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Created: Sep 30, 2015
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Sleepy Study Results. M3A2 Group 3 Tom Kasulke
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I. INTRODUCTION

The purpose of this survey was to gain a better understanding of sleep habits in regards to the time of day  worked, if respondents are sleepy or not and the amount of days a week they work.  We surveyed volunteers through the workplace, e-mail or social media.  This survey was not random due to the fact that the surveyors all had personal or professional relationships with the respondents.  This convenient sample only contains data from the population that took the time to answer the questions.  A total of 122 responses were taken. The four questions we used to solicit our responses follow.  

1. How many hours a day do you sleep? _______ hrs

2. How many days a week do you work? _________ days

3. Are you sleepy during the hours that you are awake? Y   N

4. Pick only one option that best describes the time you work: Days    Evenings     Nights


II. Looking at a Categorical Variable

Our first set of data answers the question "Pick only one option that best describes the time you work?"  The results are shown in the pie chart below.

Result 1: Pie Chart of Time of Day Worked   [Info]
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Of our 122 respondents, 61 worked days, 29 worked evenings and 32 worked nights.  In other words, 50% of the people surveyed worked days, 23.77% worked evenings and 26.23% worked nights.  The majority of the answers came from people who worked during the day, which is the most common time to work in the US.


In order to see if the time of day worked had any effect on if someone was sleepy during the day we compared the two below.

 

Result 2: Bar Plot With Time of Day VS Sleepy   [Info]
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Let's break this data down into 3 categories, days, evenings and nights.  For our days category, we see that people are a little less tired when working days.  32 people answered no to being generally sleepy during the day, while 28 said they were.  For our Evenings people, 17 said they weren't sleepy, while 13 said they were.  Our nights are split 16 said yes to sleepy, and 16 said no to being sleepy.  These answers are pretty close to being the same.  These answers lead me to conclude that there is no difference in fatigue working nights, and slight less fatigue if you work days and evenings.  

III. Looking at Numerical Variable

The responses to the question "How many hours a day do you sleep" is represented in the histogram, box plot and summary statistics below.

Result 3: Histogram of hours of sleep in 24 hours   [Info]
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Result 4: Boxplot of hours slept with outliers   [Info]
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Result 5: Summary Stats of sleep in 24 hours   [Info]
Summary statistics:
ColumnnMeanVarianceStd. dev.MedianRangeMinMaxQ1Q3
Hours of sleep per 24 hours1226.59836072.01090641.41806436.5731068

 

The histogram shows a near uniform distribution, but not 100%.  I would also classify this as a very slightly right skewed set of results.  The mean is 6.5983607, which is very close to the median of 6. By definition, this is a right skewed result becuase the mean is greater than the median.  The mode of this data is 6 hours of sleep per night.  In other words, 35 total participants in this study slept 6 hours a night, the most of the 122 respondents.  The midrange of this data is 6.5 ((3+10)/2) and could be used as a reasonable center measure of data because the median is 6.  We see also, that the least amount of sleep was 3 hours a night, and the most amount was 10. In other words, our minimum and maximum answers.  Our IQR is found by calculating Q3-Q1, or 8-6, to give us an IQR of 2.  The IQR basically gives you the range of the middle; say between 25-75 percentiles numbers of your data set. Q2 is your median, in this case 6.5.   We can further use a technique called the range rule of thumb that is simply your range (maximum - minimum) divided by 4.  In this case it's (10-3)/4 or a SD of 1.75. If we look at the numbers that STATCRUNCH has calculated for us, we see that our SD is 1.4180643, which is not too far off of 1.75 to err on the side of caution and accuracy, we'll use the SD STATCRUNCH calculated for us.  Although the findings of the range rule of thumb are not totally obscure, but not as accurate as finding the square root of the variance that STATCRUNCH has provided for us.  This variation in the provided SD and the calculated range rule of thumb is on account of the slight right skewed data.  

The boxplot was plotted with no outliers noted.  Studies have said that humans need an average of 6-8 hours of sleep a night.  This depends on the study of the day so to speak.  In other words, scientific data does not agree on a solid number of hours of sleep needed.  Our so called outliers in this study are a minimum of 3 and a maximum of 10.  These really aren't outliers at all.  They aren't far enough away from the median to raise concen.   I do believe that 3 hours of sleep is a but low, but not impossible.  Many new babies provide thier parents less than that and parents can function, although slightly delayed, on little as 3 hours of sleep.  The maximum number of 10 is a bit higher than average, but again, not high enough to cause concern.  Some depressive patients, pubescent young adults and body builders sleep more than the national average.  I do not believe that these outliers are erroneous answers to the study, but simply the minimums and maximums of the study.

Looking for a Relationship Between Two Numerical Variables

Utilizing a scatter plot to see if there is a corelation between the answers to the quesitons "how many hours a day do you sleep?" and "how many days a week do you work?"   

Result 6: Scatter Plot hours of sleep vs days of work a week (n1 vs n2)   [Info]
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As the name entails, this data is scattered.  There is no general shape, theme or pattern that can be noted from it.  There aren't obtuse outliers that would throw off the correlation coefficient. There is a weak to no linear association.

Result 7: Correlation between hours worked hours slept   [Info]
Correlation between Hours of sleep per 24 hours and Number of work days per week is:
-0.05243186

As we can see from the above results, the correlation coefficient is -0.0524 because this number is closer to 0 than -1 I would say that there is a weak, or no, correlation between number of days worked and hours of sleep. This number is also less than .196 according to table A-5 again leading to the conclusion that there is no statistical signifigance.

HTML link:
<A href="https://www.statcrunch.com/5.0/viewreport.php?reportid=52565">Sleepy Study Results. M3A2 Group 3 Tom Kasulke</A>

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