1. Quantitative methods
Lecture 1

2. Class Overview Course Description Assignment 1 Syllabus Schedule
Introductions
Questions
Assignment 1
Research Design

3. Course Objectives
The purpose of this class is to introduce students to the concepts, techniques and reasoning skills necessary to understand and undertake quantitative research. By the end of the semester students will be able to:
Design a quantitative research proposal
Conceptualize a quantitative statistical model
Estimate a quantitative statistical model
Interpret the results of descriptive analyses, t-tests and multivariate regression analyses.
Calculate statistical power

4. Assignment 1
The purpose of this assignment is to introduce students to the process of conceptualizing research questions in quantitative terms. For this assignment I would like you to think of a research question of the type that can be expressed as a model akin to the examples described in chapter 3 of Applied Statistics. It can be related to your thesis topic or some other topic. For the first class please:
Express your model in a diagram such as that done in figure 3.1 in Applied Statistics. Describe the hypothesis behind your model.
Indicate the dependent variable
Indicate the Independent variable(s)
What type of research design might you employ to test your hypothesis?

5. Assignment 1
Does neighborhood diversity influence mechanisms of social control?
Theory:
Research on gentrification uncovered conflicts over social norms
Often addressed by resorting to formal mechanisms (e.g. 311)
Theory should always be your guide

6. Assignment 1
Does neighborhood diversity influence mechanisms of social control?
Background:
Research on gentrification uncovered conflicts over social norms
Often addressed by resorting to formal mechanisms (e.g. 311)
Model
Social Control Mechanism = f(neighborhood demographics) + Error

7. Operationalize
Social Control Mechanism = f(neighborhood demographics) + Error
Social Control Mechanism = Calls to 311
Neighborhood Demographics = Population diversity (i.e. Simpson’s index of diversity)
Dependent variable?
Independent variable
Functional form?
Error term?
Unit of analysis?
Simpson’s Index of Diversity D =Sigma (n / N)2

8. Unit of Analysis
The unit of analysis is the “what” or “who” that is being analyzed
Examples: People, classes, roads, cities
Neighborhood diversity and social control, unit of analysis?
Individuals
Do observe individuals behaving differently as neighborhood diversity changes? (preferred approach)
Neighborhoods
Do we observe Neighborhood level differences in behavior in more diverse neighborhoods? (risk of an ecological fallacy)

9. Is my Hypothesis Correct?
What type of evidence would support my hypothesis that there is some type of causal relationship between neighborhood diversity and mechanisms of social control?
Theory
Time order
Covariation
Non-spuriousness

10. Is my Hypothesis Correct?
What type of evidence would support my hypothesis?
Could I conduct an experiment?

11. Is my Hypothesis Correct?
What type of evidence would support my hypothesis?
Could I conduct an experiment?
Control group
Treatment group
Random assignment

12. Experiments Experiments are the “gold standard”
Researchers can manipulate treatment and assignment to treatment and control groups
Establishes
Time-order
Covariation
Non-spuriousness
Why not always conduct experiments?
Biggest weakness of experiments?

13. Quasi-Experiments
The analyst does not have control over the treatment or assignment to groups
Generally more difficult to rule out rival hypotheses

14. What type of Sample Population
What is the population?
What type of sample would be appropriate?

15. What type of Sample? Population
What is the population?
All US neighborhoods?
All gentrifying neighborhoods?
All NYC neighborhoods?
What type of sample would be appropriate?
One neighborhood?
All neighborhoods in walking distance to Columbia University

16. What type of Analysis? Cross-Sectional? Longitudinal
Panel
What are the advantages and disadvantages of cross-sectional vs. longitudinal?

17. Validity Internal Validity Construct validity Statistical validity
Did the (Quasi) Experiment adequately test the hypothesis?
Example: Was the experiment carried out correctly?
Construct validity
Are we measuring what we think we are measuring?
Example: Do calls to 311 measure social control?
Statistical validity
Did we conduct the appropriate statistical test?
External validity
Are the results applicable elsewhere? (e.g. Chicago, Tokyo)

18. Validity Which approach is strongest in terms of internal validity?
Which approach is strongest in terms of external validity?