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

Info icon This preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon
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
Image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
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).
Image of page 2
Image of page 3
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern