The Winter Blues By Geoff Colla Matthew Heineman Brandon Wright.

The Winter BluesThe Winter Blues

ByByGeoff CollaGeoff Colla

Matthew HeinemanMatthew HeinemanBrandon WrightBrandon Wright

Our PurposeOur 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 ThoughtWhat 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 WantsWhat Everyone Wants

Data CollectionData 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 2004.

• 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 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 DesignExperimental 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

– H0: p=.5

• Alternate Hypothesis: Dartmouth students will indicate that they are lest happy during the winter term.

– Ha: p>.5

SignificanceSignificance

• 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’tSignificance 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.

PowerPower

• 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 Results

Subject Question 1 Question 2 Subject Question 1 Question 2

1 Yes Winter 17 Yes Winter

2 Yes Summer 18 Yes Winter


4 Yes Fall 20 Yes Summer

5 Yes Winter 21 No Winter

6 Yes Winter 22 Yes Spring




10 Yes Spring 26 Yes Winter






16 Yes Winter

Yes=30 No=1 Winters=26 Spring=2 Summer=2 Fall=2

ResultsResultsLeast Preferred Terms

0

5

10

15

20

25

30

Winters Spring Summer Fall

Term

Nu

mb

er o

f R

esp

on

ses

BooyahBooyah

Distribution of Probability Under the Null and Power Hypotheses

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0.18

0.2

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31

n

Pro

bab

ility

Critical Value

Test Statistic

Final ResultsFinal 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 FactorsConfounding 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’tConfounding 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 ConclusionOur Final Conclusion

The Winter Blues By Geoff Colla Matthew Heineman Brandon Wright.

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