Bullying Statistics

At the Byron Middle School, surveys are taken twice every year - once in the Fall and again in the Spring. Data has continued to accumulate over 8 years but the question begs: What do we do with it? Katie Gilbertson and I decided to volunteer to tackle the data the counselors have given us. With this information, we hoped to find the obvious as well as the not-so-obvious trends in bullying.

We were initially given the results of the survey. These results clumped all the answers in a percentage. Because of this layout, we were unable to dig into the information and accurately conclude any trends. I was however, able to compare those bullied vs. the season. Using the information we had, I made a table comparing the percentage bullied in the Spring and the percentage bullied in the Fall. After plugging these numbers into StatKey, I found a significant difference in these seasons.
 

Year	Percent Bullied
Spring 2005	36.5%
Fall 2005	24.41%
Spring 2006	36.31%
Fall 2006	27.76%
Spring 2007	31%
Fall 2007	29.58%
Spring 2008	32.26%
Fall 2008	22.31%
Spring 2009	30.78%
Fall 2009	19%
Spring 2010	25.4%
Fall 2010	n/a
Spring 2011	41.19%
Fall 2011	23.94%
Spring 2012	34.3%
Fall 2012	22.31%
Spring 2013	35.66%
Fall 2013	22.9%

This confidence interval shows that we are 95% percent confident that students are bullied on average from 6% to 13% more in the Spring versus the Fall. This means, on average, the percentage bullied increase about 9% with a margin of error of about 3%. This is a significantly large jump in bullying. We decided to conclude that this trend may be due to "Spring Fever" and students may be more comfortable around this point in the year. We also noticed that most of bullying occurs outdoors. Since it is warmer during Spring, this would make sense that more bullying, particularly outside, would happen. 

After meeting with the counselor again, we were able to obtain the raw data. This was very useful since we could compare almost any of the results. Due to limited time, we only compared a few things. I wanted to see if there was any correlation between gender and whether or not they were bullied. I took the proportion of females who were bullied over the total females and the males who were bullied over total males for each season. Using the data, I created two graphs to visualize the results.

 
In the top graph you can see the spikes in each year. This is not caused by gender but by the seasons which I explained earlier. If you look at the top graph you can see that the lines are, for the most part, close together. There are no significant drops or spikes in gender. In some years, their proportions were almost equal. In the bottom graph, you can see the comparison as bars. For the first few years, a higher percentage of females were bullied. From 2007-08, the proportion of males is higher. I didn't see any real patterns with this data, so we decided to conclude that those bullied isn't affected by gender. For further support of this conclusion, hypothesis tests and confidence intervals could be done, but we were unable to find time to do it.