Economics 105: Statistics

1. Economics 105: Statistics GH 19 not due Thur RAP assignment … datasets to look at Find the “codebook” or “survey instrument” and look at the questions they asked

2. Brief Introduction to Research Design Design Notation Internal Validity Experimental Design

3. Design Notation • Observations or measures are indicated with an “O” • Treatments or programs with an “X” • Groups are shown by the number of rows • Assignment to group is by “R,N,C” • Random assignment to groups • Nonequivalent assignment to groups • Cutoff assignment to groups • Time

4. There are two lines, one for each group. Vertical alignment of Os shows that pretest and posttest are measured at same time. X is the treatment. Subscripts indicate subsets of measures. Os indicate different waves of measurement. Design Notation Example R O1,2 X O1,2 R O1,2 O1,2 R indicates the groups are randomly assigned.

5. Yes Randomized (true experiment) No Nonexperiment Types of Designs Random assignment? No Control group or multiple measures? Yes Quasi-experiment

6. Non-Experimental Designs X O Post-test only (case study) O X O Single-group, pre-test, post-test X O O Two-group, post-test only (static group comparison)

7. Experimental Designs • Pretest-Posttest Randomized Experiment Design • If continuous measures, use t-test • If categorical outcome, use chi-squared test • Posttest only Randomized Experiment Design • Less common due to lack of pretest • Probabilistic equivalence between groups

8. Experimental Designs Solomon Four-Group Design • Advantages • Information is available on the effect of treatment (independent variable), the effect of pretesting alone, possible interaction of pretesting & treatment, and the effectiveness of randomization • Disadvantages • Costly and more complex to implement

9. Establishing Cause and Effect Single-Group Threats Multiple-Group Threats “Social” Interaction Threats Internal Validity • Internal validity is the approximate truth about inferences regarding cause-effect relationships.

10. Threats to Internal Validity History Maturation Testing Instrumentation Mortality Regression to the mean Selection Selection-history Selection- maturation Selection- testing Selection- instrumentation Selection- mortality* Selection- regression Diffusion or imitation* Compensatory equalization* Compensatory rivalry* Resentful demoralization* R X O R O Single-Group Multiple-Group Social Interaction

11. Single-Group Threatsto Internal Validity

12. Administer program Measure outcomes X O Administer program Measure outcomes X O What is a “single-group” threat? Two designs: Post-test only a single group Measure baseline O

13. Example • Diabetes educational program for newly diagnosed adolescents in a clinic • Pre-post, single group design • Measures (O) are paper-pencil, standardized tests of diabetes knowledge (e.g. disease characteristics, management strategies)

14. Pretest Program Posttest O X O History Threat • Any other event that occurs between pretest and posttest • For example, adolescents learn about diabetes by watching The Health Channel

15. Pretest Program Posttest O X O Maturation Threat • Normal growth between pretest and posttest. • They would have learned these concepts anyway, even without program.

16. Pretest Program Posttest O X O Testing Threat • The effect on the posttest of taking the pretest • May have “primed” the kids or they may have learned from the test, not the program • Can only occur in a pre-post design

17. Pretest Program Posttest O X O Instrumentation Threat • Any change in the test from pretest and posttest • So outcome changes could be due to different forms of the test, not due to program • May do this to control for “testing” threat, but may introduce “instrumentation” threat

18. Pretest Program Posttest O X O Mortality Threat • Nonrandom dropout between pretest and posttest • For example, kids “challenged” out of program by parents or clinicians • Attrition

19. Pretest Program Posttest O X O Regression Threat • Group is a nonrandom subgroup of population. • For example, mostly low literacy kids will appear to improve because of regression to the mean. • Example: height

20. Regression to the Mean pre-test scores ~ N When you select a sample from the low end of a distribution ... Selected group’s mean Overall mean the group will do better on a subsequent measure. post-test scores ~ N & assuming no effect of treatment pgm The group mean on the first measure appears to “regress toward the mean” of the population. Overall mean Regression to the mean

21. Regression to the Mean

22. Sir Francis Galton (1822 – 1911) 903 adult children & their 250 parents Regression to the Mean

24. Regression to the Mean • How to Reduce the effects of RTM (Barnett, et al., International Journal of Epidemiology, 2005) • When designing the study, randomly assign subjects to treatment and control (placebo) groups. Then effects of RTM on responses should be same across groups. • Select subjects based on multiple measurements • RTM increases with larger variance (see graphs) so subjects can be selected using the average of 2 or more baseline measurements.

25. Multiple-Group Threats to Internal Validity

26. The Central Issue • When you move from single to multiple group research the big concern is whether the groups are comparable. • Usually this has to do with how you assign units (e.g., persons) to the groups (or select them into groups). • We call this issue selection or selection bias.

