DobbinChapter9RevisedDec142010

# DobbinChapter9RevisedDec142010 - Chapter 2 Section 2.5 and...

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Chapter 2, Section 2.5 and Chapter 9, Sections 9.1 & 9.2 Analysis of Two-Way Tables: Section 2.5 The variables we have worked with recently have been quantitative variables (numbers). Now we will work with categorical variables. Two-way tables compare two categorical variables measured on a set of cases. Examples Gender versus major Political party versus voting status Two-Way Table: Describes the relationship between two categorical variables. Represents a table of counts. Example: Years of education and income. Suppose a random sample of 1,000 people was selected and the following data was obtained: <10,000 10,000- 30,000 30,001- 50,000 >50,000 Total Years None Of some College Education Bachelor Post-grad 100 85 50 15 250 85 110 60 20 275 55 95 175 50 375 10 10 15 65 100 Total 250 300 300 150 1,000 Note: Each person surveyed represents a case. Each case fits into exactly one education class and one income category, so each case fits in one and only one cell of the body of the table. The Joint Distribution of the Categorical Variables: If we want the proportion of cases associated with any cell in the table we divide the count for that cell by the grand total (the total number of cases in the entire table). If we do this for each cell, we will have the joint distribution of our two categorical variables. Lecture 15, Sections 9.1 & 9.2 Page 1

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1. Find the joint distribution for the example above. <10,000 10,000- 30,000 30,001- 50,000 >50,000 Total Years None Of some College Education Bachelor Post-grad 10% 8.5% 5% 1.5% 25% 8.5% 11% 6% 2% 27.5% 5.5% 9.5% 17.5% 5% 37.5% 1% 1% 1.5% 6.5% 10% Total 25% 30% 30% 15% 100% Marginal Distributions of Categorical variables: The marginal distributions of each categorical variable are obtained from row and column totals. Basically we are examining the distributions of a single variable in the two-way table. Marginal distributions allow us to compare the relative frequencies among the levels of a single categorical variable. 2. Find the marginal distribution of education and income for the example above.
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## This note was uploaded on 02/28/2012 for the course STAT 301 taught by Professor Staff during the Spring '08 term at Purdue.

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DobbinChapter9RevisedDec142010 - Chapter 2 Section 2.5 and...

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