Week 1: What Is Quantitative Research?

POP88162 Introduction to Quantitative Research Methods

Tom Paskhalis

Department of Political Science, Trinity College Dublin

Overview

  • Quantitative research
  • Sample vs population
  • Research questions
  • Research hypotheses
  • Designing quantitative study

What Is Quantitative Research?

  • Quantitative research uses data.
  • Data consists of a collection of observed cases.
  • Observed cases were selected from a (much) larger pool of cases.
  • The observed cases are called the observations.
  • The pool of cases is called the population.
  • The collection of observations is called the sample.

What Are We Observing?

  • One or more properties the cases might have.
  • We call these properties the variables.
  • We care about them because they vary.
  • The properties vary along a certain dimension.
  • In other words, the variables take on different values.

Example: Censuses

Ireland Census 2022 Questionnaire

US Census 2020 Questionnaire

Example: Longitudinal Election Studies

BES Cross-Section 2019

GLES Cross-Section 2021

What Do We Want to Know?

  • There is some feature of the population we’d like to know, something involving one or more variables.
  • Examples: average annual income, relationship between income and vote cast in last election.
  • That feature is called a parameter of the population.

How Will We Come to Know it?

  • We use the values of the variables from the observations in the sample to calculate a statistic.
  • We make inferences from the statistic to the parameter, from the observed to the unobserved.
  • To reiterate: we use data in our sample to construct statistics from which we infer things about the parameters of our population (terminology matters).

Is It a Sample, or Is It A Population?

  • Depends on what you are doing with it.
  • Are you concerned only with the set of observations itself?
  • Or are you using it to make inferences about a larger population?
  • If the former, it’s a population. If the latter, it’s a sample.

Example

  • Suppose I calculated the percentage of MSc students in our course from Ireland this year.
  • If all I care about is your class, then I am directly observing a parameter of this population.
  • But if I use this to estimate the percentage of M.Sc. students from Ireland in a larger set of students, it’s a statistic from a sample.
  • And which population? I could give different answers, and my sample may be better or worse depending on them.

Should We Use Quantitative Research Methods?

  • In this class, yes.
  • But in general, we have to ask ourselves two questions first:
    1. What is the problem we want to solve?
    2. Are quantitative research methods the best way to solve this problem? (Depends on the research question)

What Kind of Problems Can We Solve?

  • For political scientists, it’s usually a problem of explanation.
  • We want to know why something is happening?
  • That means, why is some variable taking on certain values at some times and not others?
  • We call this variable the dependent (response) variable (\(Y\))

Research Questions

  • Formulating a research question should be your first step.
  • It should be in principle answerable with data (falsifiable);
  • It should be of scientific importance (people care about the answer);
    • The easiest way to check is to see previous academic literature.
  • It should be relatively specific (narrow).

Why Did Representative Assemblies Appear in some Places but not Others?

Stasavage (2010)

Are Human Rights Practices Getting Better?

Fariss (2019)

Does Democracy Matter for Normatively Desirable Outcomes?

Gerring et al. (2022)

Does the Internet Facilitate Selective Exposure to Politically Congenial Content?

Guess (2021)

How Do We Solve This Problem?

  • We try to explain the values assumed by the dependent variable using another variable
  • We call that the independent (explanatory) variable (\(X\))
  • We hypothesize that the value of the dependent variable depends on the value of the independent variable, which doesn’t depend on anything else (at least in theory).

Hypothesised relationship I

  • At its core, hypothesis takes the following form: \(X \rightarrow Y\)
  • Or “\(Y\) depends on \(X\)”
  • Or “\(Y\) is associated with \(X\)”
  • Simply put, variables \(X\) and \(Y\) take on different values according to some relationship between them.

Hypothesised relationship II

  • The world is not that simple and deterministic.
  • Thus, a hypothesis is more likely to look like this: \(X \rightarrow Y: Z\)
  • Or “\(Y\) depends on \(X\) in the presence of \(Z\)”
  • Or “\(Y\) is associated with \(X\) conditional on \(Z\)”
  • Re-writing as an equation gives us: \(Y = X + Z + \epsilon\)
  • \(\epsilon\) means that the relationship is not perfect (one-to-one)!
  • There is always some error involved.

Example Hypotheses

  • Democracies are less likely to go to war with each other than non-democracies.
  • Democracies have higher economic output than non-democracies.
  • More left-leaning and economically deprived voters are more likely to support higher taxes.
  • The share of female legislators increased after the introduction of gender quotas.
  • Human rights practices improve over time.

Designing Quantitative Study

xkcd

Steps in Designing Quantitative Study

  • Identify your problem (formulate a research question);
  • Specify your dependent variable (\(Y\));
  • Explain why it is a significant problem (i.e., why should anybody care);
  • Explain how much we already know about the problem (the literature review);
  • Formulate one or more hypotheses;
  • Design a model to test your hypotheses - to explain why or how your dependent variable varies the way it does;
  • Identify a dataset suitable to testing your model/hypotheses;
  • Measure your variables;
  • Perform statistical tests on your data.

Trust, But Verify

Wikipedia

Wikipedia
  • Numbers can be wrong (poor data source, lots of bias)
  • Be critical and scrutinize them.

Next

  • Workshop:
  • Next week:
    • Descriptive Statistics