causal-inference

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.

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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

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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?

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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).

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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?

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Causal Inference Checklist for A/B Tests

Before trusting a result:

• Was assignment truly random? Check Sample Ratio Mismatch.
• Was only one thing changed?
• Is sample size sufficient for the expected effect?
• Was the test run for a full weekly cycle?
• Is the primary metric pre-specified?
• Do secondary metrics that should move actually move?
• Is there a plausible mechanism explaining why X would cause Y?
• Is the effect consistent across segments? (Check Simpson's Paradox)

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Thinking Triggers

• "What's the counterfactual? What would have happened without this change?"
• "What else changed at the same time that could explain this?"
• "Are the units we're comparing actually comparable?"
• "Is there a third variable that could explain the correlation?"
• "Does the mechanism make sense — why would X cause Y?"
• "Does disaggregating the data change the conclusion?"
• "Would we see the same result if we ran this experiment again?"