Explain What a P-Value Actually Tells You (and What It Does Not)

P-values are in almost every study that gets reported in the news. They are also almost universally misunderstood, including by researchers. Knowing what a p-value does and does not tell you changes how you read health, psychology, economics, and nutrition reporting. This explains the concept precisely, corrects the three most common false beliefs, and gives you two better questions to ask.

Explain what a p-value actually tells you in the context of statistical hypothesis testing:

1. The plain English definition: what a p-value of [0.04] would actually mean if you found one in a study, stated precisely and without jargon
2. The three things it does NOT tell you: the three most common misinterpretations of a p-value, each stated as a false belief and corrected
3. A concrete example: walk through a single example of a study where p < 0.05 but the conclusion drawn was almost certainly wrong, and explain why
4. What to look for instead: two additional things a reader should check alongside a p-value to assess whether a result is actually meaningful

Aim for clarity over completeness. Assume the reader has no statistics background but is genuinely trying to understand.