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Identify what is assumed
In a normal mean test, the null specifies a population mean and the model specifies how observations behave around it. The reference distribution answers what test statistics would be expected under those assumptions. The observed statistic is then located within that distribution.
Define the event counted
An upper-sided test counts statistics at least as large as the observed value. A two-sided normal test counts statistics with absolute magnitude at least as large. The event changes with the alternative; a p-value without its test direction is incomplete.
Keep the conditional question in its original direction
If a fictional test produces p = 0.04, its tail calculation is conditional on the null model. It has not combined prior probabilities for competing hypotheses or specified their likelihoods. Those additional inputs would be required for a posterior probability.
| Statement | Assessment |
|---|---|
| Tail probability under the specified null model | The defined p-value calculation |
| 4% probability that the null is true | Not supplied by p = 0.04 |
| 96% probability of a useful commercial effect | Not supplied by p = 0.04 |
Investigate the full report
A small p-value can prompt examination of the claim and assumptions. A large one can coexist with a wide uncertainty interval. Read the estimate and sampling design as well as the tail probability before describing the result.