# 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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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
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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