5.2 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

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

— Gausche et al. (2000), p. 157.

Data were collected from 240 college students:

  • The student type: One of ‘soccer players’ (63 students), ‘non-soccer athletes’ (96 students),
    or ‘non-athletes’ (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 5.2) to answer the following questions.

TABLE 5.2: 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. Compute the percentage of college students in the sample overall that have received one concussion.
  2. Many possible graphs exists to display the data; four are shown in Fig. 5.1. What is the main message from each graph? Which graph do you think is best? Why?
Four different graphs displaying the soccer-data. 'S' mean a soccer player; 'NS' means a non-soccer athlete; 'NA' means a non-athlete

FIGURE 5.1: Four different graphs displaying the soccer-data. ‘S’ mean a soccer player; ‘NS’ means a non-soccer athlete; ‘NA’ means a non-athlete

  1. Among the non-athletes, compute the odds of receiving two or more concussions. Interpret what this means.
  2. Among the soccer players, compute the odds of receiving two or more concussions. (Refer to Table 5.2.) Interpret what this means.
  3. 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.
  4. Create a table of column percentages. What do these tell you?
  5. Create a table of row percentages. What do these tell you?
  6. Which one of these tables is probably more sensible, and why?


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References

Gausche, Marianne, Roger J. Lewis, Samuel J. Stratton, Bruce E. Haynes, Carol S. Gunter, Suzanne M. Goodrich, Pamela D. Poore, et al. 2000. “Effect of Out-of-Hospital Pediatric Endotracheal Intubation on Survival and Neurological Outcome: A Controlled Clinical Trial.” Journal of the American Medical Association 283 (6): 783–90.