**
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:

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):

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.

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.

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Last updated: 7 August, 2015.