It is a p-value, not a Bayesian probability. A p-value is the probability of seeing data as or more extreme purely due to chance, not the probability that your data is due to chance.<p>In other words, X is the event of observing data as or more extreme than what you observed, H0 is the event that the relationship is due to random effects. P(E1 | E2) is the probability of E1 given E. You are claiming that P(H0 | X) &lt; 0.14, but the evidence is that P(X | H0) &lt; 0.14.<p>If you wanted to do Bayesian statistics, you could obtain P(H0 | X) = P(X | H0) * P(H0) &#x2F; P(X) = P(X | H0) * P(H0) &#x2F; (P(X | H0) * H0 + P(X | not H0) * (1-H0))<p>To do that, you need a prior probability of H0 - in other words, to do Bayesian inference you need a prior belief about how likely something is to be true and evidence will update your belief. If you are already absolutely certain of H0 or not H0, no amount of evidence will shift your view in Bayesian inference, as any amount of evidence is best explained as random variation.