Does a bigger p-value mean the result is more significant?

Question

AcadiFi · Accepted Answer

No. A bigger p-value means weaker evidence against the null hypothesis.

The p-value asks how unusual the sample result would be if the null hypothesis were true. If the p-value is small, the result is hard to explain under the null, so rejecting the null becomes easier. If the p-value is large, the result is not unusual enough to reject the null at common significance levels.

```mermaid
flowchart TD
  A["Small p-value"] --> B["Sample is unusual under H0"]
  B --> C["Stronger evidence against H0"]
  C --> D["Reject if p-value <= alpha"]
  E["Large p-value"] --> F["Sample is not unusual enough"]
  F --> G["Weaker evidence against H0"]
  G --> H["Fail to reject if p-value > alpha"]
```

For example, if `alpha = 0.05` and the p-value is `0.032`, reject the null. If the p-value is `0.32`, fail to reject. The second result is not "more significant"; it is much less persuasive against the null.

Does a bigger p-value mean the result is more significant?

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