The Holm-Bonferroni method works by first ranking all p-values from multiple tests in ascending order. Then, each p-value is compared against a progressively stringent threshold. The first p-value is compared with the significance level divided by the number of tests (e.g., α/k), the second with α/(k-1), and so on. If a p-value fails to meet the threshold, the hypothesis is not rejected, thus maintaining the overall familywise error rate.