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What is a p-value, and what does it not tell you?

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A p-value answers one narrow question: if the null hypothesis were true, how often would chance alone produce a result this extreme or more extreme? A small p-value means your data sits far out in the tail of what randomness usually produces.

It does not tell you the probability that the null is true. It does not tell you the probability your result is a fluke, and it says nothing about effect size. A p-value of 0.01 on a 0.05% conversion lift is statistically loud and commercially worthless.

It also does not survive abuse. Report a p-value from a test you stopped the moment it dipped under 0.05, and the number no longer means what the formula says. In practice I pair every p-value with the effect size and a confidence interval. The decision should rest on how big the change is, not on clearing a threshold.

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