Notes on Correlation vs Causation

Overview: What correlation tests

  • A correlation test checks whether a relationship exists between two or more variables. It does not tell you about causation.

In-session check (raise-your-hand interaction)

  • The speaker notes that students raised hands to indicate agreement or understanding; used as a quick feedback mechanism.
  • This demonstrates the use of a simple poll to gauge comprehension about whether a correlation implies causation.

Core question: Why does correlation not imply causation?

  • The speaker asks: Why does it not say that A causes B? A correlation does not tell me that A causes B.
  • The mental model trap: people often think there is a direct causal link when they observe a correlation.
  • The transcript emphasizes that correlation can be confusing or misinterpreted by the mind.
  • The phrase "first of all, if you feel bad… they just give you" implies that there is an intuitive narrative that correlation could be misread as causation; the speaker's mumbled examples illustrate this confusion.

Transcript fragment: illustrative example

  • The speaker mentions: "A no pill because if your sugar hasn't been on the side of your physiology." This seems to describe a scenario where giving a pill (or placebo) yields nothing if there is no physiological relation; the key takeaway is that correlation between symptoms and treatment does not imply that the treatment affects the symptom.
  • Note: The transcript ends abruptly with "It's just" indicating the speaker did not finish the thought; the example is incomplete.

Key concepts and definitions

  • Relationship vs causation: A correlation measures association, not causation.
  • Variables: Two or more quantities measured across units.
  • Causation requires manipulation and control (experimental design) or stronger inference beyond correlation.
  • Confounding variable: A third variable that influences both A and B, creating a spurious association.
  • Directionality problem: correlation does not indicate which variable influences the other.
  • Reverse causation: It could be that B causes A.

Mathematical expressions

  • Pearson correlation coefficient: r=cov(X,Y)σ<em>Xσ</em>Yr = \frac{\mathrm{cov}(X,Y)}{\sigma<em>X \sigma</em>Y}
  • Range: −1≤r≤1-1 \le r \le 1
  • Significance testing: t=rn−21−r2t = r \sqrt{\frac{n-2}{1 - r^2}} with degrees of freedom df=n−2df = n - 2
  • Note: For non-linear relationships, r may be near zero even if a strong non-linear relationship exists.

Why researchers care about not conflating correlation with causation

  • Correct interpretation prevents erroneous conclusions in science, medicine, and policy.
  • Observational data can show associations but cannot prove causation without randomized experiments or quasi-experimental designs.

Real-world relevance and examples

  • A classic cautionary example: increasing ice cream sales correlate with drowning incidents due to a third variable (temperature); this demonstrates a spurious correlation due to a confounder.
  • In medicine, correlations between a biomarker and disease risk do not prove that changing the biomarker will change risk.

Ethical and practical implications

  • Do not claim causation from correlation; require experimental or quasi-experimental evidence.
  • Transparent reporting of limitations.

Connections to foundational principles

  • Ties to experimental design, randomization, control groups, and causal inference frameworks.

Quick recap

  • Correlation tests existence of association; do not imply causation.
  • Use careful study design to draw causal conclusions.