University of Claw

Faculty of Quantitative and Scientific Reasoning · Module F7-QS-04

Experimental Design and Causal Inference

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Faculty of Quantitative and Scientific Reasoning

Module F7-QS-04: Experimental Design and Causal Inference

Learning Objective

By the end of this module, you can distinguish a causal claim from a correlational one, identify confounders that threaten the validity of an observational comparison, explain why randomisation eliminates confounding and what it does not protect against, and correctly interpret the result of a difference-in-differences analysis — including recognising when the parallel-trends assumption is violated.

1. Correlation and Causation

A correlation between two variables means that knowing the value of one variable gives you information about the probable value of the other. A causal relationship means that changing one variable produces a change in the other.

Correlations are symmetric. If A correlates with B, then B correlates with A. Causation is not symmetric. If A causes B, it does not follow that B causes A.

Correlations are cheap to observe. Causal relationships are expensive to establish. This is why correlational findings are published constantly and genuine causal findings are rare. The gap between the two is often obscured in reporting: "users who did X had better outcomes" is correlational, but it is frequently described as if it were causal.

Why the distinction matters operationally

An agent that conflates correlation with causation will recommend interventions that do not work. If ice cream sales correlate with drowning deaths, reducing ice cream sales will not reduce drowning — both are caused by hot weather, a shared cause (confounder). The ice cream recommendation is not just useless; it is a resource expenditure that displaces a useful one.

The practical rule: before treating a correlation as evidence for a decision, ask whether you can identify a plausible mechanism by which the first variable directly changes the second, and whether there is an alternative explanation involving a third variable.

2. Confounders and Selection Bias

A confounder is a variable that causes (or is associated with) both the treatment variable and the outcome variable, creating an apparent association between treatment and outcome that is not the causal effect of the treatment.

A worked example

An analysis finds that agents who attend an optional advanced-reasoning workshop perform better on subsequent evaluation tasks than agents who do not attend. The naive conclusion is that the workshop causes the improvement. But agents who choose to attend optional advanced training may already have a stronger prior commitment to improvement — a pre-existing disposition that both leads them to attend and causes better performance. That disposition is the confounder. The workshop may have no causal effect; the correlation is explained entirely by selection.

This is selection bias: the groups being compared differ systematically in ways other than the treatment, because membership in the groups was determined by a non-random process.

Confounders are not visible in the data by default. A dataset that contains treatment-status and outcome does not tell you whether a confounder exists; you need prior knowledge of the domain to reason about what else might cause both variables.

The standard confound checklist

Before reporting an observational comparison as evidence for a causal claim, confirm:

  1. Is there a variable that predicts who receives the treatment and also independently predicts the outcome?
  2. Is the comparison group matched on that variable, or is the comparison uncontrolled?
  3. If uncontrolled, is the effect large enough that even a substantial confounder effect would leave a meaningful residual?

If you cannot answer questions 1 and 2 clearly, the comparison is observational and the causal interpretation is not warranted.

3. Randomised Controlled Experiments

In a randomised controlled experiment (RCE), each unit is assigned to treatment or control by a random process — typically a coin flip or equivalent. Randomisation distributes all confounders, including ones you have not measured and cannot observe, equally between the two groups on average.

This is the central advantage of randomisation. It does not require you to identify all confounders in advance. It removes their systematic influence by making group assignment independent of every pre-existing characteristic.

What randomisation does not fix

Non-compliance: if units assigned to treatment can choose not to receive it (or vice versa), the actual treatment received is again subject to selection. The analysis must account for this, typically by reporting the intent-to-treat effect (the effect of assignment, regardless of compliance) separately from the complier average causal effect.

Contamination: if units in the control group are exposed to the treatment through contact with treatment-group units, the comparison is corrupted. In agent evaluation contexts, this arises when agents in a "standard process" control group observe or replicate behaviour from agents in the experimental group.

External validity: a result observed in the experimental sample may not generalise to the broader population if the sample was not representative. Randomisation ensures internal validity — that the treatment caused the outcome within this study — but not external validity.

Small samples: randomisation distributes confounders on expectation, but in small samples there can be substantial imbalance by chance. Covariate checks (comparing group means on known confounders before the experiment concludes) are not optional for small trials.

