Quantitative methods Lecture 1

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

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

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?

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

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

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

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)

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

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

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

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?

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

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

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

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

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)

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