Basic Statistics

162 CATEGORICAL DATA: ANALYSIS OF TWO-WAY FREQUENCY TABLES

11.5 REMARKS

The odds ratio and the chi-square test are frequently used in analyzing biomedical
data. In particular, the chi-square test is widely used in data analysis since many of the
variables measured in biomedical or public health studies are categorical or nominal
data. The test is also widely available not only in statistical programs but also in some
spreadsheet and other programs. The test is very easy to do but users of the test often
do not put enough emphasis on explaining the results so that a reader can understand
what actually happened. Simply giving a P value is usually insufficient.

PROBLEMS

11.1 In a study of weight loss, two educational methods were tested to see if they

resulted in the same weight loss among the subjects. One method was called

the standard method since it involved lectures on both eating and exercise. In

addition to lectures, the experimental method included daily reporting of dietary

intake by e-mail followed by return comments the same day. After a 1-month

period, subjects were rated as to whether they met their goals for weight loss.

11.2

Treatment

Goal Experimental Standard Total

Met 28 13 41

Not met 24 31 61

Total 52 50 102

Test whether the same proportion of the two treatment groups met their

goals for weight reduction.

Compute the relative risk of meeting their goals for the experimental and

the control groups.

Compute the odds ratio of meeting their goals for the two groups and give

95% confidence intervals.

In a casekontrol study, the investigators examined the medical records of the

last 100 consecutive patients who had been treated for colon cancer. A control

group of 100 patients from the same hospital who had been treated for abdominal

hernias was used for controls. Information on current smoking status was

obtained from the medical records. Of the 100 cases, 45 were current smokers

and 55 were not. Of the 100 controls, 26 were current smokers and 74 were

not.

(a) Compute the odds ratio of having colon cancer based on smoking status.

(b) Multiply the number of controls by 2, so there are 200 controls, 52 of whom

smoke and 148 who do not smoke. Compute the same odds ratio as in (a).