From experiments

Some contingency tables arise from experiments.

Vitamin C and colds

To test whether vitamin C reduces the risk of catching a cold, a 1961 French study involved 279 skiers over two periods of 5-7 days. Skiers in one group of 139 were given 1 gram ascorbic acid (vitamin C) per day whereas those in the other group were given a tablet that looked similar but had no active ingredient (called a placebo). None of the skiers knew which of the treatments they had received.

     Cold      No cold  
Ascorbic acid 17 122
Placebo 31 109

The contingency table above shows the results of the study.

From surveys

Surveys are conducted to ascertain voting intentions, purchases of consumer goods, satisfaction with courses, and for a variety of other research purposes. We will later discuss general principles of data collection from surveys.

Individuals from some target group are usually given a questionnaire to complete. The individual questions are often answered by ticking boxes (e.g. 'Approve', 'Neutral' or 'Disapprove') and are therefore categorical. Some of the resulting categorical variables can often be considered to split the respondents into groups.

Survey data are often reported using many contingency tables.

Drug screening of job applicants

Urine drug screening was performed on 2537 applicants for career craft positions in the US Postal Service's Boston Management Sectional Center. The frequency table below shows the distribution of test results. (Those testing positive for more than one drug were classified under the more serious of the drugs, so each individual only contributed to a single cell in the table.)

  Negative Marijuana Cocaine Other drugs
Frequency 2229 198 55 55

This distribution is interesting, but other information was also obtained from questionnaires completed by each applicant. Some of this information could be used to split the applicants into groups. The following contingency tables describe results for various groupings of the applicants.

Gender

  Negative Marijuana Cocaine Other drugs Total
Male 1465 146 33 28 1672
Female 764 52 22 27 865

Smoking

  Negative Marijuana Cocaine Other drugs Total
Smoker 684 94 22 25 825
Non-smoker 1542 103 33 30 1708

Exercise

  Negative Marijuana Cocaine Other drugs Total
Aerobic 301 28 5 6 340
Non-aerobic 736 58 18 14 826
None 1182 112 32 35 1361

(Note that a few of the 2,537 applicants did not specify whether they smoked or did exercise in the questionnaire. The totals for the smoking and exercise contingency tables are therefore slightly lower than this.)