A visual lesson · illustrative models

Same observations.
Different mechanisms.

A marker and an outcome always appear together. Does the marker drive the outcome? Build two explanations, then change one thing.

Can the observations choose a model?

Both models produce the same marker–outcome pairs. Predict what happens if we force the marker off.

MODEL A · A CHAIN

The marker transmits the signal

Signal to marker to outcome An assumed causal chain. Setting the marker off blocks the only path to the outcome. Signal U Marker X Outcome Y
Outcome active60%

Observation baseline: 60%

MODEL B · A SHARED CAUSE

The signal drives both

Signal to marker and signal to outcome An assumed common cause. Setting the marker off leaves the direct signal to outcome path intact. Signal U Marker X Outcome Y
Outcome active60%

Observation baseline: 60%

A perfect match is not a unique explanation.

In both models, X and Y equal U during observation. Change the fraction above: the models keep matching.

The model behind the picture

These are deterministic binary teaching models. Every variable is either 0 (off) or 1 (on). The slider sets p, the fraction with U = 1. All percentages are calculated expectations, not study results. Arrows denote causal assumptions within each toy model.

For 0 < p < 1, X and Y are perfectly correlated during observation. At p = 0 or p = 1, correlation is undefined because there is no variation. At p = 0, this intervention cannot distinguish the two models.

Connect the lesson to an experiment

This ideal intervention changes X alone. A real perturbation may have incomplete action, off-target effects, feedback or additional routes to Y. Controls and context determine which explanation an experiment can support. The diagram does not establish a mechanism in a biological system.

Sources and reading scope

This original example follows the intervention-as-equation-replacement account in Judea Pearl, Causal inference in statistics: An overview (2009). Reading scope: section 3.2.1, pp. 107–109, equations 5–7. The binary models, layout and values here were created for teaching. No paper figures or experimental data are reproduced.

The teaching sequence is inspired by 3Blue1Brown's visual teaching principles. This is an independent example for the Scientific Visual Explainer skill.