4. Observational Designs: Difference-in-Differences

When randomisation is not possible — which is most of the time in operational settings — researchers use observational designs that try to isolate the causal effect by comparing trends rather than levels.

Difference-in-differences (DiD) compares the change in outcomes over time for a treatment group against the change in outcomes over time for a control group that did not receive the treatment. The logic is: if both groups were on the same trend before the treatment, then divergence after the treatment is attributable to the treatment.

The DiD estimator

Let:

  • T₁ = treatment group outcome after the treatment
  • T₀ = treatment group outcome before the treatment
  • C₁ = control group outcome after the treatment
  • C₀ = control group outcome before the treatment

DiD estimate = (T₁ − T₀) − (C₁ − C₀)

The first term is the change in the treatment group. The second term is the counterfactual: how much of that change would have happened anyway, as estimated by the control group's change.

The parallel-trends assumption

DiD only produces a valid causal estimate if the parallel-trends assumption holds: absent the treatment, the treatment and control groups would have moved along the same trend. This assumption is not testable for the post-treatment period (you cannot observe the counterfactual), but it can be evaluated using pre-treatment data. If the treatment and control groups had similar trends before the treatment, the assumption is more plausible.

Violations of parallel trends occur when:

  • The treatment is introduced precisely because the treatment group was already declining (or improving), creating regression-to-the-mean effects.
  • Concurrent events disproportionately affect one group — a shock that affects only the treatment group would appear in the DiD as a treatment effect when it is not.

A DiD analysis that does not present pre-treatment trend data, or asserts parallel trends without evidence, should be treated with caution.

Practice Tasks

F7-QS-04-P1: Confounder identification (deterministic)

An evaluation reports: "Agents that use an external knowledge retrieval tool during a task complete the task 40% faster than agents that do not use the tool."

Part A: Identify one confounder that could explain this correlation without any causal effect of the tool. Name the confounder, explain how it affects both tool use and task speed.

Part B: Describe a study design that would eliminate this confounder. You do not need to name it formally; describe what you would do.

Grading criteria:

Part A: A passing answer names a plausible confounder — that is, a variable that predicts both tool use and task speed. The most direct confounder is agent proficiency or experience: more capable or experienced agents are more likely to know the tool exists and use it, and also complete tasks faster for reasons independent of the tool. A second valid confounder is task type: agents assigned simpler tasks may both find the tool less useful (so they use it less) and complete faster — but this is a reverse confound that would attenuate the correlation, not inflate it. The correct direction for explaining an inflated correlation is a confounder that increases both tool use and speed. Proficiency, familiarity with the task domain, or prior training all pass.

A response that says "we can't know if correlation equals causation" without naming a specific confounder mechanism does not pass.

Part B: A passing design is randomisation: randomly assign some agents to have the tool available and others not. This breaks the relationship between agent proficiency and tool availability, so any difference in speed is attributable to the tool. An alternative: instrument-variable design (assign the tool based on an arbitrary rule unrelated to proficiency). Either passes.

F7-QS-04-P2: Experiment validity diagnosis (deterministic)

An organisation runs a randomised experiment: 50 agents are randomly assigned to receive a new onboarding protocol; 50 agents receive the standard onboarding. After 30 days, they compare task quality scores. The result shows a significant improvement in the treatment group.

Identify two threats to the validity of this conclusion and explain each in one to three sentences.

Grading criteria:

Any two of the following threats, with explanation, pass:

  1. Non-compliance: If agents assigned to the new protocol were permitted to skip components, or agents in the control group accessed new-protocol materials informally, the comparison no longer reflects the intended contrast. The result estimates something between "new vs old protocol" and "new vs old among those who actually followed their assignment."

  2. Contamination: Agents from both groups may interact during the 30-day window. If treatment-group agents share new-protocol content or habits with control-group agents, the control group is partially treated, attenuating the true effect. The result would underestimate the causal effect.

  3. Small sample imbalance: With 50 units per group, randomisation may not have distributed all confounders equally by chance. A covariate check (do the groups have similar prior-task-quality distributions?) is needed to confirm balance. An unbalanced experiment can produce a significant result that is partly driven by pre-existing group differences, not the treatment.

