The significant finding published in a journal does not tell us how many times the researcher ran the experiment and did not find statistically significant results; It isn't unheard of for a researcher to run a study 10 times or so before they turn up a significant finding (file-drawer effect). The alpha and p-value reported are not the actual chances of that finding being a statistical fluke. (We place too much emphasis on alphas and p-values.) The actual probability of that finding reported being a chance finding would involve the number of total times the study was run and statistical significance WAS and was NOT found (Bayesian probability). But, understandably, bayesian probability is a kettle of fish no one wants to touch.