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Table 3 Change in prior probabilities of cafestol not affecting serum cholesterol to posterior probabilities using data of the present study and Bayesian analysis

From: Coffee bean extracts rich and poor in kahweol both give rise to elevation of liver enzymes in healthy volunteers

Prior probability Prior odds (Yes/No) Posterior odds Posterior probability
0.90 (very strong) 0.9/(1-0.9) = 9 9x Bayes factor = 3.22 3.22/(1+3.22) = 0.76
0.75 (strong) 0.75/(1-0.75) = 3 3x Bayes factor = 1.07 1.07/(1+1.07) = 0.52
0.50 (equivocal) 0.50/(1-0.50)= 1 1x Bayes factor = 0.36 0.36/(1+1.07) = 0.26
0.25 (weak) 0.25/(1-0.25) = 0.33 0.33x Bayes factor = 0.12 0.12/(1+0.12) = 0.11
0.10 (very weak) 0.10/(1-0.10) = 0.11 0.11x Bayes factor = 0.04 0.04(1+0.04) = 0.04
  1. A priori probabilities were converted to a priori odds and multiplied by the minimum Bayes factor*. The obtained a postiori odds were converted to a postiori probabilities. *Bayes factor = e to the power -Z 2/2, where Z is the Z-score corresponding to the P-value for obtaining an effect of 0.27 mmol/l under the null hypothesis. P-value = 0.15, Z-score = 1.43 the minimum Bayes factor = 0.36