The Winter Blues By Geoff Colla Matthew Heineman Brandon Wright

Our Purpose While trying to brainstorm ideas about what to study for this project, we started to question why so many of our “friends” go tanning at Adventures in Paradise on the Miracle Mile in West Lebanon. It dawned on us that students resort to tanning to combat the depression of a bitter, cold, and wet winter. Being that the winter term is the most commonly taken off term, it seemed natural that it is the least favorite of Dartmouth students. Thus, we decided to test this theory.

What We Thought Given a population of experienced Dartmouth seniors we believe that a significant amount will report being least happy during the winter term. Furthermore, we felt that at least 80% of those polled would have an opinion on the issue.

What Everyone Wants

Data Collection Though we first wanted to compile a list of all students, we could only get our hands on a large list of the class of From this population, we randomly selected a sample of 100 students by assigning each subject a number and using a random number generator to select 100 numbers.

Data Collection Con’t We then blitzed each subject from our sample and asked them to respond to two questions. –Question 1: From your Dartmouth experience, do you prefer one of the terms over another? –Question 2: During which Term are you least happy at Dartmouth?

Experimental Design What we were looking for: Do Dartmouth students dislike the Winter term more than the others? Null Hypothesis: Dartmouth students do not dislike the winter term more than the others –H 0 : p=.5 Alternate Hypothesis: Dartmouth students will indicate that they are lest happy during the winter term. –H a : p>.5

Significance In order to ensure that our conclusions were statistically significant, we chose a significance level of.05. Thus there was only a 5% chance that we would determine that Dartmouth students dislike the winter term more than any other, even though they are actually evenly preferred. We felt that a 5% significance level is a reasonable amount given the relatively modest sample size to disprove our null hypothesis.

Significance Con’t To achieve such a level of significance we need to get a test statistic 1.65 standard deviations away from p=.5. –Given our sample size of n=31, we needed to get a test statistic of at least 65% or 20 subjects who least preferred the winter.

Power We decided on using 80% because we believed that there would be a large, to quite large majority of people who are bitter towards winter.

Results SubjectQuestion 1Question 2SubjectQuestion 1Question 2 1YesWinter17YesWinter 2YesSummer18YesWinter 3YesWinter19YesWinter 4YesFall20YesSummer 5YesWinter21NoWinter 6YesWinter22YesSpring 7YesWinter23YesWinter 8YesWinter24YesWinter 9YesWinter25YesWinter 10YesSpring26YesWinter 11YesWinter27YesWinter 12YesWinter28YesWinter 13YesWinter29YesWinter 14YesWinter30YesWinter 15YesWinter31YesWinter 16YesWinter Yes=30No=1Winters=26Spring=2Summer=2Fall=2

Results

Booyah

Critical Value Test Statistic

Final Results We can reject the null with more than 99.9% certainty. –That is, there is only a 1 in ½ Million chance that the null hypothesis was true.

Confounding Factors Population –It was not a full representation of the senior class Response bias –Only 31 of the 100 surveyed responded –Ideally, we would have had a much larger sample size

Confounding Factors Con’t Ambiguous Questions –Answers had to be interpreted because we did not offer specific answers First Question (Preference?) –We were looking for a Yes/No response rather than a specific term, which was the most common response. –In retrospect, we should have given the precise answers we were looking for (Yes/No) Second Question (Least happy when?) –Many of the subjects responded with “Freshman Winter” or “Sophomore Summer” –We felt that by narrowing their answer down to a specific term they might not have looked at their entire Dartmouth experience and generalized with one of the seasons –Instead, we should have specified that we were looking for a season rather than a particular term that they experienced

Our Final Conclusion