day2class - Relationships between two categorical variables...

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Relationships between two categorical variables Examples: Is gender or race related to political preference? What type of music makes people relax best? Are people who make more money more satisfied with their jobs? A two-way table is a way to display the data from two categorical variables. Income level vs. Job Satisfaction Income Job Satisfaction Row Total 1 2 3 4 < 30K 20 24 80 82 206 30K-50K 22 38 104 125 289 50K-80K 13 28 81 113 235 > 80K 7 18 54 92 171 C. Total 62 108 319 412 901 What percent of people with income less than 30K are very satisfied with their job? 398 . 206 82 = What percent of people with income more than 80K are very unsatisfied with their job? 041 . 171 7 = This is a two-way table with income level as the row variable and job satisfaction as the column variable.
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The distributions of income alone and job satisfaction alone are called the marginal distributions . Relationships between categorical variables are described by calculating appropriate percents from the counts given in each cell. Income level vs. Job Satisfaction Income Job Satisfaction Row Total 1 2 3 4 < 30K 20 24 80 82 206 30K-50K 22 38 104 125 289 50K-80K 13 28 81 113 235 > 80K 7 18 54 92 171 C. Total 62 108 319 412 901 Marginal Distribution of Job Satisfaction and Income Job Satisfaction Income 0 50 100 150 200 250 300 350 400 450 1 2 3 4 0 50 100 150 200 250 300 <30K 30K-50K 50K-80K 80K
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Conditional Distributions Often one is interested in knowing: the job satisfaction distribution among all people within a particular income group, say people earning more than 80K; the income distribution among all people who are very satisfied with their job. These are called conditional distributions . Income Job Satisfaction Row Total 1 2 3 4 < 30K 20 24 80 82 206 30K-50K 22 38 104 125 289 50K-80K 13 28 81 113 235 > 80K 7 18 54 92 171 C. Total 62 108 319 412 901 Example : The conditional distribution of job satisfaction among people with income greater than 80K: Job Satisfaction: 1 2 3 4 Percent: (Here we computed the row proportions)
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Income Job Satisfaction Row Total 1 2 3 4 < 30K 20 24 80 82 206 30K-50K 22 38 104 125 289 50K-80K 13 28 81 113 235 > 80K 7 18 54 92 171 C. Total 62 108
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This note was uploaded on 11/28/2009 for the course STATS STATS10 taught by Professor Sugano during the Spring '09 term at UCLA.

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day2class - Relationships between two categorical variables...

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