maximize your ability to use, share, and adapt it. The citation key on the fol owing slide provides information about how you may share and adapt this material. Copyright holders of content included in this material should contact open.michigan@umich.edu with any questions, corrections, or clarification regarding the use of content. For more information about how to cite these materials visit http://open.umich.edu/privacy-and-terms-use. Any medical information in this material is intended to inform and educate and is not a tool for self-diagnosis or a replacement for medical evaluation, advice, diagnosis or treatment by a healthcare professional. Please speak to your physician if you have questions about your medical condition. Viewer discretion is advised : Some medical content is graphic and may not be suitable for al viewers. 1 / 22
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Categorical data and contingency tables Kerby Shedden Department of Statistics, University of Michigan April 8, 2011 2 / 22
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Proportions Suppose we have an independent and identically distributed (iid) sample X 1 , . . . , X n of binary responses. For example, each X i may be an individiual’s response to a yes/no question in a survey. The distribution of each X i is characterized by the “success probability” p P ( X i = 1) . The mean and variance of each X i are EX i = p var ( X i ) = p (1 - p ) . The mean and variance of ¯ X are E ¯ X = p var ( ¯ X ) = p (1 - p ) / n . 3 / 22
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We can form an approximate 95% confidence interval for p in the same way we would form a CI for the expected value EX : ¯ X ± σ/ n or ˆ p ± 2 p ˆ p (1 - ˆ p ) / n . 4 / 22
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categorical - Author(s): Kerby Shedden, Ph.D., 2010...

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