1. Lecture 3. Data Compression for Two Variables: Scatterplots, Cross- Tabulations, and Correlation David R. Merrell 90-786 Intermediate Empirical Methods for Public Policy and Management

2. Lecture 3: Agenda Review of Lecture 2 Cross-Tabulations Comparison Bar Charts Parallel Box Plots Scatterplots Correlation Coefficients

3. Review of Lecture 2 Mean or Median Models for Data

4. Mean or Median Complaints have reached the city manager that Tardy City is taking too long to pay its bills. Data are days taken to pay seven bills: 34 27 64 31 30 26 35 Calculate the mean and median. What do you conclude?

5. Models for Data Data = Fit + Residual Fit as a Center Mean Median Mode Example: Number of Stat Courses Taken by Students in 90-786

8. Summary Statistics (Excel)

9. Summary Statistics (Minitab) Descriptive Statistics Variable N Mean Median Tr Mean StDev SE Mean C1 19 1.158 1.000 1.118 0.602 0.138 Variable Min Max Q1 Q3 C1 0.000 3.000 1.000 1.000

10. Measures of Error

11. Data Compression for Two Variables...And More Two-Variable Description Cross-Tabulations Comparison Bar Charts Parallel Box Plots Scatterplots Scatterplot Matrix Correlation Coefficients

12. Two-Variable Description

13. Structure of a Cross-Tabulation

14. Street Repair Practices Study street repair practices of local government Cities and counties handle street repairs: using their own public employees exclusively by contracting out part of the work contracting out all the work

15. Table 1. Street Repair: Counts Type of Local Government Street Repair Practices by Type of Government: Public Employees and Contracting by Cities and Counties in the United States

16. Table 2. Street Repair: Percents Type of Local Government Street Repair Practices by Type of Government: Public Employees and Contracting by Cities and Counties in the United States

17. Educational Achievement Residents of Allegheny County that are in labor force Random sample survey of Allegheny County residents in labor force in 199? Variables: gender and highest educational achievement

18. Educational Achievement: Coding of Ordinal Variables 1 if grade 4 or less 2 if grades 5-7 3 if grade 8 4 if high school incomplete (9-11) 5 if high school graduate (12) 6 if technical, trade, or business after high school 7 if college/ university incomplete 8 if college/university graduate or more

19. Educational Achievement Table

20. Bar Chart

21. Job Satisfaction and Income for Postal Employees

22. Five Number Summary Age of Allegheny County residents by location: individuals in labor force in 199?.

23. Parallel Box Plots 10 20 30 40 50 60 70 80 o o o o The Mon ValleyPittsburgh Other

24. Scatterplots Creating via Excel ChartWizard Transformation of Variables Scatterplot Matrices

25. Scatterplot 1 Salary Years employed

26. Scatterplot 2 Salary Years employed

27. Scatterplot 3 Salary Years employed

28. Scatterplot Matrix

29. Correlation Coefficient, r

30. Properties of r

31. International Adoption Visas: 1991 vs 1988 r:/academic/90-786/ Chatterjee/ Adopt.dat

32. International Adoption Visas Country 1988 1991 1992 Etc.

35. Excel Calculation of r Use statistical function, correl Eliminate missing data values Identify X data Identify Y data Finish Value: r = 0.879098 (.88)

36. Minitab Calculation of r Correlations (Pearson) Correlation of log 1988 and log 1992 = 0.873

37. Next Time... Ethics and the Value of Data Social Value of Data Privacy Issues Confidentiality Applications in Health Care