## 9.7 **Optional**: Two-way tables

*(Answers available in Sect. A.9)*

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).

Which

**one**of these five sets of hypotheses is*not*valid for this situation? Why?- \(H_0\): 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*. - \(H_0\): 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*. - \(H_0\): 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*. - \(H_0\): 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*. - \(H_0\): 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*.

- \(H_0\): No association between having hepatitis C and having a tattoo
Compute the percentage of people overall in the sample with a tattoo.

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.In the sample, 25 people had Hep. C

*and*a tattoo. Use this information to create the two-way table summarising the data (Table 9.3).

Had Hep. C | Did not have Hep. C | Total | |
---|---|---|---|

Had tattoo | |||

Did not have tattoo | |||

Total | 626 |

- In the sample, what are the odds that someone has Hep. C, among those with a tattoo?
- In the sample,
what are the odds that someone has Hep. C,
among those
*without*a tattoo? - 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, Robert W., and R. Paul Fischer. 2001. “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* 80: 134–51.