Is Breakfast Really a “Lucky
Charm?”
MYTH
MYTH: SKIPPING BREAKFAST DOES NOT AFFECT GPA
For years, breakfast has been labeled the “most important
meal of the day.” Breakfast companies create enticing
commercials, depicting happy families and children eating
Cheerios to promote “heart health,” or orange juice workers
bringing juice straight from the fields to your fridge. Teachers
and parents encourage their children to eat breakfast,
insisting that it improves overall health and mental capacities.
Their claims are not without cause--Harvard University
research has found that children who ate a healthy breakfast
had higher energy levels and better learning ability than
similar students who did not eat breakfast. Another study
conducted by Harvard researchers found that students who
ate breakfast were "…significantly more attentive in the
classroom, earned higher grades in math, and had
significantly fewer behavioral and emotional problems.“
However, how significant is the impact of breakfast on
academic performance, if it exists at all? To find out the
answer, we developed a survey and statistical analysis, after
eating a hearty breakfast of course.
Introduction




We studied the relationship between eating breakfast
and academic success.
To gather data, we surveyed students and asked them
whether they consistently eat breakfast, what they eat,
and what their GPA is.
We classified what they eat as healthy or unhealthy
according to set standards (ex. fruit, eggs, milk, and
oatmeal were considered healthy and cinnamon rolls
and doughnuts were considered unhealthy.
We plan to study how eating or not eating breakfast, and
the type of food that is eaten, affects GPA.
Bias





During our survey we also asked for the
respondent’s grade level, in order to insure we
fully represented each age group.
Our sample size is greater than 30, and
therefore the CLT should hold, insuring that our
results will be approximately normal.
Our survey was given randomly to students;
however, voluntary response bias may occur.
The surveys were administered as an SRS, and
individuals can only answer one, making sure
the responses are independent.
Non-response bias also occurred.
Eat Breakfast
Data
Don’t Eat Breakfast
GPA
GPA
2.0
2.0
2.8
2.4
2.8
2.5
3.8
2.5
3.8
2.7
3.87
2.8
3.9
3.4
3.9
3.5
4
3.7
4.1
3.8
4.2
3.8
4.2
3.8
4.2
3.8
4.4
3.827
4.41
3.85
4.5
4.0
4.55
4.1
4.8
4.3
4.8
4.4
Histogram
Do You Eat Breakfast Consistently?
8
7
6
5
Count 4
3
2
1
0
Yes
No
2.0- 2.5- 3.0- 3.5- 4.0- 4.52.5 3.0 3.5 4.0 4.5 5.0
GPA
Analysis of Those Who Eat
Breakfast Consistently

Without considering the outliers, the
distribution of those who eat breakfast
consistently is slightly skewed left. The
min is 2.0 and the max is 4.8, with a
median of 4.1 and a Q1 of 3.8 and a Q3 of
4.41.
Modified Boxplot of Those Who Eat
Breakfast Consistently

When the 3 outliers (2.0, 2.8, 2.8) are
excluded, the distribution is roughly normal
with a min of 3.8, max of 4.8, median of
4.2, Q1 of 3.9 and Q3 of 4.455.
Modified Boxplot
Boxplot of Those Who Don’t Eat
Breakfast Consistently

The boxplot of those who don’t eat
breakfast is approximately normal with a
min of 2, a max of 4.4, a median of 3.8, a
Q1 of 2.7 and a Q3 of 3.85. There are no
outliers.
Conditions to Use Two-Sample TTest
We have 2 SRSs from distinct populations.
 The samples are independent of each
other.
 The same variable is measured for both
samples.
 The mean and standard deviations of the
populations are unknown.

Calculations
Running calculations on a calculator (2 variable stats), we determined the
mean GPA of breakfast eaters is 3.949 and the mean GPA of those who
don’t eat breakfast is 3.430
Xy= 3.949
Sy=.716
Xn= 3.430
Sn=.715
Our null hypothesis is that the GPA of those who do and don’t eat
breakfast will be equal: μy = μn
Our alternative is that breakfast eaters will have higher GPAs:
μ y > μn
T= 3.939-3.430/ ((.716^2/19)+
(.715^2/19))^.5
T=2.192652663
Df=18
Tcdf (2.192652663,10^10,18)=
P=.0208572693
We used the conservative
approach in establishing our
degrees of freedom. A two
sample t test on the calculator
gave us a p value of .0159.
Conclusion About Eating
Breakfast



Our statistical conclusion is significant at the 5%
alpha level (.02<.05).
Therefore it is reasonable to reject the null
hypothesis and support the alternative that
people who consume breakfast consistently will
have a higher GPA than those who do not.
Because our sample size is not incredibly large,
there may be slight bias and further tests should
be run to draw a generalized conclusion.
Data
Healthy Breakfast
Unhealthy Breakfast
GPA
GPA
2.8
2
3.8
2.8
3.8
3.87
3.9
4
3.9
4.1
4.2
4.2
4.2
4.4
4.41
4.5
4.55
4.8
4.8
Histogram
What type of breakfast do you eat?
7
6
5
4
Count
3
2
1
0
Healthy
Unhealthy
2.0- 2.5- 3.0- 3.5- 4.0- 4.52.5 3.0 3.5 4.0 4.5 5.0
GPA
Analysis of Those Who Eat Healthy
Breakfasts


In the boxplot of those who eat healthy
breakfasts, without considering the outlier at 2.8,
the min is 2.8, the max is 4.8, the median is 4.2,
Q1 is 3.9 and Q3 is 4.5. This distribution is
slightly skewed left.
Excluding the outlier at 2.8, the min is 3.8, the
max is 4.8, the median is 4.2, Q1 is 3.9 and Q3
is 4.5. This distribution is slightly skewed right.
Analysis of Those Who Eat
Unhealthy Breakfasts

The distribution of those who eat
unhealthy breakfasts is slightly skewed left
with no outliers. The min is 2, the max is 4,
the median is 3.335, Q1 is 2.4 and Q3 is
3.935.
Healthy vs. Unhealthy
Null Hypothesis: Healthy breakfast eaters
and unhealthy breakfasts result in the
same GPA (μ = μ )
 Alternative Hypothesis: Those who eat
healthy breakfasts will have higher GPAs
than those who do not eat healthy
breakfasts (μ > μ )

h
h
uh
uh
Calculations

Mean of healthy breakfasts: 4.157


Standard Deviation: .497
Mean of unhealthy breakfasts: 3.168

Standard Deviation: .946
TWO SAMPLE T TEST (see previous equation and
conditions that apply)
(4.157-3.168)/((.497^2/15)+(.946^2/4))^.5
t=2.02
tcdf (2.02,10^10, 3)
p=.0683
Conclusion About Healthy
Breakfasts




P=.0683
Our data is not significant at the 5% alpha level;
however, it is significant at the 10% alpha level.
There is good, but not overwhelming, evidence
to reject the null in favor of the alternative,
stating that healthy breakfasts result in higher
GPAs.
Our sample size for unhealthy breakfasts was
very small and may have resulted in some bias,
additional tests with a greater sample size will be
more helpful in establishing more solid statistical
conclusions.
Final Conclusion
Our data showed that those who eat
breakfast do indeed have higher GPAs,
and those who eat a healthier breakfast
have a slight edge over those who love
starting their day with big bowls of sugar.
 Therefore, it is advantageous to eat any
type of breakfast, because it helps you
start your day and grades off right.

MYTH: SKIPPING BREAKFAST DOES NOT AFFECT GPA