Most sports injuries are immediate and obvious, like a broken leg. However, some

Question

Most sports injuries are immediate and obvious, like a broken leg. However, some can be more subtle, like the neurological damage that may occur when soccer players repeatedly head a soccer ball. To examine effects of repeated heading, McAllister et al. (2013) examined a group of football and ice hockey players and a group of athletes in noncontact sports before and shortly after the season. The dependent variable was performance on a conceptual thinking task. Following are hypothetical data from an independent-measures study similar to the one by McAllister et al. The researchers measured conceptual thinking for contact and noncontact athletes at the beginning of their first season and for separate groups of athletes at the end of their second season.

Using the data below please answer the following questions:

1. a brief statement describing the variables presented in the problem (i.e., explain the research by specifically mentioning both variables and their levels)

2. the probability of a Type I error

3. the conclusion for the interaction term of the ANOVA in words supported by the results of the test in parentheses

4. an explanation of the interaction term results in words that refers to each cell of the ANOVA table

5. the sample size, mean and standard deviation for each cell of the ANOVA table

6. the conclusion for the main effect of the treatment variable in words supported by the results of the test in parentheses

7. an explanation of the main effect of the treatment variable results in words that refers to each marginal mean and standard deviation for variable A in the ANOVA table

8. the conclusion for the main effect of the gender variable in words supported by the results of the test in parentheses

Factor B: Time Before the First Season n=20 M=9 T= 180 SS= 380 n=20 M=9 T= 180 SS 350 After the Second Season n=20 Contact Sport Factor A: Sport T=80 SS= 390 n=20 Non- contact Sport T= 160 SS = 400 LY = 6360

Explanation / Answer

1. a brief statement describing the variables presented in the problem (i.e., explain the research by specifically mentioning both variables and their levels)

Variables are "Sport" and "Time"
The levels of the variable "Sport" are "Contact Sport" and Non-Contact Sport"
The levels of the variable "Time" are "Before the First Season" and "After the Second Season"
The research is to measure and compare the conceptual thinking for contact and noncontact athletes at the beginning of their first season and for separate groups of athletes at the end of their second season.

2. the probability of a Type I error
The significance level at F = 3.98 (critical value) and df=1, 70 is 0.05
So the probability of a Type I error = significance level of the research problem = 0.05

3. the conclusion for the interaction term of the ANOVA in words supported by the results of the test in parentheses

There is significant interaction between the levels of Sport and Time as the observed value of F (4.00) is greater than the critical value of F (3.98)

4. an explanation of the interaction term results in words that refers to each cell of the ANOVA table

For Contact Sport, the mean decreases from 9 (Before the First Season) to 4 (After the second season)
For Non-Contact Sport, the mean decreases from 9 (Before the First Season) to 8 (After the second season)
Hence, the lines are not parallel, that is the mean does not decrease with the same slope for contact and non-contact sport from before the first season to after the second season.
Hence, there is significant interaction of Contact Sport with levels of Time.
As, the decrease in the mean (from 9 to 8) in non-contact sport is low, we can say that there is less interaction between non-contact sport and time.

For "Before the first season", the mean remains same (9) for contact and non-contact sport.
Hence there is no interaction between "Before the first season" level and Sport.
For "After the second season", the mean increases from 4 (contact sport) to 8 (non-contact sport).
So, there is significant interaction between "After the second season" level and Sport.

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