A simple formula finds the worst-case pattern in matched-pair studies without complex computation.

Scientists often test treatments using matched pairs, where one person gets a treatment and a similar person does not. When the outcome is simply yes or no, finding the average treatment effect without making unproven assumptions is hard. Researchers solved this by using the random coin flip that decided who got treated. Usually, finding the hardest scenario to test requires slow computer searches. Here, the team used math rules about symmetry to pinpoint this worst-case scenario directly as a single boundary corner. This allows them to test claims using fast calculations instead of complex programs. Their method also checks how hidden biases might distort observational studies, offering a formula that shows when these studies can successfully detect real effects.

Why it matters

This matters for researchers in clinical trials or social experiments because it provides a trustworthy way to measure treatment effects without guessing about data patterns. It makes rigorous analysis faster and more accessible.

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