Causal inference basics quiz

Question 1

What is the fundamental distinction between correlation and causation, and why can't observational correlation alone establish a causal effect?

Accepted Answer

Correlation is symmetric association; causation requires that intervening on the cause changes the effect's distribution

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Correlation implies causation when the sample size is large enough

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Causation is just a stronger correlation coefficient (above 0.8)

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Correlation and causation are identical for normally distributed data

Question 2

In the potential outcomes (Rubin) framework, define the individual treatment effect and explain the 'fundamental problem of causal inference.'

Accepted Answer

For each unit only one potential outcome is observable, so the individual effect is never directly measured

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We can observe both potential outcomes but measurement error obscures the difference

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Potential outcomes are always equal in expectation, making the effect zero

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The problem is that treatment is randomly assigned

Question 3

Define the Average Treatment Effect (ATE), the Average Treatment effect on the Treated (ATT), and the Average Treatment effect on the Controls (ATC).

Accepted Answer

ATE is the population effect, ATT is the effect among the treated, ATC is the effect among the untreated

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ATE conditions on T=1, ATT conditions on T=0, and ATC is the population average

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All three are identical by definition regardless of effect heterogeneity

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ATT and ATC are only defined for continuous treatments

Question 4

State the SUTVA assumption and give an example of a setting where it is violated.

Accepted Answer

SUTVA requires no interference between units and a single well-defined version of treatment

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SUTVA requires treatment to be randomly assigned

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SUTVA requires the outcome to be normally distributed

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SUTVA requires equal group sizes in treatment and control

Question 5

What is a confounder, and which structural conditions make a variable a confounder in a causal DAG?

Accepted Answer

A variable that causally affects both the treatment and the outcome

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A variable caused by both treatment and outcome

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A variable on the causal path from treatment to outcome

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Any variable correlated with the outcome only

Question 6

Explain why randomized controlled trials (RCTs) are the gold standard for causal inference.

Accepted Answer

Randomization makes treatment independent of all confounders, including unobserved ones, ensuring exchangeability

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RCTs eliminate measurement error in the outcome

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RCTs require no statistical assumptions whatsoever

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RCTs guarantee the treatment effect is large

Question 7

What is a collider, and why does conditioning on a collider induce bias?

Accepted Answer

A collider is a common effect of two variables; conditioning on it opens a spurious path and induces bias

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A collider is a common cause; conditioning on it removes confounding

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A collider is a mediator; conditioning on it estimates the direct effect

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Colliders never affect causal estimates

Question 8

State Pearl's backdoor criterion for identifying a causal effect by covariate adjustment.

Accepted Answer

Z must block all backdoor paths into T and contain no descendants of T

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Adjust for every variable measured in the dataset

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Z must include the treatment's descendants to capture mediation

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Z must be a single variable that is correlated with the outcome

Question 9

What does the do-operator P(Y | do(T=t)) represent, and how does it differ from the conditional P(Y | T=t)?

Accepted Answer

do(T=t) is an intervention severing incoming arrows to T; conditioning is passive observation and can reflect confounding

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They are always equal by Bayes' rule

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Conditioning is the interventional quantity and do() is observational

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The do-operator only applies to continuous treatments

Question 10

Define the propensity score and state the key theorem that makes it useful for causal inference.

Accepted Answer

e(x)=P(T=1|X=x); conditioning on it suffices for unconfoundedness given X (balancing score)

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The probability the outcome is positive given treatment

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The correlation between treatment and outcome

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The expected treatment effect given covariates

Question 11

Write the Inverse Probability of Treatment Weighting (IPW) estimator for the ATE and state its main assumptions.

Accepted Answer

Weight by inverse probability of received treatment; requires unconfoundedness, positivity, and correct propensity model

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Weight each unit by its outcome variance

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Weight only the treated group by the propensity score

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Multiply outcomes by the propensity score directly

Question 12

State the positivity (overlap) assumption and explain why it is necessary for identifying treatment effects.

Accepted Answer

Every unit must have a positive probability of each treatment level given covariates

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The outcome must be positive for all units

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The treatment effect must be positive

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Propensity scores must all equal 0.5

Question 13

What is the ignorability / unconfoundedness / conditional exchangeability assumption, and why is it untestable?

Accepted Answer

{Y(0),Y(1)} ⟂ T | X; it is untestable because it involves unobserved counterfactuals

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T ⟂ X; testable via a chi-square test

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Y ⟂ X | T; verified by cross-validation

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It is the same as positivity and can be checked from propensity scores

Question 14

Explain the core idea of instrumental variables (IV) and the three conditions a valid instrument must satisfy.

Accepted Answer

Relevance, exclusion restriction, and independence from confounders

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Linearity, normality, and homoscedasticity

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Positivity, SUTVA, and ignorability

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The instrument must directly cause the outcome

Question 15

In two-stage least squares (2SLS), what happens in each stage and what does it estimate?

