What does a p-value represent in hypothesis testing?

Question

BlackTom AI · Accepted Answer

A p-value is the probability of obtaining a test statistic at least as extreme as the one observed, assuming the null hypothesis (H0) is true.

Relevant concepts:
- Null hypothesis (H0): the baseline statement we assume true for calculating probabilities.
- Test statistic: a standardized value computed from sample data (e.g., z, t).
- p-value: P(data as extreme as observed | H0). It quantifies how compatible the observed data are with H0, not the probability that H0 is true.
- Significance level (α): a threshold for deciding whether the p-value is small enough to reject H0.

Step-by-step reasoning:
1. Formulate H0 and an alternative hypothesis (H1).
2. Collect sample data and compute the appropriate test statistic (e.g., t_obs).
3. Under the assumption that H0 is true, determine the sampling distribution of the test statistic.
4. Compute the p-value: the tail probability of getting a value as extreme as (or more extreme than) the observed statistic under that distribution. For a one-tailed test, p = P(T ≥ t_obs | H0) (or ≤ for the other tail); for a two-tailed test, p = 2·P(T ≥ |t_obs| | H0).
5. Compare p to α: if p ≤ α, reject H0; if p > α, fail to reject H0.

Why option c is correct:
Option c states exactly the definition: "The probability of observing the sample result if the null hypothesis is true." This matches the conditional probability formulation of a p-value.

Why the other options are incorrect:
- a: The p-value is not P(H0 is true). It is computed assuming H0 is true; it does not give the posterior probability of H0.
- b: Strength of correlation refers to a correlation coefficient (e.g., r), not a p-value.
- d: Effect size (e.g., Cohen’s d) measures practical magnitude of an effect, not the p-value.

Confirming final answer: The correct choice is c.

What does a p-value represent in hypothesis testing?单项选择题

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