Questions / Quant research, Research decisions
Interpret the p-value
A valid test returns p=0.03. Which interpretation matches its frequentist definition?
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Answer: A. It is a 3% null-model tail probability for the test statistic.
- Assume the specified null model and test assumptions hold.
- Calculate how often the test statistic would be at least as extreme in the stated tail or tails.
- A p-value of 0.03 reports that tail probability. It does not reverse the conditioning to give P(null | data).
Interview shortcut. p = P(statistic this extreme | null), not P(null | data).
Takeaway. Always state what probability is conditioned on.
Why the other choices fail
- It is the probability that the observed effect is real. A p-value is not a probability about the hypothesis.
- It is a 3% posterior probability that the null is true. A frequentist p-value conditions on the null model. It does not assign a posterior probability to the hypothesis.
- It is a 3% probability that the result will fail to replicate. Replication depends on effects, power, design, and future sampling. It is not the complement of a p-value.
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