Multiple choice questions: Categorical data

This is a section from my text book An Introduction to Medical Statistics, Fourth Edition. I hope that the topic will be useful in its own right, as well as giving a flavour of the book. Section references are to the book.

13.11 Multiple choice questions: Categorical data

(Each branch is either true or false)

13.1 The standard chi-squared test for a 2 by 2 contingency table is valid only if:
(a) all the expected frequencies are greater than five;
(b) both variables are continuous;
(c) at least one variable is from a Normal distribution;
(d) all the observed frequencies are greater than five;
(e) the sample is very large.

13.2 In a chi-squared test for a 5 by 3 contingency table:
(a) variables must be quantitative;
(b) observed frequencies are compared to expected frequencies;
(c) there are 15 degrees of freedom;
(d) at least 12 cells must have expected values greater than 5;
(e) all the observed values must be greater than 1.

13.3 In Table 13.17:

Table 13.17 Cough first thing in the morning in a group of schoolchildren, as reported by the child and by the child’s parents (Bland et al. 1979)
Parents’ Report Child’s Report Total
Yes No
Yes 29 104 133
No 172 5097 5269
Total 201 5201 5402

**Table 13.17** Cough first thing in the morning in a group of schoolchildren, as reported by the child and by the child’s parents (Bland *et al.* 1979)
Parents’ Report	Child’s Report	Total
Yes	No
Yes	29	104	133
No	172	5097	5269
Total	201	5201	5402

(a) the association between reports by parents and children can be tested by a chi-squared test;
(b) the difference between symptom prevalence as reported by children and parents can be tested by McNemar’s test;
(c) if McNemar’s test is significant, the contingency chi-squared test is not valid;
(d) the contingency chi-squared test has one degree of freedom;
(e) it would be important to use the continuity correction in the contingency chi-squared test.

13.4 Fisher’s exact test for a contingency table:
(a) applies to 2 by 2 tables;
(b) usually gives a larger probability than the ordinary chi-squared test;
(c) usually gives about the same probability as the chi-squared test with Yates’ continuity correction;
(d) is suitable when expected frequencies are small;
(e) is difficult to calculate when the expected frequencies are large.

13.5 When an odds ratio is calculated from a two by two table:
(a) the odds ratio is a measure of the strength of the relationship between the row and column variables;
(b) if the order of the rows and the order of the columns is reversed, the odds ratio will be unchanged;
(c) the ratio may take any positive value;
(d) the odds ratio will be changed to its reciprocal if the order of the columns only is changed;
(e) the odds ratio is the ratio of the proportions of observations in the first row for the two columns.

13.6 Table 13.18 appeared in the report of a case control study of infection with Campylobacter jejuni (Section 3.12):

Table 13.18 Bird attacks on milk bottles reported by cases of Campylobacter jejuni infection and controls (Southern et al. 1990)
Number of days of week
when attacks took place Number of OR
cases controls
0 3 42 1
1-3 11 3 51
4-5 5 1 70
6-7 10 1 140

**Table 13.18** Bird attacks on milk bottles reported by cases of *Campylobacter jejuni* infection and controls (Southern *et al.* 1990)
Number of days of week when attacks took place	Number of	OR
cases	controls
0	3	42	1
1-3	11	3	51
4-5	5	1	70
6-7	10	1	140

(a) A chi-squared test for trend could be used to test the null hypothesis that risk of disease does not increase with the number of bird attacks;
(b) ‘OR’ means the odds ratio;
(c) A significant contingency chi-squared test for a 4 by 2 table would show that risk of disease increases with increasing numbers of bird attacks;
(d) ‘OR’ provides an estimate of the relative risk of Campylobacter jejuni infection;
(e) Kendall’s rank correlation coefficient, τ_b, could be used to test the null hypothesis that risk of disease does not increase with the number of bird attacks.

13.7 McNemar’s test could be used:
(a) to compare the numbers of cigarette smokers among cancer cases and age and sex matched healthy controls;
(b) to examine the change in respiratory symptom prevalence in a group of asthmatics from winter to summer;
(c) to look at the relationship between cigarette smoking and respiratory symptoms in a group of asthmatics;
(d) to examine the change in PEFR in a group of asthmatics from winter to summer;
(e) to compare the number of cigarette smokers among a group of cancer cases and a random sample of the general population.

References

Bland, J.M., Bewley, B.R., and Banks, M.H. (1979) Cigarette smoking and children’s respiratory symptoms: validity of questionnaire method. Revue d’Epidemiologie et Sante Publique 27 69-76.

Southern, J.P., Smith, R.M.M, and Palmer, S.R. (1990) Bird attack on milk bottles: possible mode of transmission of Campylobacter jejuni to man. Lancet 336 1425-7.

Go to Solutions to these questions.

Adapted from pages 207–208 of An Introduction to Medical Statistics by Martin Bland, 2015, reproduced by permission of Oxford University Press.

Back to An Introduction to Medical Statistics contents.

Back to Martin Bland’s Home Page.

This page maintained by Martin Bland.
Last updated: 7 August, 2015.