What does a p-value represent?

What does a p-value represent?

• A. Probability of obtaining the observed results if the null hypothesis is true
• B. Probability that the null hypothesis is true
• C. Probability that the alternative hypothesis is true
• D. Probability of sampling error

Answer: (A)

The p-value tells you how compatible the observed data are with the assumption that the null hypothesis is true. It is the probability, under that assumption, of obtaining the observed result or something as or more extreme in the direction of interest. In a two‑sided test, this means extreme in either direction. It is a conditional probability of the data given the null hypothesis (P(data or more extreme | H0)), not the probability that the null itself is true (that would be a Bayesian idea) and not the probability that the alternative is true. It also isn’t a direct measure of sampling error. A small p-value suggests the data are unlikely under the null and leads to rejecting it at your chosen significance level, while a large p-value indicates the data are reasonably consistent with the null.

The p-value tells you how compatible the observed data are with the assumption that the null hypothesis is true. It is the probability, under that assumption, of obtaining the observed result or something as or more extreme in the direction of interest. In a two‑sided test, this means extreme in either direction. It is a conditional probability of the data given the null hypothesis (P(data or more extreme | H0)), not the probability that the null itself is true (that would be a Bayesian idea) and not the probability that the alternative is true. It also isn’t a direct measure of sampling error. A small p-value suggests the data are unlikely under the null and leads to rejecting it at your chosen significance level, while a large p-value indicates the data are reasonably consistent with the null.