1. Categorical Data! Frequency Table –Records the totals (counts or percentage of observations) for each category. If percentages are shown, it is a relative frequency table. Distribution –Shows the possible values of the variable and the relative frequency of each value

2. Types of Graphs Picture –Remember… –Ex: Stem & Leaf

3. Bar Chart – counts for comparison

4. Pie Chart – pieces for proportion

5. Segmented Bar Chart

6. Contingency Table Displays counts and sometimes percentages of individuals falling into named categories on two or more variables. Shows how individuals are distributed along each variable contingent on the value of another variable. –Marginal distribution: distribution of either variable by itself (last row or column) –Conditional Distribution: distribution of 1 variable for those individuals satisfying a condition on another variable. Considers a smaller group isolated from the whole.

7. Independence??? Independence…think impact! –Variables are independent (one variable does not influence the value of the other variable) if the conditional distribution of 1 variable is the same for each category of the other.

8. Slide 3 - 8 Contingency Tables A contingency table allows us to look at two categorical variables together. It shows how individuals are distributed along each variable, contingent on the value of the other variable. –Example: we can examine the class of ticket and whether a person survived the Titanic:

9. Slide 3 - 9 Contingency Tables (cont.) The margins of the table, both on the right and on the bottom, give totals and the frequency distributions for each of the variables. Each frequency distribution is called a marginal distribution of its respective variable. –The marginal distribution of Survival is:

10. Slide 3 - 10 Contingency Tables (cont.) Each cell of the table gives the count for a combination of values of the two values. –For example, the second cell in the crew column tells us that 673 crew members died when the Titanic sunk.

11. Slide 3 - 11 Conditional Distributions A conditional distribution shows the distribution of one variable for just the individuals who satisfy some condition on another variable. –The following is the conditional distribution of ticket Class, conditional on having survived:

12. Slide 3 - 12 Conditional Distributions (cont.) –The following is the conditional distribution of ticket Class, conditional on having perished:

13. Python Eggs ColdNeutralHot Number of Eggs 2756104 Number hatched 163875 1)What percent of cold eggs hatched? 2)Neutral eggs hatched represent what percent of the total? 3)Are temperature and eggs hatched independent?

14. Smoking by Students & Parents Neither Parent Smokes One Parent Smokes Both Parents Smoke Student Does Not Smoke 116818231380 Student Smokes 188416400

15. Neither Parent Smokes One Parent Smokes Both Parents Smoke Student Does Not Smoke 116818231380 Student Smokes 188416400 4371 1004 1356223917805375 The Marginal Distribution

16. What percent of children have no parent that smokes? Students and both parents that smoke compose what percent of the total? Of 1 parent smokers, what is the percentage of children who smoke?

17. Is student smoking preference independent of parent choice? Neither Parent Smokes One Parent Smokes Both Parents Smoke Student Does Not Smoke 1168 86.1% 1823 81.4% 1380 77.5% Student Smokes 188 13.9% 416 18.6% 400 22.5% 4371 1004 1356223917805375

18. Year Response of families19912001 Both work full time142131 1 full time, 1 part time274244 1 full time, 1 work from home152173 1 full time, 1 homemaker396416 No Opinion51 Is there evidence of a change in working patterns in families???

19. Conditional distribution by hospital size Slide 2 - 19

20. How I get to school Slide 2 - 20

21. Simpson’s Paradox When averages “pooled” together AND taken across different groups appear to be contradictory. Example: Baseball PlayerOverallvs LHPvs RHP A33/103 (.320)28/81 (.346)5/22 (.227) B45/151 (.298)12/32 (.375)33/119 (.277)