Here are a few options, aiming for similar size and meaning: * **Causal Inference: A web guide exploring cause & effect, beyond simple patterns.** * **From Pattern to Proof: A web guide to understanding causal inference.** * **Web Guide: Causal inference basics – proving cause, not just observing.** * **Unveiling Causation: A web guide to the principles of causal inference.** * **Beyond Correlation: A web guide to establishing causal relationships.**
Here are a few rewrites, all roughly the same size: * For each individual, only one reality is seen. The unlived—the **counterfactual**—remains unseen. * Each person experiences a single reality. The "what if"—the **counterfactual**—stays concealed from view. * We each experience a single world. The unexplored possibility—the **counterfactual**—is permanently out of reach.
Person A
Outcome is Observed
Outcome is Unobserved
To gauge impact unseen, we compute the **population-wide Average Effect (ATE)**.
E [Y(1)] - E [Y(0)]
Average Outcome (Treated) - Average Outcome (Control)
Select a representative group from the population.
(External Validity)
Split the sample into two identical-on-average groups.
(Internal Validity)
Here are a few options, all similar in length and conveying the same meaning: * This isolates the treatment as the sole variable. * Thus, the treatment is the sole differentiating factor. * This guarantees treatment is the exclusive variation. * This establishes the treatment as the only change. * The treatment is therefore the unique distinction.
Here are a few options, all similar in length and conveying the same idea: * Without random assignment, group differences skew outcomes. * Non-random groupings can introduce bias through pre-existing factors. * When groups aren't randomized, pre-existing traits distort findings. * Failing to randomize allows prior traits to bias group comparisons.
🔵 = Motivated, ⚪️ = Not Motivated
Mostly motivated people self-select.
Groups are not comparable.
Here are a few options, all similar in length and meaning: * Units operate independently; uniform treatment applied. * Independent operations, with standardized treatment protocols. * No unit influence; all receive identical treatment. * Units are isolated, and treatment is fully uniform.
In a randomized controlled trial (RCT), treatment allocation is independent of what would happen.
Every group has some possibility of either getting or not getting the treatment.
Here are a few options, all similar in length and capturing the essence of the IV concept: * (For IVs) The instrument *only* impacts results via the treatment. * (IV context) Treatment is the *sole* pathway for the instrument. * (Regarding IVs) The instrument's effect is exclusively treatment-mediated. * (IV setup) Treatment is the only causal link from instrument to result.