Lecture12_print

# Lecture12_print - Chapters 2 9 Analysis and Inference of...

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Chapters 2 & 9: Analysis and Inference of Two-way Tables Readings: Sections 2.5, 9.1 1 Analysis of Two-way Tables Two-way tables: Describe the relationship between two categorical variables. * Gender versus major, * Political party versus voting status, * Pre-operative use of antibiotic versus post-operative infection. Represents a tables of counts. Example 1 : Years of education and income. Suppose a random sample of 1000 people was selected and the following data was obtained: Income Per Year Years Of < 10 , 000 10 , 000 - 30 , 001 - > 50 , 000 Total Education 30 , 000 50 , 000 No College 100 85 50 15 250 Some College 85 110 60 20 275 Bachelor 55 95 175 50 375 Post-grad 10 10 15 65 100 Total 250 300 300 150 1000 Some vocabulary: Years of Education is the row variable because each horizontal row represents a different education level. Income per year is the column variable because each vertical column represents a different income level. Each combination of values for the two variables is called a cell . 1.1 Joint Distribution The table above uses “counts” or numbers of people. This isn’t always the most useful form for us. We usually like to convert the count table over to a joint distribution table in either % or probabilities/proportions by dividing all of the individual counts in the middle of the table by the grand total, in this case 1000. All the joint distributions should add to 1 (or 100%). The joint distribution of years of education and income level is: Income Per Year Years Of < 10 , 000 10 , 000 - 30 , 001 - > 50 , 000 Total Education 30 , 000 50 , 000 No college 10% 8.5% 5% 1.5% Some College 8.5% 11% 6% 2% Bachelor 5.5% 9.5% 17.5% 5% Post-grad 1% 1% 1.5% 6.5% Total 1

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The %s in the middle of the table are the joint distributions . What do these numbers mean? 15/1000 = 0.015 or 1.5% is the joint distribution for people with no college AND earning over 50,000 per year. Joint distributions go with the word “and”. 1.2 Marginal Distribution We are also interested in each individual variable. The marginal distribution allows us to study one variable at a time. You get them just by adding across a row or down a column for the specific variable you are interested in. The marginals are written in the margins of the table (far right and very bottom).
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