IB Math Studies Internal Assessment
What is the relationship between daily coffee consumption and sleeping habits?
Exam Session: May 2012
Candidate Number:
School Name: Murrieta Valley High School
Date: February 23, 2012
Course: IB Math Studies
Word Count: 1,612
Name:
Table of Contents
Introduction: Page 2
Raw Data: Pages 3-4
Graphing of data: Page 5
Chi Square Test: Pages 6-7
Discussion/Validity: Page 8
Conclusion: Page 9
Works Cited: Page 10
Introduction:
Sleeping is a seductive habit that every human being eventually succumbs to. Due to
this fact, there is an apparent need to investigate and analyze all of the factors that
influence sleeping habits. Caffeine, the primary active ingredient in coffee, has been
considered the most popular drug in the world, and is found naturally in over 60
plants (Caffeine and Sleep). This wide range of popularity and availability makes
studying caffeine’s effect on sleep important and relevant in today’s society.
Furthermore, caffeine has been categorized as a stimulant, and is seen to have side
effects ranging from sleep disturbance to excessive urination (Caffeine and Sleep). It
is for these reasons that I have decided to delve into the relationship between the
consumption of caffeine and sleeping patterns.
Task: For this IB math studies statistics project, the main purpose is to determine
whether there is a relationship between a high school student’s coffee drinking
habits and hours of sleep per night. I find this subject to be interesting as I am an
avid coffee drinker, and also have done much research into sleep patterns and
disorders on my own. It will be interesting to see the extent to which these two
variables affect one another.
Plan: The data will be collected during the second semester of the 2012 school year
at Murrieta Valley High School. All data will be collected from students ranging from
sophomore to senior year. I will ask the students whether or not the students drink
coffee daily, and then ask if they sleep, on average, 0-4 hours, 4-7 hours, or 8+ hours
per night. I will graph the data, as well as perform a X2 test in order to quantitatively
determine the relationship between coffee consumption and sleeping habits.
Mathematical Investigation
Collected Data:
Table 1: Raw Data Collected on average Hours of Sleep a Night and Whether or
not the Student Drinks Coffee
Number
1
2
Drink Coffee
Daily
Yes
Yes
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
No
No
Yes
No
yes
No
Yes
No
Yes
Yes
Yes
No
No
No
No
No
Yes
Yes
Yes
No
Yes
No
No
0-4hours sleep
4-8 hours
sleep
x
8+ hours of
sleep
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
Number
Drink Coffee
Daily
no
yes
no
no
yes
no
Yes
yes
No
Yes
No
Yes
Yes
yes
yes
No
No
No
No
no
Yes
yes
yes
no
yes
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
0-4 hours of
sleep
x
4-8 hours of
sleep
8+ hours of
sleep
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
Table 2: Sum of Data in Table 1
Participants Drink
Coffee Daily
50
25
Do not
Drink
Coffee
25
0-4 Hours
of Sleep
4-8 Hours
of Sleep
8+ Hours of
Sleep
14
18
18
Graph 1: Coffee Consumption Vs. Hours
of Sleep
14
12
10
8
0-4 hours of sleep
4-8 hours of sleep
6
8+ hours of sleep
4
2
0
Drinks Coffee Daily
Does not Drink Coffee
Graph 1 displays the sleep patterns of the two groups of the participants; those being
consuming coffee daily and those who do not. From this visual chart, it is evident that
those in the group who drink coffee daily appear to have a higher percentage of
participants sleeping 0-4 hours than the group that does not consume coffee. The
correlation cannot be deduced here as it would be entirely speculative and thus a
statistical analysis must be done to determine the correlation between these two
variables.
Table 3: Percentage of Participants Within Each Sub-Category
Percent of “Daily
Coffee Drinkers”
group.
Percent of “Does
not Drink Coffee”
group.
0-4 hours of sleep
9/25=0.36
4-8 hours of sleep
10/25=0.4
8+ hours of sleep
6/25=0.24
36%
5/25=0.2
40%
8/25=0.32
24%
12/25=0.48
20%
32%
48%
Calculation of a Chi Square Test
The Chi Square test is used to compare observed data with that of expected data,
meaning the data that would be expected under the given circumstances. This
statistical test quantifies whether or not the observed data is significant.
The formula for the Chi Square test is:
The degrees of freedom are critical to a Chi Square test, as they determine what the
critical value is to compare to the final result of the Chi Square test.
Null Hypothesis (H0): Coffee consumption and sleep patterns are independent of
one another.
Alternative Hypothesis (H1): Coffee consumption and sleep patterns are dependent
on one another.
