March 15, 2019

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

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)

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

(spurious correlation,**bias****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** occurs when some other variable \(W\) is causally linked to \(X\) (independent variable) *and* \(Y\) (dependent variable).

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)

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

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

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

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

**Test this hypothesis in Germany (2015-2017)**:

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

- Should expect
**positive**correlation

**Are they correlated?**

**Can you infer causality?**