March 15, 2019

## 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: (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?