The seed paper is the ideal worked example: the lead association at ABCC9 has P = 2.6 x 10^-18, which looks overwhelming, and an effect of beta = 0.11 SD per allele, or about 2.1 Hz, which is small. A student who reads the exponent as a measure of importance will get this paper exactly backwards. The node must also carry the mechanism, not just the slogan: precision scales with sample size, so a study of 12,901 people testing 39.2 million sequence variants is built to make genuinely small effects statistically certain — a design strength and an interpretation hazard at once.
The page defines the p-value as the probability, under the null hypothesis, of a test statistic at least as extreme as the one observed, and shows how it is computed for one- and two-sided tests. It …