Economics 105: Statistics

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# Economics 105: Statistics - PowerPoint PPT Presentation

Economics 105: Statistics. Any questions? No GH due Friday. For next couple classes, please r ead first 4 sections of Chapter 13 and Freakonomics , Chapter 5 (copy is in P:\economics\Eco 105 (Statistics) Foley\ freakonomics Ch_5.pdf). Brief Introduction to Research Design.

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### Economics 105: Statistics

Any questions?

No GH due Friday. For next couple classes, please read first 4 sections of Chapter 13 and Freakonomics, Chapter 5

(copy is in P:\economics\Eco 105 (Statistics) Foley\freakonomics Ch_5.pdf)

### Brief Introduction to Research Design

Design Notation

Internal Validity

Experimental Design

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

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.

Yes

Randomized

(true experiment)

No

Nonexperiment

Types of Designs

Random assignment?

No

Control group or

multiple measures?

Yes

Quasi-experiment

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)

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
Experimental Designs

Solomon Four-Group Design

• 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
• Costly and more complex to implement

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.
• “Internal” means internal to the study, not “external”, that is, not talking about generalizing the results yet.
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

### Single-Group Threatsto Internal Validity

program

Measure

outcomes

X

O

program

Measure

outcomes

X

O

What is a “single-group” threat?

Two designs:

Post-test only a single group

Measure

baseline

O

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)

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

Pretest

Program

Posttest

O

X

O

Maturation Threat
• Normal growth between pretest and posttest.
• They would have learned these concepts anyway, even without program.

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

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

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

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
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

### Regression to the Mean

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.

### Multiple-Group Threats to Internal Validity

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.

O

X

O

O

O

The Multiple Group Case

Alternative

explanations

Measure

baseline

program

Measure

outcomes

program

Measure

baseline

Measure

outcomes

Alternative

explanations

Example
• Pre-post comparison group design
• Measures (O) are standardized tests of diabetes knowledge

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.

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.

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.

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

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

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.

### “Social Interaction” Threats to Internal Validity

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).
Diffusion or Imitation of Treatment
• Controls might learn about the treatment from treated people (for example, kids in the diabetes educational group and control group share the same hospital cafeteria and talk with one another).
Compensatory Equalization of Treatment
• Administrators give a compensating treatment to controls.
• Researchers feel badly and give control group kids a video to watch pertaining to diabetes. Contaminates the study!

=

Compensatory Rivalry
• Controls compete to keep up with treatment group.
Resentful Demoralization
• Controls "give up" or get discouraged
• Likely to exaggerate the posttest differences, making your program look more effective than it really is
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

Model of Two-Group

Randomized Clinical Trial

What are the characteristics of a Clinical Trial?

• Begins with a primary research question, and the trial design flows from this question (constrained by practicalities)
• Everything must be exhaustively defined in advance (to prevent accusations of fishing for a positive finding)
• The hypothesis (“-es”)
• Population to be studied
• inclusion criteria
• exclusion criteria
• contraindications to therapy
• indications to therapy
• Treatment strategy (treatment, exact dosage, dosage schedule, etc)
• The outcome(s)

Beta-Blocker Heart Attack Trial (BHAT)

• Published in Journal of the American Medical Association
• JAMA 1982; 247: 1701 - 1714
• JAMA 1983; 250: 2814 – 2819
• Up until about 25 years ago, the treatment of myocardial infarction consisted of bed rest, alleviation of symptomatic pain, possible administration of early antiarrhythmics
• But a third of people who have a heart attack die from it ‘suddenly’
• In 1976, NIH sponsored a conference to discuss potential agents to be used in either a primary or secondary prevention setting to reduce sudden death, for which there was no treatment.
• The conference made an official recommendation to do a clinical trial.

Beta-Blocker Heart Attack Trial (BHAT)

• Primary Research Question
• To test in a multicenter, randomized, double-blind, placebo, controlled trial, whether the daily administration of propranolol to patients who had had at least one documented MI would results in a significant reduction in all-cause mortality during 2 to 4 years of follow-up (expected mean follow-up = 36 months).

Beta-Blocker Heart Attack Trial (BHAT)

• Inclusion criteria
• Men/Women
• Aged 30 to 69 yrs
• Documented (defined) MI within 5 to 21 days of randomization
• Exclusion criteria
• Contraindication to propranolol (e.g., asthma, severe bradycardia)
• Likely to be prescribed propranolol (e.g., for severe angina)
• Unlikely to be a compliant participant
• Likely to die of noncardiac cause (e.g., cancer)
• What do these do to generalizability?

BHAT Design and Conduct

1916 Patients - Propranolol

138

Deaths

188

1921 Patients - Placebo

Deaths

Screened

Randomized

16,400

3,837

Patients

Treat and

Participants

Collect

Follow-up Data

Time

M

ean 2 yrs (trial stopped early)

Follow-up

Time

Beta-Blocker Heart Attack Trial (BHAT)

• Results
• BHAT (and similar trials) demonstrated great benefitin reducing all-cause mortality and cardiac-specific mortality (including sudden death)in three-quarters of Post-MI Patients (1/4 had contraindication to propranolol)
• Relevance today?
• Beta-blockers still should be given post-MI
• What happened after BHAT is illustrative of what often happens a clinical trial result is published
• Results reported in 1981 (short report in JAMA)
• In 1987, only 36% of post-MI patients on a beta-blocker
• In 1989, 40%
• In 1992, 63%
• In 1993, only 33% of post-MI women
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).

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.

RCT for Credit Card Offers

Source: Agarwal, et al. (2010), Journal of Money, Credit & Banking, 42 (4)

RCT for Education in India

Source: Banerjee, et al. (2007), Quarterly Journal of Economics

RCT for Education in India

Source: Agarwal, et al. (2010), Journal of Money, Credit & Banking, 42 (4)