Causal Inference

Core principle: Correlation is not causation — but sometimes it is, and knowing which matters enormously. Use counterfactuals, confounders, and causal structure to ask "did X actually cause Y?" rigorously before acting on data.

The Core Distinction

Correlation: X and Y move together. Causation: Changing X changes Y — and we know why.

Why it matters:

Intervening on a correlate with no causal path wastes effort
Missing a confounder leads to attributing effects to the wrong cause
Acting on spurious correlation can make things worse

Key Concepts

Counterfactual Reasoning

The fundamental question:

"What would have happened to Y if X had been different, all else equal?"

You never observe both the treated and untreated state of the same unit at the same time — the fundamental problem of causal inference. Every causal claim is implicitly counterfactual; make it explicit.

Confounders

A third variable Z that causally affects both X and Y, creating correlation between them without a direct causal path.

Z → X
Z → Y

X and Y correlate, but X doesn't cause Y. Intervening on X does nothing.

Example: Ice cream sales and drowning rates correlate. Confounder: hot weather → more ice cream AND more swimming → more drowning. Banning ice cream doesn't reduce drowning.

Common confounders in product/engineering work:

Seasonality (feature adoption and engagement move together)
Selection bias (users who adopt are already more engaged)
External events (a competitor shut down the same week you shipped)
Time trends (both metrics were already moving before intervention)

Mediators vs. Confounders

A mediator is on the causal path — X → M → Y. Blocking it blocks the effect. A confounder is upstream of both — control for it.

Confusing them causes overcorrection (controlling for a mediator removes the effect you're looking for).

Simpson's Paradox

An observed trend can reverse when data is aggregated. A treatment can appear harmful in aggregate but beneficial in every subgroup (or vice versa) due to unequal group sizes.

Always ask: Does disaggregating change the conclusion?

Tools for Establishing Causation

Randomized Controlled Experiment (Gold Standard)

Random assignment eliminates confounding by making treatment independent of all other variables.

In product work: A/B tests are RCTs. Validity depends on:

Random assignment (not self-selection)
Sufficient sample size (statistical power)
Single treatment change (no simultaneous changes)
No interference between units (SUTVA)
Correct metric selection

A/B test failure modes:

Novelty effect: early lift decays as users habituate
Sample Ratio Mismatch: unequal group sizes indicating randomization failure
Multiple comparisons: 20 metrics gives 1 false positive by chance at p=0.05
Peeking: stopping early when results look good inflates false positive rate

Difference-in-Differences (DiD)

Compare the change for a treated group vs. control over time.

Effect = (Treated_after - Treated_before) - (Control_after - Control_before)

Assumes: Without treatment, both groups would have followed parallel trends. Use when: You have pre/post data and a natural control group but couldn't randomize.

Natural Experiments

External factors create quasi-random treatment variation — policy changes, geographic boundaries, system outages, cohort-based rollouts.

Example: Feature rolled out by sign-up date — early users are treatment, later users are control (if no self-selection in timing).

Causal Graph (DAG)

Map all variables and their causal relationships. Makes confounders and mediators explicit and determines what to control for.

[Confounder Z] → [Treatment X] → [Mediator M] → [Outcome Y]
      ↓___________________________________↑

Reading the DAG: control for Z (confounder), don't control for M (mediator).

Output Format

🔍 Causal Claim Under Examination

Stated claim: [What is asserted to cause what]
Reformulated as counterfactual: "Would Y have been different if X had not occurred, all else equal?"

🕸️ Causal Structure

Sketch the causal graph:

Proposed causal paths?
Potential confounders?
Mediators (on the causal path)?
Colliders (caused by both X and Y — controlling opens spurious paths)?

⚠️ Threats to Causal Interpretation

For each: Present / Possible / Unlikely

Threat	Present?	Evidence	Impact on Conclusion
Confounding
Selection bias
Reverse causation (Y → X)
Common cause (Z → X, Z → Y)
Seasonality / time trend
Coincidental timing
Simpson's Paradox

📊 Evidence Quality

Design used: [RCT / DiD / Natural experiment / Observational]
Evidence strength: [Strong / Moderate / Weak]
Key assumptions: [What must be true for the design to be valid]
Assumption violations: [Any signs assumptions don't hold]

🎯 Conclusion

Causal claim warranted?: [Yes / Probably / Unclear / No]
If yes: Estimated effect size and confidence
If unclear: What evidence would resolve it?
If no: What alternative explanation better fits the data?

🔬 Next Steps

What experiment would establish causation most efficiently?
What natural variation in the data could be exploited?
What confounders should be measured and controlled for?