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Created: Jun 15, 2019
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Analysis of sleep; descriptive report. M3A2.
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Introduction

This survey focused on individuals who worked the night shift, age and gender were not factored into this survey. Also surveyed, was if the night shift was the individual's preferred shift to work, how much sleep an individual had prior to working and not working, and how they felt while working the night shift. The questions asked in the survey can be seen below:

1.    Do you prefer to work the night shift? Y or No

2.    How many hours do you sleep prior to your shift?____Hours

3.    How many hours do you sleep when you are not working?____Hours

4.    Describe how you feel while you are at work (Select One): Extremely tired, Moderately tired, Somewhat tired, Full of energy.

Samples were obtained numerous ways, such as personal interviews, survey questionnaires sent out via social media, such as on Facebook, and e-mails. Data from the survey was then stored using Stat Crunch.

Looking at a Categorical Variable

This report focused on individuals working the night shift and how they felt while at work. The choices were as follows; Extremely tired, Moderately tired, Somewhat tired or Full of energy.

Result 1: Pie Chart of alertness at work   [Info]
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As you can see from the Pie Chart, 14% of individuals surveyed are extremely tired at work, 30% of individuals are moderately tired at work, 34% of individuals are somewhat tired at work and 22% of individuals are full of energy while at work. 

In order to see if the response from C2 coordinates or differs from C1, we will examine below in a Bar Plot. Question C1: "Do you prefer to work the night shift?" and C2: "Describe how you feel at work?"

Result 2: Bar Plot of alertness at work and preferred shift   [Info]
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 Looking at night shift preference and how individuals feel at work, we can conclude that those individuals who prefer to work the night shift, which is 55%, either feel full of energy or only somewhat tired.

Looking at a Numerical Variable

Looked at were the response to questions N1: "How many hours do you sleep prior to your shift?" and N2: "How many hours do you sleep when you are not working?" 

Result 3: Histogram of hours slept prior to working   [Info]
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Plotted out in graphs are data from the survey of 86 participants. Below are shown in the histogram, how many hours do you sleep prior to working. Also shown is a boxplot and summary statistics.

Result 4: Box Plot of how many hours slept prior to working the night shift   [Info]
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Result 5: Summary Stats of hours slept prior to working vs hours slept when not working   [Info]

Summary statistics:


ColumnnMeanVarianceStd. dev.Std. err.MedianRangeMinMaxQ1Q3SumIQRUnadj. varianceUnadj. std. dev.Coef. of var.SkewnessKurtosisMode
Hrs slept prior to working865.44186054.01422712.00355360.2160487469094.574682.53.967551.99187136.817438-1.0235681.21232556
Hrs slept when not working867.91860471.78741451.33694220.144166198841278.56811.51.76663061.329146616.8835580.49973051.52897118

 

The histogram shows a slight skew to the left, which is negatively skewed. Although the majority of data is to the right of the median and the mean. The center of skewed data shows that the majority of individuals surveyed slept an average of 5.5 hours prior to working the night shift. These values do not seem to be affected by extreme data that can be seen in the boxplot. The midrange, minimum data value=0, and maximum data value=10, divided by two is 5 hours. The midrange is very sensitive to extreme values and for this reason is not commonly used. 

The mean of the data, how many hours slept prior to working is 5.441. The mean uses every data value by adding the sum of all data and dividing by the number of data values. The mean is what most individuals consider the "average". 

The median of the data, how many hours slept prior to working is 6. The survey results for sleep ranged from zero hours to 12 hours. The median is considered the "middle value" of data, with half the data greater than the center and half the data less than the center. 

There is a moderate amount of variation in the response to this question, with the minimum amount of sleep prior to working being zero and the maximum hours slept prior to working being 9, this would be the range. The standard deviation is 2 hours of sleep. The IQR, which is the interquartile range (Q3-Q1) is 2.5 hours of sleep. The IQR gives the range of the middle half of the data. The Range Rule of Thumb slightly over estimates the standard deviation by 0.25 hours.

The boxplot reveals that there are a few outliers of zero hours slept prior to working a shift. We can assume that these outliers of zero are not accurate information, and that the few individuals that chose zero hours, did not understand the question or actually went days without sleeping. To find the outlier it needs to be an amount greater than 1.5 x the IQR, either above Q3 or below Q1. The average amount of time slept prior to working a shift was 4.5 to 7 hours. The outlier in this case was 3.75 hours below the Q1. 

 Looking at Relationships Between Two Numerical Variables

Here we will look at the relationship between the responses to the questions, "How many hours do you sleep prior to your shift?" and "How many hours do you sleep when you are not working?" We will look at the scatter plot of the paired data. 

Result 6: Scatter Plot of hours of sleep prior to working vs hours of sleep when not working   [Info]
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The scatter plot reveals that there is a negative linear regression. The hours that an individual sleeps prior to working a night shift is less than the hours slept when not working. As noted previously, outliers can affect the results, including the correlation coefficient. The outliers that stand out are: 0 hours slept prior to working, 12 hours slept when not working. 0 hours slept prior to working, 10 hours slept when not working. 0 hours slept prior to working, 9 hours slept when not working. 0 hours slept prior to working, 8 hours slept when not working. 

The correlation coefficient for the paired data is -0.2795, this is a weak negative correlation. 

Result 7: Simple Linear Regression   [Info]

Simple linear regression results:


Dependent Variable: Hrs slept when not working
Independent Variable: Hrs slept prior to working
Hrs slept when not working = 8.9338536 - 0.18656284 Hrs slept prior to working
Sample size: 86
R (correlation coefficient) = -0.27958475
R-sq = 0.078167631
Estimate of error standard deviation: 1.2912444

Parameter estimates:


ParameterEstimateStd. Err.AlternativeDFT-StatP-value
Intercept8.93385360.40508613 ≠ 08422.054208<0.0001
Slope-0.186562840.069903352 ≠ 084-2.66886830.0091

Analysis of variance table for regression model:


SourceDFSSMSF-statP-value
Model111.87602611.8760267.1228580.0091
Error84140.054211.667312
Total85151.93023

Result 8: Simple Linear Regression   [Info]
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A linear correlation is a numerical measure of strength of a relationship between two variables. The correlation can be either negative (-) or positive (+), and the value is always between -1 and 1. If a correlation coefficient is closest to zero this would indicate that there is a weak linear association. 

The value of r (correlation coefficient) is -0.279584, with the absolute value of r being .212 (Triola, 2015. Table A-5). We can conclude that there is a weak correlation of hours slept prior to working and hours slept when not working. However, the scatter plot would indicate that there is a weak negative correlation, most likely due to the outliers. 

Reference

Triola, M.F. (2015). Essentials of statistics (5th Ed.), Upper Saddle River, NJ: Pearson Higher Education https://excelsior.instructure.com/courses/12981/files/7086331/download?wrap=1    

 

 

 

 

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