27. O X O O O The Multiple Group Case Alternative explanations Measure baseline Administer program Measure outcomes Do not administer program Measure baseline Measure outcomes Alternative explanations

28. Example • Diabetes education for adolescents • Pre-post comparison group design • Measures (O) are standardized tests of diabetes knowledge

29. O X O O O Selection-History Threat • Any other event that occurs between pretest and posttest that the groups experience differently. • For example, kids in one group pick up more diabetes concepts because they watch a special show on Oprah related to diabetes.

30. O X O O O Selection-Maturation Threat • Differential rates of normal growth between pretest and posttest for the groups. • They are learning at different rates, even without program.

31. O X O O O Selection-Testing Threat • Differential effect on the posttest of taking the pretest. • The test may have “primed” the kids differently in each group or they may have learned differentially from the test, not the program.

32. O X O O O Selection-Instrumentation Threat • Any differential change in the test used for each group from pretest and posttest • For example, change due to different forms of test being given differentially to each group, not due to program

33. O X O O O Selection-Mortality Threat • Differential nonrandom dropout between pretest and posttest. • For example, kids drop out of the study at different rates for each group. • Differential attrition

34. O X O O O Selection-Regression Threat • Different rates of regression to the mean because groups differ in extremity. • For example, program kids are disproportionately lower scorers and consequently have greater regression to the mean.

35. “Social Interaction” Threats to Internal Validity

36. What Are “Social” Threats? • All are related to social pressures in the research context, which can lead to posttest differences that are not directly caused by the treatment itself. • Most of these can be minimized by isolating the two groups from each other, but this leads to other problems (for example, hard to randomly assign and then isolate, or may reduce generalizability).

37. What Are “Social” Threats? • Diffusion or imitation of Treatment • Compensatory Equalization of Treatment • Compensatory Rivalry • Resentful Demoralization

38. What is a Clinical Trial? • “A prospective study comparing the effect and value of intervention(s) against a control in human beings.” • Prospective means “over time”; vs. retrospective • It is attempting to change the natural course of a disease • It is NOT a study of people who are on drug X versus people who are not • http://www.clinicaltrials.gov/info/resources

39. Example: Job Corps • What is Job Corps? http://jobcorps.doleta.gov/ • January 5, 2006 Thursday Late Edition – Final SECTION: Section C; Column 1; Business/Financial Desk; ECONOMIC SCENE; Pg. 3HEADLINE: New (and Sometimes Conflicting) Data on the Value to Society of the Job CorpsBYLINE: By Alan B. Krueger. Alan B. Krueger is the Bendheim professor of economics and public affairs at Princeton University. His Web site is www.krueger.princeton.edu. He delivered the 2005 Cornelson Lecture in the Department of Economics here at Davidson (that’s the big econ lecture each year).

40. Example: Job Corps • Quotations from “New (and Sometimes Conflicting) Data on the Value to Society of the Job Corps” by Alan B. Krueger. • Since 1993, Mathematica Policy Research Inc. has evaluated the performance of the Job Corps for the Department of Labor. • Its evaluation is based on one of the most rigorous research designs ever used for a government program. From late 1994 to December 1995, some 9,409 applicants to the Job Corps were randomly selected to be admitted to the program and another 6,000 were randomly selected for a control group that was excluded from the Job Corps. • Those admitted to the program had a lower crime rate, higher literacy scores and higher earnings than the control group.

44. RCT for Credit Card Offers A1: 0% APR for first 8 months & 9.99% on balance transfers, then 9.99% on purchases A2: 0% APR for first 12 months, & 9.99% on balance transfers, then 9.99% on purchases A3: 0% APR for first 8 months & 8.99% on balance transfers, then 8.99% on purchases Source: Agarwal, et al. (2010), Journal of Money, Credit & Banking, 42 (4)

45. RCT for Education in India Source: Banerjee, et al. (2007), Quarterly Journal of Economics

46. RCT for Education in India

47. RCT for the Effect of High Rewards on Performance Source: Ariely, Gneezy, Loewenstein, and Mazar (2009), Review of Economic Studies

48. RCT for the Effect of High Rewards on Performance Random assignment !

49. Recommended Reading Amazon link Amazon link Amazon link

50. Introduction to Regression Analysis • Correlation analysis only measures the strength of the association (linear relationship) between two variables … not necessarily a causal relationship • Regression analysis is used to: • Predict the value of a dependent variable based on the value of at least one independent variable • Explain the impact of changes in an independent variable on the dependent variable • Dependent variable: the variable we wish to predict or explain variation in ... outcome variable, Y. • Independent variables: the variables used to explain variation in Y ... covariates, explanatory variables, r.h.s. vars, X-variables