Degrees of Freedom are calculated by taking (rows-1)(columns-1)
Table 4: Observed Values
Drink Coffee
Daily
Do Not Drink
Coffee
Total
0-4 Hours of
Sleep
4-8 Hours of
Sleep
8+ Hours of
Sleep
Total
9
10
6
25
5
8
12
25
14
18
18
50
Table 3 displays the original and observed data for this experiment. It will be used as a
basis for the Chi Squared test.
Table 5: Calculations for Expected Values
Drink Coffee
Daily
Do Not Drink
Coffee
Total
0-4 Hours of
Sleep
14X25
50
14X25
50
4-8 Hours of
Sleep
18X25
50
18X25
50
8+ Hours of
Sleep
18X25
50
18X25
50
Total
25
25
14
18
18
50
Table 4 demonstrates the calculations for each of the expected values based on the
observed values.
Table 6: Expected Values
Drink Coffee
Daily
Do Not Drink
Coffee
Total
0-4 Hours of
Sleep
4-8 Hours of
Sleep
8+ Hours of
Sleep
Total
7
9
9
25
7
9
9
25
14
18
18
50
Table 5 illustrates what the expected Values were for this experiment found through
the calculations in Table 4.
X2= (9-7)2 + (10-9)2 + (6-9)2 +(5-7)2 + (8-9)2 + (12-9)2
7
9
9
7
9
9
X2= 3.365
Df= (rows-1)(columns-1)
Df= (2-1)(3-1)
Df= 2
The X2 critical value at 5% significance with two degrees of freedom is 5.991. The X2
value from this experiment was lower than the critical value, (3.365<5.991) and thus
the null hypothesis must be accepted and the two variables, coffee consumption and
sleep patterns, are assumed independent of one another.
Discussion/Validity
Limitations:
Throughout this investigation, there were many limitations that could have altered
or changed the result of the experiment.
One such limitation can be seen in the way data was collected. Both of the questions
that were asked of the participants were dependent on the participant’s recollection
of his/her habits. It is very likely that some, if not many, of the participants were not
able to recall their sleeping habits accurately, or how often they consume coffee. For
this reason, memory is a limitation for this experiment.
Another limitation could be that the participant’s coffee consumption/sleeping
habits fluctuate throughout the week, or even throughout the day, and therefore the
simple yes or no question could have been difficult to answer for said participants.
Furthermore, the use of a yes or no question for daily coffee consumption is
something that is not quantifiable, and therefore limited the amount of statistical
analysis that could have been done with the data, such as a least square regression
calculation.
In addition, only 50 participants from Murrieta Valley High School were involved in
this experiment, and thus cannot be generalized into greater populations, or even
the high school for that matter. This was due to a lack of availability of a large
population sample off campus.
Also, many factors influence sleeping habits, such as stress, hormonal levels, gender,
eating habits, exercise habits, etc., and thus isolating coffee’s effect on sleep patterns
is extremely difficult to do.
A further limitation could be that those who said no to drinking coffee could have
been receiving coffee’s active ingredient, caffeine, through a variety of other drinks,
such as energy drinks. This would skew the data and make isolating coffee’s effect
on sleep patterns extremely difficult.
The data collected does not take into account gender, culture, or ethnic background,
which could all play a part in sleeping patterns. These outside factors reduce the
validity of this experiment and make it much harder in isolating coffee’s effect on
sleep patterns.
Conclusions
I performed a X2 test with this data in order to quantify the extent to which the two
variables, coffee consumption and sleeping patterns, are dependent upon one
another. The X2 test demonstrates that this experiment does not display a
correlation between coffee consumption and sleeping patterns. This is due to the
fact that the X2 value of 3.37 is lower than the critical value of 5.991. However, there
were many limitations in the design of this experiment, as listed previously, and
thus one cannot say from this experiment that there is no correlation between the
two variables. Due to these limitations, this experiment should be regarded as not
containing much validity. A much more thorough, scientifically advanced
investigation must be undergone before examining this question any further. Julie
Carrier, a professor at the University of Montreal, has carried out such an
experiment, and found that; “all subjects who consumed caffeine pills had their
sleep negatively affected, especially older participants who slept 50 percent less
than usual. In both age groups, caffeine decreased sleep efficiency, sleep duration,
slow-wave sleep (SWS) and REM sleep” (Caffeine Cuts into Sleep, Even Hours Later).
This study also has its limitations, however it demonstrates that other research has
discovered a correlation between these two variables. From this, it is apparent that
this investigation failed in isolating caffeine’s effect on sleep, however was based on
other valid scientific research.
Works Cited
"Caffeine and Sleep." National Sleep Foundation. Web. 23 Feb. 2012.
http://www.sleepfoundation.org/article/sleep-topics/caffeine-and-sleep
"Caffeine Cuts into Sleep, Even Hours Later." LiveScience.com. Web. 23 Feb. 2012.
<http://www.livescience.com/7923-caffeine-cuts-sleep-hours.html>.