"Conditional probabilities refer to the likelihood of an event occurring given that another event has occurred or will occur. For example, if we know that a die roll has resulted in an odd number i.e. the only possible outcomes are 1, 3, or 5, we know that P(4)=0 and that P(1)=1/3. Conditional probabilities have their own special notation: P(event2|event1)=x. In English, this means, given that Event1 has occurred, the probability of event2 occurring is equal to x, where x is again a number ≥0 and ≤1. Our odd number die rolling example would be written as P(1|odd roll)=1/3."
"Conditional probabilities refer to the likelihood of an event occurring given that another event has occurred or will occur. For example, if we know that a die roll has resulted in an odd number i.e. the only possible outcomes are 1, 3, or 5, we know that P(4)=0 and that P(1)=1/3. Conditional probabilities have their own special notation: P(event2|event1)=x. In English, this means, given that Event1 has occurred, the probability of event2 occurring is equal to x, where x is again a number ≥0 and ≤1. Our odd number die rolling example would be written as P(1|odd roll)=1/3."
"alpha error: P(clinical trial+|effect does not exist) = x, i.e. given that there is no difference between groups (e.g. screened vs unscreened test subjects), the probability of a clinical trial being positive equals x"
"beta error: P(clinical trial-|effect exists) = x, i.e. given that there is a difference between groups (e.g. screened vs unscreened test subjects), the probability of a clinical trial being negative equals x"
"specificity: P(T-|D-) = x, i.e. given that a patient does not have the disease, the probability of testing negative equals x"
"P(A|B) = (P(A) x P(B|A))/P(B)"
Expected headings
"Examples"
"Conditional probabilities refer to the likelihood of an event occurring given that another event has occurred or will occur. For example, if we know that a die roll has resulted in an odd number i.e. the only possible outcomes are 1, 3, or 5, we know that P(4)=0 and that P(1)=1/3. Conditional probabilities have their own special notation: P(event2|event1)=x. In English, this means, given that Event1 has occurred, the probability of event2 occurring is equal to x, where x is again a number ≥0 and ≤1. Our odd number die rolling example would be written as P(1|odd roll)=1/3."
"Conditional probabilities play an important role in science and medicine. For example, sensitivity, specificity, positive predictive value (PPV), negative predictive value (NPV), statistical power, alpha error (Type I) and beta (Type II) error can all be written as conditional probabilities."
"P(A|B) = (P(A) x P(B|A))/P(B)"
"P(D+|T+)=[P(D+) x P(T+|D+)]/[P(D+) x P(T+|D+) + P(D-) x (T+|D-)]"
"P(D-|T-)=[P(D-) x P(T-|D-)]/[P(D-) x P(T-|D-) + P(D+) x P(T-|D+)]"
"where P(D+) is the disease prevalence, P(D-) is 1-prevalence, P(T+|D+) is sensitivity, P(T+|D-) is 1-specificity, P(T-|D-) is specificity and P(T-|D+) is 1-sensitivity."
"Conditional probabilities play an important role in science and medicine. For example, sensitivity, specificity, positive predictive value (PPV), negative predictive value (NPV), statistical power, alpha error (Type I) and beta (Type II) error can all be written as conditional probabilities."
"Bayes' theorem is another conditional probability and in medicine can be used to calculate the probability that a patient has a particular disease once new information, such as from diagnostic testing becomes available. There are many versions of Bayes' theorem. Its’ simplest form is:"