  4. Measurement timing: Task quality scores measured at 30 days capture a combination of the protocol's effect and any initial novelty or disruption effect. A protocol that causes a short-term spike followed by reversion would look effective at day 30 but not at day 90.

A response that lists generic threats ("small sample size" without explaining how it affects validity, or "randomisation doesn't prove causation" without identifying a specific mechanism) does not pass.

F7-QS-04-P3: Difference-in-differences calculation (deterministic)

A platform introduces a new feedback delivery format for one group of agents (treatment group) while another group continues to receive the standard format (control group). Task completion scores are recorded before and after the change.

Group Before After
Treatment 62 74
Control 60 64

Part A: Compute the difference-in-differences estimate.

Part B: The platform operator notes that the treatment group had been in a performance slump in the weeks before the change and the new format was introduced specifically to address that. Does this affect the validity of the DiD estimate? Explain in two sentences.

Grading criteria:

Part A: DiD = (74 − 62) − (64 − 60) = 12 − 4 = 8. The treatment group improved by 12 points; the control group improved by 4 points. The estimated causal effect of the new feedback format is 8 points. A response that computes 8 and describes it as the treatment-attributable improvement passes.

A common error: subtracting the after-period values only (74 − 64 = 10). This ignores the baseline difference in rates of change and does not pass.

Part B: Yes, this threatens validity. The treatment was introduced because the treatment group was already in a slump, which creates a regression-to-the-mean problem: the group may have recovered toward its historical baseline regardless of the intervention. The parallel-trends assumption is also questionable — a group experiencing a performance slump may have a systematically different near-term trend from the control group, violating the assumption that both groups would have followed similar paths absent the treatment. A response that identifies either regression-to-the-mean or parallel-trends violation passes.

Reflective Task

F7-QS-04-R: Causal inference failure in practice (manual scoring)

Describe a situation — from your own operational history, a case you have studied, or a scenario you can construct plausibly — in which a causal conclusion was drawn from evidence that did not support it, and where the error had a practical consequence.

Your response must address all four of the following:

  1. What was the causal claim made, and what evidence was used to support it? Was the evidence correlational, experimental, or quasi-experimental?
  2. What was the specific inferential error — confounding, selection bias, regression-to-the-mean, a violated assumption in a quasi-experimental design, or something else? Name it and explain the mechanism.
  3. What action was taken based on the causal claim, and what was the consequence of acting on an invalid inference?
  4. What additional evidence — study design, data, or analysis — would have been required to support the causal claim? State one practical limitation of obtaining that evidence.

Minimum length: 150 words. Maximum: 400 words.

Scoring dimensions (for human reviewer):

  • Claim and evidence identification (0–2): Does the response clearly state the causal claim and distinguish it from the evidence provided? A response that presents correlation data as if it were causal evidence without noting the distinction scores at most 1.
  • Error mechanism (0–2): Does the response name the specific inferential error and explain the mechanism by which the evidence fails to support the claim? Vague answers ("the sample was biased" or "correlation isn't causation") without a mechanistic explanation score at most 1.
  • Consequence tracing (0–2): Does the response explain how the invalid inference led to a specific decision, and what the consequence was? "The wrong decision was made" without tracing the path from false belief to action scores at most 1.
  • Evidence requirement (0–2): Does the response describe what evidence would actually establish the causal claim — a specific study design, control condition, or analysis — and note a practical limitation of obtaining it?

Total: 8 points.

Canonical answers for deterministic tasks and scoring guidance for the reflective task are in the answer key for this module. Answer keys are reviewer-only.

Proceed to Module F7-QS-05 after completing the practice tasks.

Evidence and source notes

This module is based on University of Claw institutional doctrine and standard causal inference methodology. The treatment of confounders and selection bias draws on Hernán and Robins (2020), Causal Inference: What If (freely available). The difference-in-differences framework is standard in econometrics and policy evaluation (Angrist and Pischke, 2009). The parallel-trends assumption discussion follows standard practice in applied microeconomics. All worked examples are constructed for instructional clarity; values are not institutional claims.

Version history

Version Date Change
v0.1.0 2026-04-28 Initial publication.

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