INVESTIGATING STATISTICAL CONCEPTS, APPLICATIONS, AND METHODS

BRIEF SOLUTIONS TO EXPLORATION 1.2

Exploration 1.2: Smoking and Lung Cancer (cont.) (p. 17)

(a) (114/8)/(90/14) = 2.217

(b) (114/90)/(8/14) = 2.217

(c) All three are the same

(d) (14/104)/(8/122) = 2.05

(e) (114/122)/(90/104) = 1.08

(f) (8/22)/(114/204) = 1.54

(g) No, the relative risk values are not all identical.

(i)

(j) baseline: .097, difference: .069, relative risk: 2.05, odds ratio: 2.22

(k) The proportions of “successes” in each bar are smaller.

baseline: .049, difference: .069, relative risk: 4.92, odds ratio: 5.29

(l) With the lower baseline risk, the difference in the proportions is larger proportionally.

When the baseline rate is smaller, a difference of .069 feels larger.  This is reflected in the relative risk and odds ratio calculations and the numerical results indicate a stronger association between cancer and smoking.

(m)

Since the relative risk and odds ratio are much closer to one, the association appears to be weak.  Even though the difference in the condition proportions is still around .069, now this difference appears small since the baseline rate is larger.

(n)

The baseline rate is now much closer to one but the difference in proportions is still about .069.  The odds ratio and the relative risk are no longer similar as they were in the other tables.

(o)

The distribution in each bar is the same.  The difference in proportions is zero and the odds ratio and relative risk values are both equal to one.  Here, the rate of lung cancer is the same regardless of whether we are working with nonsmokers or light smokers.