14.9 Exercises

Selected answers are available in Sect. D.14.

Exercise 14.1 A study of hangovers (Köchling et al. 2019) recorded, among other information, when people vomited after consuming alcohol. Table 14.11 shows how many people vomited after consuming beer followed by wine, and how many people vomited after consuming just wine.

  1. Compute the row proportions. What do these mean?
  2. Compute the column percentages. What do these mean?
  3. Compute the overall percentage of drinkers who vomited.
  4. Compute the odds a wine-only drinker vomited.
  5. Compute the odds that a beer-then-wine drinker vomited.
  6. Compute the odds ratio, comparing the odds of vomiting for wine-only drinkers to beer-then-wine drinkers.
  7. Compute the odds ratio, comparing the odds of vomiting for beer-then-wine drinkers to wine-only drinkers.
TABLE 14.11: How many people vomited and did not vomit, by type of alcohol consumed
Beer then wine Wine only
Vomited 6 6
Didn’t vomit 62 22

Exercise 14.2 In a study of wallabies at the East Point Reserve (Darwin) (Stirrat 2008), the sex of adult and young wallabies was recorded. In December 1993, 91 males and 188 female adult wallabies were recorded. At the same time, 13 male and 22 female young wallabies were recorded.

  1. For adult wallabies, what proportion of adult wallabies were males?
  2. For adult wallabies, what are the odds that a female was observed?
  3. For young wallabies, what are the odds that a female was observed?
  4. For young wallabies, what percentage of wallabies were males?
  5. What is the odds ratio of observing an adult wallaby to a young wallaby, for just the female wallabies?

Exercise 14.3 The Southern Oscillation Index (SOI) is a standardised measure of the pressure difference between Tahiti and Darwin, and has been shown to be related to rainfall in some parts of the world (Stone et al. 1996), and especially Queensland (Stone and Auliciems 1992; Dunn 2001).

As an example (Dunn and Smyth 2018), the rainfall at Emerald (Queensland) was recorded for Augusts between 1889 to 2002 inclusive, for months when the monthly average SOI was positive, and for months when the SOI was non-positive (that is, zero or negative), as shown in Table 25.9.

  1. Compute the percentage of Augusts with no rainfall.
  2. Compute the percentage of Augusts with no rainfall, in Augusts with a non-positive SOI.
  3. Compute the percentage of Augusts with no rainfall, in Augusts with a positive SOI.
  4. Compute the odds of no August rainfall.
  5. Compute the odds of no August rainfall, in Augusts with a non-positive SOI.
  6. Compute the odds of no August rainfall, in Augusts with a positive SOI.
  7. Compute the odds ratio of no August rainfall, comparing Augusts with non-positive SOI to Augusts with a positive SOI.
  8. Interpret this OR.
TABLE 14.12: The SOI, and whether rainfall was recorded in Augusts between 1889 and 2002 inclusive
Non-positive SOI Positive SOI
No rainfall recorded 14 7
Rainfall recorded 40 53

Exercise 14.4 A study (Haselgrove et al. 2008) asked boys and girls in Western Australia about back and pain from carrying school bags (Table 14.13).

  1. Compute the percentage of boys reporting back pain from carrying school bags.
  2. Compute the percentage of girls reporting back pain from carrying school bags.
  3. Compute the odds of boys reporting back pain from carrying school bags.
  4. Compute the odds of girls reporting back pain from carrying school bags.
  5. Compute the odds of a child reporting back pain.
  6. Compute the odds ratio of reporting back pain, comparing boys to girls.
  7. Interpret this OR.
TABLE 14.13: The number of boys and girls reporting back pain from carrying school bags
Males Females
No 330 226
Yes 280 359

References

Dunn PK. Bootstrap confidence intervals for predicted rainfall quantiles. International Journal of Climatology. 2001;21(1):89–94.
Dunn PK, Smyth GK. Generalized linear models with examples in R. Springer; 2018.
Haselgrove C, Straker L, Smith A, O’Sullivan P, Perry M, Sloan N. Perceived school bag load, duration of carriage, and method of transport to school are associated with spinal pain in adolescents: An observational study. Australian Journal of Physiotherapy. Elsevier; 2008;54(3):193–200.
Köchling J, Geis B, Wirth S, Hensel KO. Grape or grain but never the twain? A randomized controlled multiarm matched-triplet crossover trial of beer and wine. The American Journal of Clinical Nutrition. 2019;109(2):345–52.
Stirrat SC. Age structure, mortality and breeding in a population of agile wallabies (Macropus agilis). Australian Journal of Zoology. 2008;56:431–9.
Stone RC, Auliciems A. SOI phase relationships with rainfall in eastern Australia. International Journal of Climatology. 1992;12:625–36.
Stone RC, Hammer GL, Marcussen T. Prediction of global rainfall probabilities using phases of the southern oscillation index. Nature. 1996;384:252–5.
Peter K. Dunn, 2021: CC BY-NC-SA 4.0