#
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.

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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
*χ*^{2} = 124.5, with
it we get *χ*^{2} = 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 *τ*_{b}
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).

Back to multiple choice questions.

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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