March 15, 2019

Testing Causal Theories

Plan for Today:

(1) Correlation

  • correlation
  • confounding (with diagrams)
  • reverse causality
  • direction of bias
  • relationships that are NOT confounding
    • antecedent variables
    • intervening variables

Correlation

correlation:

degree of association or relationship between the observed values taken by two variables (\(X\) and \(Y\))

  • Many different ways of doing this (compare group means, regression) are all fundamentally about correlation.
  • correlations have a direction:
    • positive: implies that as \(X\) increases, \(Y\) increases
    • negative: \(X\) increases, \(Y\) decreases
  • correlations have strength (has nothing to do size of effect):
    • strong: \(X\) and \(Y\) almost always move together
    • weak: \(X\) and \(Y\) do not move together very much
  • There is also a technical definition of correlation (later)

Correlation

To infer causality from correlation, need to know what problems we have to assume are absent

Two types of problems

  • bias (spurious correlation, confounding): \(X\) and \(Y\) are correlated but the correlation does not result from causal relationship between those variables

  • random association: correlations between \(X\) and \(Y\) occur by chance and do not reflect

Confounding (again)

confounding occurs when some other variable \(W\) is causally linked to \(X\) (independent variable) and \(Y\) (dependent variable).

or if we diagram

If we diagram causal links between variables using this notation: \(X \to Y\) implies \(X\) causes \(Y\), then…

confounding occurs when there is a path between \(X\) and \(Y\) that is non-causal (goes the "wrong way" on at least one arrow)

Confounding (Diagram)

Correlation: Bias/Confounding?

Confounding (again)

Confounding (again)

Confounding: (Another Example)

Causal claim:

Anti-refugee hate speech on social media causes anti-refugee violence?

Causal theory

hate-speech \(\to\) increase perceived threat \(\to\) decrease acceptance of refugees \(\to\) violence perceived as justified \(\to\) violence

variables

IV: exposure to anti-refugee statements on Facebook; DV: incidents of violence against refugees

Hypothesis

Increase exposure to anti-refugee content online associated with increase in violence against refugees

Confounding: (Another Example)

Mueller and Schwarz (2018)

Test this hypothesis in Germany (2015-2017):

  • Observe anti-refugee content on AfD Facebook page (overtime)
  • Observe anti-refugee violence reported (overtime)

What is the correlation?

  • Should expect positive correlation

Are they correlated?

Can you infer causality?

Confounding: (Another Example)