Why does a two-tailed test split alpha across both tails?

Question

AcadiFi · Accepted Answer

The significance level is the total probability of rejecting the null when it is true. In a two-tailed 5% test, unusual results in either direction count against the null, so the total 5% rejection probability is split across the two tails.

That means:

2.5% in the left tail.
2.5% in the right tail.
5.0% total rejection probability.

That means:

- 2.5% in the left tail.
- 2.5% in the right tail.
- 5.0% total rejection probability.

```mermaid
flowchart LR
  A["Left tail 2.5 percent"] --> B["Fail to reject region 95 percent"]
  B --> C["Right tail 2.5 percent"]
```

If you put 5% in each tail, the total rejection probability would be 10%, not 5%.

Why does a two-tailed test split alpha across both tails?

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