Is Breakfast Really a “Lucky Is Breakfast Really a “Lucky Charm?”Charm?”

MYTHMYTH

MYTH: SKIPPING BREAKFAST DOES NOT AFFECT GPAMYTH: SKIPPING BREAKFAST DOES NOT AFFECT GPA

For years, breakfast has been labeled the “most For years, breakfast has been labeled the “most important meal of the day.” Breakfast companies create important meal of the day.” Breakfast companies create

enticing commercials, depicting happy families and children enticing commercials, depicting happy families and children eating Cheerios to promote “heart health,” or orange juice eating Cheerios to promote “heart health,” or orange juice

workers bringing juice straight from the fields to your fridge. workers bringing juice straight from the fields to your fridge. Teachers and parents encourage their children to eat Teachers and parents encourage their children to eat

breakfast, insisting that it improves overall health and mental breakfast, insisting that it improves overall health and mental capacities. Their claims are not without cause--Harvard capacities. Their claims are not without cause--Harvard

University research has found that children who ate a healthy University research has found that children who ate a healthy breakfast had higher energy levels and better learning ability breakfast had higher energy levels and better learning ability

than similar students who did not eat breakfast. Another than similar students who did not eat breakfast. Another study conducted by Harvard researchers found that students study conducted by Harvard researchers found that students who ate breakfast were "…significantly more attentive in the who ate breakfast were "…significantly more attentive in the

classroom, earned higher grades in math, and had classroom, earned higher grades in math, and had significantly fewer behavioral and emotional problems.“ significantly fewer behavioral and emotional problems.“ However, how significant is the impact of breakfast on However, how significant is the impact of breakfast on

academic performance, if it exists at all? To find out the academic performance, if it exists at all? To find out the answer, we developed a survey and statistical analysis, after answer, we developed a survey and statistical analysis, after

eating a hearty breakfast of course.eating a hearty breakfast of course.

IntroductionIntroduction We studied the relationship between eating breakfast We studied the relationship between eating breakfast

and academic success.and academic success. To gather data, we surveyed students and asked them To gather data, we surveyed students and asked them

whether they consistently eat breakfast, what they eat, whether they consistently eat breakfast, what they eat, and what their GPA is.and what their GPA is.

We classified what they eat as healthy or unhealthy We classified what they eat as healthy or unhealthy according to set standards (ex. fruit, eggs, milk, and according to set standards (ex. fruit, eggs, milk, and oatmeal were considered healthy and cinnamon rolls oatmeal were considered healthy and cinnamon rolls and doughnuts were considered unhealthy.and doughnuts were considered unhealthy.

We plan to study how eating or not eating breakfast, and We plan to study how eating or not eating breakfast, and the type of food that is eaten, affects GPA.the type of food that is eaten, affects GPA.

BiasBias During our survey we also asked for the During our survey we also asked for the

respondent’s grade level, in order to insure we respondent’s grade level, in order to insure we fully represented each age group.fully represented each age group.

Our sample size is greater than 30, and Our sample size is greater than 30, and therefore the CLT should hold, insuring that our therefore the CLT should hold, insuring that our results will be approximately normal. results will be approximately normal.

Our survey was given randomly to students; Our survey was given randomly to students; however, voluntary response bias may occur.however, voluntary response bias may occur.

The surveys were administered as an SRS, and The surveys were administered as an SRS, and individuals can only answer one, making sure individuals can only answer one, making sure the responses are independent.the responses are independent.

Non-response bias also occurred. Non-response bias also occurred.

GPAGPA GPAGPA

2.02.0 2.02.0

2.82.8 2.42.4

2.82.8 2.52.5

3.83.8 2.52.5

3.83.8 2.72.7

3.873.87 2.82.8

3.93.9 3.43.4

3.93.9 3.53.5

44 3.73.7

4.14.1 3.83.8

4.24.2 3.83.8

4.24.2 3.83.8

4.24.2 3.83.8

4.44.4 3.8273.827

4.414.41 3.853.85

4.54.5 4.04.0

4.554.55 4.14.1

4.84.8 4.34.3

4.84.8 4.44.4

Eat Breakfast Don’t Eat BreakfastDataData

012345678

Count

2.0-2.5

2.5-3.0

3.0-3.5

3.5-4.0

4.0-4.5

4.5-5.0

GPA

Do You Eat Breakfast Consistently?

Yes

No

HistogramHistogram

Analysis of Those Who Eat Analysis of Those Who Eat Breakfast ConsistentlyBreakfast Consistently

Without considering the outliers, the Without considering the outliers, the distribution of those who eat breakfast distribution of those who eat breakfast consistently is slightly skewed left. The consistently is slightly skewed left. The min is 2.0 and the max is 4.8, with a 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 median of 4.1 and a Q1 of 3.8 and a Q3 of 4.41.4.41.