Accepted Answer

Stage 1 predicts T from the instrument; stage 2 regresses Y on the predicted T

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Stage 1 regresses Y on Z; stage 2 regresses T on Y

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Both stages regress Y on T with different samples

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Stage 1 matches units; stage 2 computes differences

Question 16

Describe the difference-in-differences (DiD) design and its key identifying assumption.

Accepted Answer

Its key assumption is parallel trends: treated and control would trend identically absent treatment

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It assumes random assignment of treatment timing

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It requires the treatment effect to be constant across units

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It assumes no time trend in either group

Question 17

What is the identifying logic of a regression discontinuity design (RDD)?

Accepted Answer

It exploits a treatment-assignment threshold; the outcome jump at the cutoff identifies a local effect

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It compares all treated vs all control units globally

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It requires randomization of the running variable

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It estimates the population ATE directly

Question 18

Explain Simpson's paradox and its relevance to causal inference.

Accepted Answer

An association reverses after conditioning on a third variable; the correct choice depends on the causal structure

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A sampling error that disappears with larger samples

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A guarantee that subgroup analysis is always correct

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A paradox unique to continuous variables

Question 19

What is a mediator, and what is the difference between the total, direct, and indirect effects?

Accepted Answer

A mediator lies on the T->M->Y path; the total effect splits into direct and indirect (mediated) components

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A mediator is a common cause; adjust for it to remove confounding

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A mediator is identical to a collider

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Adjusting for a mediator always estimates the total effect

Question 20

Distinguish confounders, mediators, and colliders in terms of whether you should adjust for them.

Accepted Answer

Adjust for confounders; do not adjust for mediators (for total effect) or colliders

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Adjust for all three to be safe

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Adjust only for colliders

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Never adjust for any of them

Question 21

State Pearl's frontdoor criterion and when it is useful.

Accepted Answer

It identifies the effect via a fully mediating observed variable when T-Y confounding is unobserved

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It is used only when there are no confounders

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It requires the instrument to be randomized

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It is equivalent to inverse probability weighting

Question 22

What are the three rungs of Pearl's 'ladder of causation'?

Accepted Answer

Association (seeing), Intervention (doing), Counterfactuals (imagining)

Answer

Correlation, regression, classification

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Sampling, estimation, testing

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Bias, variance, noise

Question 23

What is a counterfactual in causal inference, and why does answering counterfactual queries require a structural causal model?

Accepted Answer

It is the outcome under an unreceived treatment; answering it needs an SCM (abduction-action-prediction)

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A counterfactual is just a prediction from a regression model

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Counterfactuals equal interventional distributions exactly

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Counterfactuals require only observational data

Question 24

What is the d-separation rule, and what does it tell us about a causal DAG?

Accepted Answer

A graphical criterion for reading conditional (in)dependencies implied by a DAG

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A rule for ordering nodes topologically

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A method to estimate edge weights

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A test for normality of residuals

Question 25

Explain covariate (nearest-neighbor) matching for estimating treatment effects and one of its main limitations.

Accepted Answer

It pairs similar treated/control units but degrades with many covariates (curse of dimensionality)

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It requires no overlap assumption

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It always yields the population ATE without bias

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It eliminates unmeasured confounding

Question 26

What is double/debiased machine learning (DML), and what two properties make its estimates robust?

Accepted Answer

It combines Neyman-orthogonal scores with cross-fitting for robust, root-n inference

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It fits a single deep network end-to-end on the outcome

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It requires linear nuisance models only

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It abandons the unconfoundedness assumption

Question 27

Define CATE (Conditional Average Treatment Effect) and explain its role in uplift / heterogeneous-effect modeling.

Accepted Answer

tau(x)=E[Y(1)-Y(0)|X=x], the treatment effect conditional on covariates

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The marginal probability of treatment given x

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The average outcome in the treated group

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The correlation between covariates and outcome

Question 28

Compare the S-learner, T-learner, and X-learner meta-learners for estimating heterogeneous treatment effects.

Accepted Answer

S=single model with T as feature; T=separate per-arm models; X=imputed-effect refinement of T-learner

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All three require fitting exactly one model

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T-learner uses an instrument; X-learner uses a DAG

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They differ only in the loss function used

Question 29

What is selection bias in causal inference, and how does it differ structurally from confounding bias?

Accepted Answer

Selection bias comes from conditioning on a common effect (collider); confounding from a common cause (backdoor)

Answer

They are identical and fixed the same way

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Selection bias only occurs in RCTs

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Confounding is fixed by ignoring covariates

Question 30

What is a placebo / negative-control test, and how does it help validate a causal study?

Accepted Answer

A check of an effect that should be zero; a non-zero result flags bias or violated assumptions

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A test that maximizes the estimated effect

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A method to randomize treatment retroactively

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A way to increase statistical power

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