background - Research methods: background and review Kerby...

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Research methods: background and review Kerby Shedden Department of Statistics, University of Michigan April 7, 2011 1 / 167
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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. 2 / 167
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How to use the annotations The green stars like this are annotations that become visible when you hold the pointer over the star (try it). The annotations should work when using a recent version of Adobe Acrobat Reader. Unfortunately, some other PDF viewers are not able to display the annotations. The annotations cannot display some mathematical expressions in the same way as they are displayed in the rest of the slides. Thus we use some alternative notations in the annotations. The main thing to be aware of is that we use ** to represent exponentiation, so x**2 means “ x 2 ”. 3 / 167
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Random variables A random variable is a mathematical description of something that is intrinsically random (like a coin toss), or something that varies when measured on different individuals (like a person’s blood pressure). The sample space is the set of values that a random variable can take on. Here are some examples of random variables and their sample spaces: I We flip a coin and let X = 1 denote the occurrence of a head and X = 0 denote the occurrence of a tail; the sample space is { 0 , 1 } . I We flip a coin 10 times and let X denote the number of heads that occur; the sample space is { 0 , 1 , . . . , 10 } . I We select a University of Michigan student at random and let X denote his or her height; the sample space is [0 , ). 4 / 167
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Measurement types Random variables are commonly considered to belong to one of the following three categories, based on the type of measurement that is made: I Nominal I Ordinal I Quantitative 5 / 167
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Measurement types A nominal random variable (also called qualitative or categorical ) takes on values in a set of names or labels.
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This note was uploaded on 02/06/2012 for the course STAT 403 taught by Professor Kerbyshedden during the Winter '12 term at University of Michigan-Dearborn.

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background - Research methods: background and review Kerby...

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