Problem

Participants self-assign to a treatment rather than receiving random assignments. Analyze possible confounding, causal attribution, and the separate question of population generalization.

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Participants receive random treatment labels rather than self-selecting. The groups are comparable in expectation and support a causal comparison; generalization still depends on recruitment.

There is no random assignment: participants self-select. Their groups may differ in preferences or confounders, so the design alone does not support causal attribution; generalization depends separately on recruitment.

Participants choose their own treatment. The resulting groups are guaranteed identical on every confounder, so the treatment effect is proved with certainty and generalizes broadly.

Participants choose their own treatment. Self-selection balances confounders in expectation, supports a causal treatment comparison, and makes participants representative of the population.

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Participants self-assign to a treatment rather than receiving random assignments. Analyze possible confounding, causal attribution, and the separate question of population generalization.

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