C HAPTER 4: M ORE ON T WO V ARIABLE D ATA Section 4.3 – Relations in Categorical Data.

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C HAPTER 4: M ORE ON T WO V ARIABLE D ATA Section 4.3 – Relations in Categorical Data

To analyze categorical data we use counts or percents of individuals that fall into various categories. Two way tables contain two categorical variables, one represented in the rows and one in the columns. A NALYZING C ATEGORICAL D ATA Row variable Column variable

Marginal distributions – The totals of each row and column that appear in the margins are referred to the marginal distributions. Roundoff error – The difference between actual and the marginal distributions due to rounding of the sums. In the table the total of 35-54 age group doesnt match the total list. This is because the table is in thousands of persons and each is rounded to the nearest thousand. D EFINITIONS Marginal distributions

M ARGINAL D ISTRIBUTION EducationDid not finish HS Completed HS 1-3 years of college 4 years of college Percent15.933.125.425.6

E XAMPLE 1 – H OW C OMMON IS C OLLEGE ? Create a bar graph that compares the percents of the three age groups who have completed 4 or more years of college.

C ONDITIONAL D ISTRIBUTIONS In the last example we only compared the percents of people who finished college (4 years) If you look back you can see that its simply a distribution of percents. The percents dont add up to 100%. If we were to take the age group 25- 34-year olds, the percents would add up to 100% because all 25- to 34- year-olds would fall into one of the educational categories. These four percents all together would be a conditional distribution. Conditional distribution – The total counts or percents of a given categorical variable. Education for 25- 34-year-olds Did not finish HS Completed HS1-3 years of college 4 years of college Percent11.830.628.329.3

E XAMPLE 2 – C ONDITIONAL D ISTRIBUTION Find the conditional distribution of years of school completed among people age 55 and over. Education for 55 years and over Did not finish HS Completed HS1-3 years of college 4 years of college Percent25.435.819.918.9

R EADING A T WO -W AY T ABLE G ENERATED FROM S OFTWARE

Homework: p.245- #s 53, 54, 59, 62-64, & 68

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