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.

Contraception and sexual health

The Office for National Statistics in Britain conducts a variety of surveys each year relating to health. The contingency tables below present some results from a survey on contraception and sexual health that was carried out in 2000. There were slightly over 4,200 respondents to the survey.

Why contraceptives were not used
This table gives the main reason for not using contraception by the 410 women aged 16-49 who were in a sexual relationship, not using contraception and not sterilised.
  Age
  16-29 30-39 40-49
Partner sterilised 6 81 127
Wants to become pregnant 12 28 11
Pregnant now 15 20 2
Menopause 0 2 11
Possibly infertile 6 18 19
Doesn't like contraception 3 7 6
Other reason 15 8 13
Number of sexual partners in previous year
For men:
  Men, aged
Sexual partners 16-19 20-24 25-29 30-34 35-39 40-44
None 52 21 13 15 16 18
One 63 113 147 205 223 211
Two or three 37 49 28 25 24 18
Four or more 4 6 2 1 1 0
For women:
  Women, aged
Sexual partners 16-19 20-24 25-29 30-34 35-39 40-44
None 68 10 17 17 26 33
One 91 145 195 244 290 280
Two or three 41 37 30 14 10 10
Four or more 8 12 5 3 3 0
Use of emergency contraception
This table gives information about where hormonal emergency contraception (the 'morning after pill') was obtained by women aged 16-49 who had used it in the previous year.
  Marital status
     Single    Married or
cohabiting
Widowed,
divorced or separated
Family planning clinic (at least once) 32 10 3
Other 45 34 10