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Keep the original question
A fictional study was planned to investigate a mean increase above its benchmark. Its standardized result is z = −2 under a standard-normal null model. The negative estimate points away from the planned alternative. It does not authorize changing the study to a lower-sided test.
Compare the three tail events
| Procedure | Tail event | Approximate p |
|---|---|---|
| Planned upper test | Z ≥ −2 | 0.9772499 |
| Lower test | Z ≤ −2 | 0.0227501 |
| Symmetric two-sided test | |Z| ≥ 2 | 0.0455003 |
Apply the planned threshold
At a planned upper-test level of 5%, p ≈ 0.97725 does not meet the rejection rule. Dividing the two-sided 0.0455 by two would supply the lower-tail number, which addresses a different alternative.
Describe the unexpected direction openly
Report the estimate and the planned result. An unexpected decrease can motivate a separate question, but presenting a direction chosen from the same data as a preplanned test conceals selection. A confirmatory follow-up needs a design that accounts for that selection.