From experiments

Some contingency tables arise from experiments.

Marketing of educational videos

A company that produces and markets continuing education programs for the financial industry has traditionally emailed sample videos with previews of the programs to prospective customers. The company was concerned by the number of these emails that did not result in sales.

There had been some feedback indicating that the sample videos did not give enough information to prospective buyers, so the sales team decided to investigate whether giving temporary access to the full video would increase the number of purchases.

Eighty contacts were selected from the email list and 40 were randomly selected to be given access to the complete videos; the other 40 received the normal sample videos.

  Purchased Not purchased
Sample video 6 34
Full video 14 26

The contingency table above shows the results of the study. Does it indicate that sales are improved by giving access to the full videos?

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.)