Lecture13.chapt9

Lecture13.chapt9 - Lecture 13, Sections 9.1 &...

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Unformatted text preview: Lecture 13, Sections 9.1 & 9.2 Analysis of Two-Way Tables: 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 55 10 85 110 95 10 50 60 175 15 15 20 50 65 250 275 375 100 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. Lecture 13, Sections 9.1 & 9.2 Page 1 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. 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% 5.5% 1% 8.5% 11% 9.5% 1% 5% 6% 17.5% 1.5% 1.5% 2% 5% 6.5% 25% 27.5% 37.5% 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. <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% 5.5% 1% 8.5% 11% 9.5% 1% 5% 6% 17.5% 1.5% 1.5% 2% 5% 6.5% 25% 27.5% 37.5% 10% Total 25% 30% 30% 15% 100% Lecture 13, Sections 9.1 & 9.2 Page 2 Conditional Distributions of Categorical variables: In conditional distributions, we find the distribution of one categorical variable given a common level of another categorical variable....
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Lecture13.chapt9 - Lecture 13, Sections 9.1 &...

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