The Bayesian Probability Tree

Visualize why a "positive" result isn't always a true discovery.

P(H1 | Positive Result)
TP / (TP + FP) 0%
Total Trials 1000 H1 True 100 H0 True 900 True Positives 80 False Negatives 20 False Positives 45 True Negatives 855
Before conducting a power calculation a researcher must choose alpha and power. This will depend on their tolerance for a false positive for the trial and also on their expectations for the trial. This is expressed as a Prior probability. If the evidence is very good that the intervention will work, then this may be >50%. However, as many interventions tested do not work it may be that it is much less than 50%. This will depend on prior trials in the field and the strength of the evidence for the intervention (e.g. from biological plausibility, pre-clinical studies, pilot studies, observational studies).
© John W Pickering, August 2026