371chapter13f2011

371chapter13f2011 - Chapter 13 Two Dichotomous Variables...

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Chapter 13 Two Dichotomous Variables 13.1 Populations and Sampling Apopu la t ionmode lfo rtwod icho tomou sva r iab le scana r isefor a collection of individuals— aFn i tepopu t ion—o rasama thema t ica lmode rap rocessthat generates two dichotomous variables per trial. Here are two examples. 1. Consider the population of students at a small college. Thetwovariablesaresexwithpossi- ble values female and male; and the answer to the following question, with possible values yes and no. Do you usually wear corrective lenses when you attend lectures? 2. Recall the homework data on Larry Bird shooting pairs of free throws. If we view each pair as a trial, then the two variables are: the outcome of the Frst shot; and the outcome of the second shot. We begin with terminology and notation. With two responses per subject/trial, it sometimes will be too confusing to speak of successes and failures. Instead, we proceed as follows. The Frst variable has possible values A and A c . The second variable has possible values B and B c . In the above example of a Fnite population, A could denote female; A c could denote male; B could denote the answer ‘yes;’ and B c could denote the answer ‘no.’ In the above example of trials, A could denote that the Frst shot is made; A c could denote that the Frst shot is missed; B could denote that the second shot is made; and B c could denote that the second shot is missed. It is important that we now consider Fnite populations and trials separately. We begin with Fnite populations. 151
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Table 13.1: The Table of Population Counts. BB c Total AN AB N AB c N A A c N A c B N A c B c N A c N B N B c N Table 13.2: Hypothetical Population Counts for Study of Sex and Corrective Lenses. Yes ( B )N o ( B c )T o t a l Female ( A )3 6 0 2 4 0 6 0 0 Male ( A c )1 4 0 2 6 0 4 0 0 500 1000 13.1.1 Finite Populations Table 13.1 presents our notation for population counts for a ±nite population. Remember that, in practice, only Nature would know these numbers. This notation is fairly simple to remember: all counts are represented by N ,w i tho rw i thou tsubsc r ip ts . Thesymbo l N without subscripts represents the total number of subjects in the population. An N with subscripts counts the number in the population with the feature(s) given by the subscripts. For example, N AB is the number of population members with variable values A and B ; N A c is the number of population members with value A c on the ±rst variable; i.e. for this, we don’t care about the second variable. Note also that these guys sum in the obvious way: N A = N AB + N AB c . In words, if you take the number of subjects whose variable values are A and B ;andaddtoi tthe number of subjects whose variable values are A and B c then you get the number of subjects whose value on the ±rst variable is A .
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This note was uploaded on 12/10/2011 for the course STATS 371 taught by Professor Hanlon during the Fall '11 term at Wisconsin.

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371chapter13f2011 - Chapter 13 Two Dichotomous Variables...

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