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Precision is about variability while accuracy (in contrast to precision) is about bias. This tag pertains to measurement or estimation; use [precision-recall] when talking about classifiers.

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How should tiny $p$-values be reported? (and why does R put a minimum on 2.22e-16?)

A lot of other stats packages just go to 0.0001, so this is a much higher level of precision. But I haven't seen too many papers reporting $p < 2.22\cdot 10^{-16}$ or $p = 2.22\cdot 10^{-16}$. …
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