• = How do I calculate and interpret conditional probabilities? =

Gigerenzer (2002) suggests a way to obtain conditional probabilities using frequencies in a decision tree.

Cortina and Dunlap(1997) give an example evaluating the detection rate of a test (positive/negative result) to detect schizophrenia (disorder).

This is a more intuitive way of illustrating the Bayesian equation:

P(No disorder|+ result) = $$\frac{\mbox{P(No disorder) * P(+ result | No disorder)}}{\mbox{P(No disorder) * P(+ result | No disorder) + P(Disorder) * P(- result | Disorder)}}$$

References

Cortina JM, Dunlap WP (1997) On the logic and purpose of significance testing Psychological methods 2(2) 161-172.

Gigerenzer G. (2002) Reckoning with risk: learning to live with uncertainty. London: Penguin.