# homework 4

Sport concussions are a leading epidemic causing impairments in cognitive, motor, and emotional function. Because of this you have been funded by the National Institutes of Health to conduct a public health study on the number of concussions between different sports. The results from this study would help policymakers target specific sports in need of improved safety. To scientifically address this study aim, you collected data on the number of concussions from four different sports over three years (collecting data from two different states). The specific sports include Soccer, Lacrosse, Basketball, and Softball/Baseball. Your goal is to compare the average number of concussions between different sports to determine if there are any differences among the sports. Your data is saved in a SPSS dataset called concussion.sav.
In the dataset your independent variable (sport group) is labeled Group and has four levels (1 = Soccer, 2 = Lacrosse, 3 = Basketball, 4 = Softball/Baseball). Your dependent variable (outcome) is labeled Concussions.
1. What type of analysis should you use to test for differences in number of concussions among the four sports? Please justify your answer in full sentences. (1 point)
2. State your null and alternative hypotheses (1 point):
H0:
H1:
3. Use the Explore command to look at the mean and standard deviations for the number of concussions for the four sports. In full sentences please:
(Hint: Pay close attention to the notes to determine how to output mean and SD for each of the four groups separately)
a.  Provide the mean and standard deviation for the number of concussions for each sport (1 point)
Use this information to make educated decisions about the following questions:
b. Do the four sports appear to have equal variances? (1 point)
c. Looking at the means, which sports do you think differ on average number of concussions and how (i.e., which pairs of sports are likely significantly different in number concussions)? (1 point)
4. Using the output from the Explore command please paste the Box Plot showing the distribution of concussions within each sport (hint: remember that box plots tell us about the dispersion of data as well as the mean of data and you should have one box plot for each group). How does this plot justify your educated decisions from Question 3? Please describe in full sentences below the pasted plot. (1 point)
5. Perform normality tests to test the assumption that concussions are normally distributed within each of the four sports. Paste the output below and decide for all four sports if this assumption is violated (i.e., decide if the variable, concussions, is normally or non-normally distributed in each sport) using observed p-values from the Shapiro-Wilk test in full sentences. (2 points)
6. In SPSS, perform the appropriate analysis on the difference among the four sports on the average number of concussions. Using this command, also provide a Levene’s test of homogeneity of variances to test if the four sports have equal variances on the number of concussions. Paste your output for the appropriate analysis as well as Levene’s test below (1 point).
7. Based on Levene’s test, was the assumption of equal variances violated? How does this compare to your educated decision from Question 3? (1 point)
Note: Remember that this is not the test for differences in
8. Report the results of the analysis for differences in number of concussions in full sentences using the correct APA formatting rules [F (between groups df, within groups df) = observed F-value, p = observed p-value]. Do you reject or fail to reject the null hypothesis? Based on this, what is your conclusion about differences in the number of concussions reported among sports? (4 points)
9. Perform a Bonferroni post-hoc test to test the difference among average number of concussions between the four sports. Paste your output below. (1 point)
10. Based on the result of Bonferroni post-hoc tests, which specific sports are significantly different from each other (in terms of the number of concussions that occur in each)? State in full sentences. (1 point)
Note: My students have had trouble answering this last question in the past. The post-hoc test is simple once you understand how to read it. If you’re having trouble, please look at my Practice Problems on Canvas.
11. You now need to write up your entire statistical process for a prestigious psychology journal. Write up 2-4 paragraphs explaining the following (1 point for each topic covered; a total of 9 points):

The experiment (restating the purpose      and description of the experiment in your own words)
Your means and standard deviations of      each sport
The statistical test you chose to      compare the mean number of concussions and why
How you checked the assumption of      normality of concussions in each sport and your decision based on the      output (was the assumption met?)
How you checked the assumption of equal      variances of concussions within in each sport and your decision based on      the output (was the assumption met?)
The results of the post-hoc tests      (which post-hoc test was used, which sports were significantly different      from each other)
Describe your post-hoc results in      everyday language. Which sports had higher/lower number of concussions      over the last three years compared to each other.
Based on your findings which sports      should the National Institutes of Health focus on for improved safety?

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Reminder: Write 2-4 Paragraphs and remember to address each bullet point. Do not just write an answer under each bullet point. This is your chance to demonstrate adequate ability to write a scientific interpretation of statistical procedures and output.
Tip: look in the folder for Lab 5 on Canvas for a file titled “One-Way ANOVA paper” for a research article that may help you as your write your response.
Write full interpretation below:

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