Understanding p-values
A p-value is the probability of obtaining a test statistic at least as extreme as the one observed, assuming the null hypothesis is true. A small p-value (typically below 0.05) suggests that the observed result is unlikely under the null hypothesis, providing evidence to reject it.
For a z-test, the p-value comes from the standard normal distribution. For a t-test, it comes from the Student's t-distribution with the specified degrees of freedom. For a chi-square test, the p-value is computed from the chi-square distribution and is always right-tailed.
Two-tailed p = 2 × P(Z > |z|)
Two-tailed p-value from a z-score using the standard normal CDF.
Left-tailed p = P(T ≤ t)
Left-tailed p-value from the cumulative distribution function.