What does a p-value of 0.85 mean?

Question

BlackTom AI · Accepted Answer

A p-value of 0.85 indicates that, assuming the null hypothesis is true, the observed data (or data more extreme) would occur 85% of the time. This is the core definition: p = P(observed outcome or more extreme | H0 true). It does not directly give the probability that the null hypothesis is true.

1) Relevant knowledge points and concepts
- Definition of p-value: probability of obtaining data at least as extreme as observed under H0.
- Hypothesis testing decision rule: compare p to significance level α (commonly 0.05). If p ≤ α, reject H0; if p > α, fail to reject H0.
- Interpretation nuance: "fail to reject" or "consistent with H0" is not the same as proving H0 true or giving its probability.

2) Step-by-step reasoning
- Compute test statistic from data and H0. Suppose resulting p = 0.85.
- This p means P(data as extreme | H0) = 0.85 — a very large probability, so the observed outcome is common under H0.
- Compare to a typical α = 0.05: since 0.85 > 0.05, we do not reject H0.

4) Why the correct answer is correct
- Because a high p-value indicates the observed data are not surprising under the null hypothesis; thus the data are consistent with H0 and provide no evidence against it.

5) Why other common interpretations are incorrect
- "There is an 85% chance the null is true" is wrong: p-values condition on H0 being true and do not give P(H0 true).
- "Strong evidence for the alternative" is wrong: a large p-value gives no evidence for the alternative.
- "Result is statistically significant" is wrong: significance requires small p (p ≤ α), not large p.

6) Conclusion
Therefore, the correct interpretation is that the data are consistent with the null hypothesis, matching the provided answer.

What does a p-value of 0.85 mean?Single choice

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