Question

3. The following contingency table represents a study to determine if a new drug is effective in treating lower back pain. Participants were asked their pain levels two weeks after taking the two different treatments. No Pain Moderate Pain High Pain Drug 36 131 82 Placebo 12 194 157 a. How many of the patients had no pain or took the drug? (5) b. What percent of the patients had a high pain level? (5) c. What percent of the patients who took the drug, had no pain? (5) d. What percent of the patients both took the placebo and had moderate pain? (5)

Answer 1

a) Number of patients who had no pain or took the drug

= Number of patients who had no pain + Number of patients who took the drug - Number of patients who had no pain and took the drug

= (36 + 12) + (36 + 131 + 82) - 36

= 261

b) Total number of patients = 36 + 12 + 131 + 194 + 82 + 157 = 612

Number of patients who had a high pain level = 82 + 157 = 239

The percent of the patients had a high pain level

$= 100*\frac{239}{612}$

$\approx 100*0.3905$

c) Number of patients who had no pain and took the drug = 36

Number of patients who took the drug = 36 + 131 + 82 = 249

The percent of the patients who took the drug, had no pain

$= 100*\frac{36}{249}$

$\approx 14.46\%$

d) Number of patients who both took the placebo and had moderate pain = 194

The percent of the patients both took the placebo and had moderate pain

$= 100*\frac{194}{612}$

$\approx 31.7\%$