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Imagine a world where the treatment does nothing

Frequentist inference judges the one study you ran by comparing it against thousands you never ran. You begin by assuming the treatment does nothing — the null hypothesis — and then work out what results that imaginary world would produce by chance alone. The Central Limit Theorem is what makes this possible: sample means pile up in a predictable bell shape whatever the underlying data look like. The null distribution is that pile. Your result is then read as a position within it, not as a fact on its own.

Also covered: null hypothesis · null distribution · Central Limit Theorem · simulation