Statistical Analysis of Anger in Student Athletes

A study was conducted on Rice University Students with the question in mind-do student athletes deal with anger in a different fashion than non-athletes? In addition, does a behavioral difference between men and women exist in this regard? A questionnaire was conducted on 78 students, both athletes and non-athletes, where the following metrics were self assessed:

Anger-Out (AO)high scores demonstrate that people deal with anger by expressing it in a verbally or physically aggressive fashion
high scores demonstrate that people experience anger but do not express it (suppress their anger)
Control-Out (CO)high scores demonstrate that people control the outward expression of angry feelings
Control-In (CI)high scores demonstrate that people control angry feelings by calming down or cooling off

From these metrics an anger index was assigned using the formula 

(Anger-Out) + (Anger-In) - (Control-Out) - (Control-In) + 48.

Essentially the higher a person's anger index, the greater the anger they experience whether they express it or not. The constant of 48 was chosen to ensure all index numbers are positive.

The summary of the data collected is as follows:

A box-plot of the Anger Index comparing Athletes and Non-athletes shows a surprising result:

The "non-athlete" category actually has a higher average Anger Expression Index than the "athlete" category. Is this because athletes have a useful outlet for exerting their natural aggression? Or is this due to another lurking factor? Next, let us see the same chart for gender instead of athlete vs non-athlete.
While not super informative, this graphic seems to prove that there is no clear influence between a student's gender and their anger index. The means are nearly equivalent and both ranges are similar. Next, we inspect a subset of this previous visual- if we separate athletes from non-athletes and then group by gender, what do we find?

The male athlete figure is clearly negatively skewed with a lower mean. Female athletes have a larger range and a higher mean. Are female athletes "angrier" than male athletes? Let us take a look at non-athletes for a comparison.

The reverse appears to be true for non-athletes. Again, the male category appears slightly negatively skewed but the mean anger index for male non-athletes is now higher than for female non-athletes. Can we use this data to make any type of claims about student athletes as a whole? Are these two factors severe enough to be statistically significant? Below we have the results for the t-test:

data:  non_athletes_index_males and non_athletes_index_females
t = 0.97378, df = 39.222, p-value = 0.1681
alternative hypothesis: true difference in means is greater than 0
95 percent confidence interval:
 -2.68451      Inf
sample estimates:
mean of x mean of y 
 42.00000  38.32258 

Our alternative hypothesis was that female non-athletes' anger index is lower than male non-athletes. With a t-score of .97 and a p-value of .16, these results are not significant. Sometimes statistical analysis ends with a eureka moment, but oftentimes that is not the case. While no grand claims are practical at this juncture, perhaps this study could be performed again with a larger sample size. 

However, if we jump back to our original comparison of athletes vs non-athletes, we get the following t-test readout: 

data:  angry_moods$Anger_Expression[angry_moods$Sports == 1] and angry_moods$Anger_Expression[angry_moods$Sports == 2]
t = -3.2103, df = 57.513, p-value = 0.001085
alternative hypothesis: true difference in means is less than 0
95 percent confidence interval:
      -Inf -4.260045
sample estimates:
mean of x mean of y 
 30.96000  39.84906 

This p-value indicates that these results are in fact significant, and that we can reject the claim that there is no difference between athletes and non-athletes' anger index value. The non-athlete index figure is larger to the extent that an argument can be made that non-athletes may experience more anger than athletes. Again, there may be lurking factors at hand. Perhaps athletes feel less anger because they have a safe outlet in sports. Alternatively, perhaps athletes need to have a "level-head" in terms of anger in order to reach the collegiate level. Either way, I hesitate to claim that all non-athletes worldwide are more angry than their athletic counterparts, but a statistically significant result is always exciting! 

This study was conducted at Rice University, with all research credit to Emily Zitek and Mindy Ater
The source materials for this post can be found in excel format and html format


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