The useful version

A p-value tells you how unusual your data would be under a particular null model. That can be useful. It is a measure of surprise, assuming the null model and analysis plan are reasonable.

The dangerous version

The trouble starts when the p-value becomes a ritual. It does not measure importance, truth, practical value or replication probability. A tiny effect can be statistically significant in a huge sample. A meaningful effect can be uncertain in a small sample.

What to report alongside it

Effect sizes, uncertainty intervals, plots, sample sizes and design details usually matter more than the star next to a coefficient. Statistical evidence is a bundle, not a single magic number.

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