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A scientific hypothesis is tested by evaluating the logical consistency of its implications and/or the accuracy of its predictions. Other grounds for assessing hypotheses include breadth of prediction, scientific fertility, simplicity, and aesthetic appeal; however, the term hypothesis testing refers only to accuracy. Statistical hypothesis testing, a form of inductive inference, is used extensively in medical research and described here as a form of proof by contradiction.

A hypothesis is rejected by a test if the hypothesis logically implies something false or strongly predicts something contradicted by data. The 2,500-year-old proof by Hippasus of Metapontum that √2 is not a ratio of whole numbers exemplifies the former. Hypothesizing the opposite, that √2 = a/b for whole numbers a and b, Hippasus deduced the impossible: that both ...

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