CHAPTER 10 - Part I

# CHAPTER 10 - Part I - Chapter 10 Association between Two...

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Chapter 10 Association between Two Categorical Variables What we have seen so far?? o In Chapters 3 and 11 we analyzed the association between a response variable and a explanatory variable using simple regression analysis. o In Chapter 12 we we analyzed the association between a response variable and both and explanatory variables using multiple regression analysis. We will now learn how to analyze the association between two variables BOTH of which are with 2 or more categories. Example: Last year when Gator Basketball team won the game that put them in the Final Four, 101 students in a Statistics class were asked to report their gender and whether or not have watched the whole game, part of it or not at all. The following table summarizes their responses:

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Portion watched Gender Total Male Female Whole game 10 21 31 Part of Game 12 24 36 None 4 30 34 Total 26 75 101 In the above example, we have categorical variables : (i) Portion of game watched : This has categories viz and . (ii) Gender : This has two categoies viz and We want to know whether there is any between your gender and how much of the game you watched i.e whether the time you spent watching the game depends of your gender or not. Before doing that we have to specify the and the variables. In this case portion of the game watched is more likely to be the variable and gender should be the variable. Tables like the above which cross classifies two categorical variables are known as Contingency tables .
To compare the differences of how much male and female UF students watched the game, its better to find in each response category. For that we will divide the numbers in each cell of the above table by the total number of students of each gender and then multiply it by 100. Thus, we have : Portion watched Gender Total Male Female Whole game 38.5% (10/26) 28.0% (21/75) 30.7% (31/101) Part of Game 46.2% (12/26) 32.0% (24/75) 35.6% (36/101) None 15.4% ( 4/26) 40.0% (30/75) 33.7% (34/101) Total 100.0% (26/26) 100.0% (75/75) 100.0% (101/101) The three percentages in a particular are the percentages - they form the for the portion of game watched given a particular . The corresponding (in the brackets) are the estimated of the categories of the response given a particular So, for females, the conditional distribution of watching the game is ( ) . Moreover, given a

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student is male, the estimated probability that he watched part of the game is Interpretations : In the above table, we see that students watched more of the game than the . So, right away we can say that is associated with the portion of the game being watched. But
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CHAPTER 10 - Part I - Chapter 10 Association between Two...

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