## 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' . Some researchers suspect that repeatedly 'heading' the ball may impair brain function.

A study 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.

TABLE 4.2: Data on concussions experienced by college students
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
1. Classify the two variables.
2. Compute the percentage of college students in the sample overall that have received exactly one concussion.
3. 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?
4. Among the non-athletes, compute the odds of receiving two or more concussions. Interpret what this means.
5. Among the soccer players, compute the odds of receiving two or more concussions. Interpret what this means.
6. 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.
7. Create a table of column percentages. What do these tell you?
8. Create a table of row percentages. What do these tell you?
9. Which one of these tables is probably more sensible, and why?

### References

Kirkendall DT, Jordan SE, Garrett WE. Heading and head injuries in soccer. Sports Medicine. Springer; 2001;31(5):369–86.