10.6 Optional: Two-way tables

This question is optional; for example, if you need more practice, or you are studying for the exam.

(Answers available in Sect. A.10)

Applying tattoos carries health risks as the skin is broken during application. An American study examined if a relationship existed between having hepatitis C and having tattoos (Haley and Fischer 2001).

To study this, 626 people were interviewed as part of an observational study, and asked about two issues: Whether they had hepatitis C (47 people) or not (579 people); and if they had a tattoo (113 people), or no tattoos (513 people).

  1. Which one of these five sets of hypotheses is not valid for this situation? Why?

    1. \(H_0\): No association between having hepatitis C and having a tattoo in the population;
      \(H_1\): An association between having hepatitis C and having a tattoo in the population.
    2. \(H_0\): The odds of having hepatitis C is the same with or without a tattoo in the population;
      \(H_1\): The odds of having hepatitis C is not the same with or without a tattoo in the population.
    3. \(H_0\): The mean number of people having hepatitis C is the same for those with and without a tattoo in the population;
      \(H_1\): The mean number of people having hepatitis C is not the same for those with and without a tattoo in the population.
    4. \(H_0\): The odds ratio of having hepatitis C, comparing those with or without a tattoo, is one in the population;
      \(H_1\): The odds ratio of having hepatitis C, comparing those with or without a tattoo, is not one in the population.
    5. \(H_0\): The proportion having hepatitis C is the same with or without a tattoo in the population;
      \(H_1\): The proportion having hepatitis C is not the same with or without a tattoo in the population.
  2. Compute the percentage of people overall in the sample with a tattoo.

  3. Assuming the null hypothesis about the population is true, compute the number of people in the sample with hepatitis C that you would expect have a tattoo. Use the information above to answer the question.

  4. In the sample, 25 people had Hep. C and a tattoo. Use this information to create the two-way table summarising the data (Table 10.3).

TABLE 10.3: Five-year mortality for artifical limb users
Had Hep. C Did not have Hep. C Total
Had tattoo
Did not have tattoo
Total 626
  1. In the sample, what are the odds that someone has Hep. C, among those with a tattoo?
  2. In the sample, what are the odds that someone has Hep. C, among those without a tattoo?
  3. From the sample information, compute the odds ratio of having Hep. C, comparing students with a tattoo to those without a tattoo. Carefully explain what this value means.

References

Haley RW, Fischer RP. Commercial tattooing as a potentially important source of Hepatitis C infection: Clinical epidemiology of 626 consecutive patients unaware of their Hepatitis C serologic status. Medicine. 2001;80:134–51.