## 4.3 Two-way tables

Soccer is a unique in that one aspect is 'the purposeful use of the unprotected head for controlling and advancing the ball' (Gausche et al. 2000). Some researchers suspect that repeatedly 'heading' the ball may impair brain function.

A study (Gausche et al. 2000) was conducted to determine (p. 157)

...whether long-term or chronic neuropsychological dysfunction (i.e. concussion) was present in collegiate soccer players

Data were collected from \(240\) college students for two variables:

- The student type: One of 'soccer player' (\(63\) students), 'non-soccer athlete' (\(96\) students), or 'non-athlete' (\(81\) students).
- The number of head concussions: Each student was asked about the number of head concussions they had experienced; 'zero' (\(158\) students), 'one' (\(45\) students), or 'two or more' (\(37\) students) concussions.

Use the study data (Table 4.2) to answer the following questions.

0 | 1 | 2 or more | Total | |
---|---|---|---|---|

Soccer players | 45 | 5 | 13 | 63 |

Non-soccer athletes | 68 | 25 | 3 | 96 |

Non-athletes | 45 | 15 | 21 | 81 |

Total | 158 | 45 | 37 | 240 |

- Classify the two variables.
- Compute the percentage of college students in the
*sample*overall that have received exactly one concussion. - Many possible graphs exists to display the data; four are shown in Fig. 4.2. What is the main message from each graph? Which graph do you think is best? Why?
- Among the
**non-athletes**, compute the odds of receiving two or more concussions. Interpret what this means. - Among the
**soccer players**, compute the odds of receiving two or more concussions. Interpret what this means. - Compute the odds ratio comparing the odds of a non-athlete player receiving two or more concussions to the odds of a soccer player receiving two or more concussions.
- Create a table of
**column**percentages. What do these tell you? - Create a table of
**row**percentages. What do these tell you? - Which one of these tables is probably more sensible, and why?

### References

Gausche M, Lewis RJ, Stratton SJ, Haynes BE, Gunter CS, Goodrich SM, et al. Effect of out-of-hospital pediatric endotracheal intubation on survival and neurological outcome: A controlled clinical trial. Journal of the American Medical Association. 2000;283(6):783–90.