Consider the following contingency (frequency) table, in which a drug was being

Question

Consider the following contingency (frequency) table, in which a drug was being tested for allergy symptom relief:

                             Drug Group   Placebo Group
Symptom Relief           35                    28
No Relief                      15                    22

(a) Estimate the probability that a subject was in the drug group, or had symptom relief, or both (the union).

(b) Estimate the probability that a subject who was in the drug group had symptom relief.

(c) Estimate the probability that a subject who was in the placebo group had symptom relief.

(d) Estimate the probability that a subject had symptom relief overall, regardless of group.

(e) How much higher was the estimated probability of symptom relief in the drug group vs. the placebo group?

Explanation / Answer

P(D) = 35 + 15 = 50, P(P) = 28 + 22 = 50, P(R) = 35 + 28 = 63

(a) P(D or R) = P(D) + P(R) - P(D and R) = 50/100 + 63/100 - 35/100 = 78/100 = 0.78

(b) P(R | D) = P(R and D)/P(D) = (35/100)/(50/100 = 7/10 = 0.70

(c) P(R | P) = P(R and P)/P(P) = (28/100)/(50/100) = 56/100 = 0.56

(d) P(R) = 63/100 = 0.63

(e) It is 0.70 - 0.56 = 0.14

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