Answers to multiple choice questions: Categorical data

These are the solutions to the multiple choice questions as given in An Introduction to Medical Statistics, Fourth Edition. Section references are to the book. 

Answers to 13.11 Multiple choice questions: Categrical data

13.1 TFFFF. Section 13.3. 80% of 4 is greater than 3, so all expected frequencies must exceed 5. The sample size can be as small as 20, if all row and column totals are 10.

13.2 FTFTF. Section 13.1, Section 13.3. (5 − 1) × (3 − 1) = 8 degrees of freedom, 80% × 15 = 12 cells must have expected frequencies greater than 5. It is O.K. for an observed frequency to be zero.

13.3 TTFTF. Section 13.1, Section 13.9. The two tests are independent. There are (2−1) × (2−1) = 1 d.f. With such large numbers Yates’ correction does not make much difference. Without it we get χ2 = 124.5, with it we get χ2 = 119.4 (Section 13.5.).

13.4 TTTTT. Section 13.4-5. The factorials of large numbers can be difficult to calculate and the number of possible tables with the same row and column totals can be astronomical.

13.5 TTTTF. Section 13.7. The more closely related the variables are, the bigger the odds ratio will be. Reversing the order of both rows and columns turns the ad/bc formula to da/cb, the same, but reversing only the columns gives us bc/ad. The ratio of the proportions, or relative risk, would be (a/(a+c))/(b/(b+d)).

13.6 TTFTT. Chi-squared for trend and Kendall’s τb will both test the null hypothesis of no trend in the table, but an ordinary chi-squared test will not (Section 13.8). The odds ratio (OR) is an estimate of the relative risk for a case-control study (Section 13.7).

13.7 TTFFF. The test compares proportions in matched samples (Section 13.9). For a relationship, we use the chi-squared test (Section 13.1). PEFR is a continuous variable, we use the paired t method (Section 10.2). For two independent samples, we use the contingency table chi-squared test (Section 13.1). 

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Adapted from page 381 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.

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