Use randomized-experiment data and simulations to compare treatments and judge significance.
Classify statistical and practical importance on two axes
Problem
An observed increase is \(0.1~\text{point}\) with \(p~<~0.001\), \(\text{alpha}~=~0.05\), and a practical threshold of \(2~\text{points}\). Classify its statistical significance and practical importance separately.
Big Picture
What this problem is really about
Make two independent comparisons. Statistical significance comes from p versus alpha and describes evidence against the null, while practical importance comes from the absolute effect magnitude versus a declared context threshold. A very small p-value can accompany a tiny effect, so neither axis should be used as a substitute for the other.
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