Modified Boxplot of Those Who Eat Modified Boxplot of Those Who Eat Breakfast ConsistentlyBreakfast Consistently

When the 3 outliers (2.0, 2.8, 2.8) are When the 3 outliers (2.0, 2.8, 2.8) are excluded, the distribution is roughly normal excluded, the distribution is roughly normal with a min of 3.8, max of 4.8, median of with a min of 3.8, max of 4.8, median of 4.2, Q1 of 3.9 and Q3 of 4.455.4.2, Q1 of 3.9 and Q3 of 4.455.

Modified Boxplot

Boxplot of Those Who Don’t Eat Boxplot of Those Who Don’t Eat Breakfast ConsistentlyBreakfast Consistently

The boxplot of those who don’t eat The boxplot of those who don’t eat breakfast is approximately normal with a breakfast is approximately normal with a min of 2, a max of 4.4, a median of 3.8, 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 Q1 of 2.7 and a Q3 of 3.85. There are no outliers.outliers.

Conditions to Use Two-Sample T-Conditions to Use Two-Sample T-TestTest

We have 2 SRSs from distinct populations.We have 2 SRSs from distinct populations.The samples are independent of each The samples are independent of each

other.other.The same variable is measured for both The same variable is measured for both

samples.samples.The mean and standard deviations of the The mean and standard deviations of the

populations are unknown.populations are unknown.

CalculationsCalculations

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 Conclusion About Eating BreakfastBreakfast

Our statistical conclusion is significant at the 5% Our statistical conclusion is significant at the 5% alpha level (.02<.05).alpha level (.02<.05).

Therefore it is reasonable to reject the null Therefore it is reasonable to reject the null hypothesis and support the alternative that hypothesis and support the alternative that people who consume breakfast consistently will people who consume breakfast consistently will have a higher GPA than those who do not.have a higher GPA than those who do not.

Because our sample size is not incredibly large, Because our sample size is not incredibly large, there may be slight bias and further tests should there may be slight bias and further tests should be run to draw a generalized conclusion.be run to draw a generalized conclusion.

DataData

GPAGPA GPAGPA

2.82.8 22

3.83.8 2.82.8

3.83.8 3.873.87

3.93.9 44

3.93.9

4.14.1

4.24.2

4.24.2

4.24.2

4.44.4

4.414.41

4.54.5

4.554.55

4.84.8

4.84.8

Healthy Breakfast Unhealthy Breakfast

HistogramHistogram

01234567

Count

2.0-2.5

2.5-3.0

3.0-3.5

3.5-4.0

4.0-4.5

4.5-5.0

GPA

What type of breakfast do you eat?

Healthy

Unhealthy

Analysis of Those Who Eat Healthy Analysis of Those Who Eat Healthy BreakfastsBreakfasts

In the boxplot of those who eat healthy In the boxplot of those who eat healthy breakfasts, without considering the outlier at 2.8, breakfasts, without considering the outlier at 2.8, the min is 2.8, the max is 4.8, the median is 4.2, 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 Q1 is 3.9 and Q3 is 4.5. This distribution is slightly skewed left. slightly skewed left.

Excluding the outlier at 2.8, the min is 3.8, the 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 max is 4.8, the median is 4.2, Q1 is 3.9 and Q3 is 4.5. This distribution is slightly skewed right.is 4.5. This distribution is slightly skewed right.

Analysis of Those Who Eat Analysis of Those Who Eat Unhealthy BreakfastsUnhealthy Breakfasts

The distribution of those who eat The distribution of those who eat unhealthy breakfasts is slightly skewed left unhealthy breakfasts is slightly skewed left with no outliers. The min is 2, the max is 4, with no outliers. The min is 2, the max is 4, the median is 3.335, Q1 is 2.4 and Q3 is the median is 3.335, Q1 is 2.4 and Q3 is 3.935.3.935.

Healthy vs. UnhealthyHealthy vs. Unhealthy

Null Hypothesis: Healthy breakfast eaters Null Hypothesis: Healthy breakfast eaters and unhealthy breakfasts result in the and unhealthy breakfasts result in the same GPA (same GPA (μ μ hh = = μ μ uhuh))

Alternative Hypothesis: Those who eat Alternative Hypothesis: Those who eat healthy breakfasts will have higher GPAs healthy breakfasts will have higher GPAs than those who do not eat healthy than those who do not eat healthy breakfasts (breakfasts (μ μ hh > > μ μ uhuh))

CalculationsCalculations

Mean of healthy breakfasts: 4.157Mean of healthy breakfasts: 4.157 Standard Deviation: .497Standard Deviation: .497

Mean of unhealthy breakfasts: 3.168Mean of unhealthy breakfasts: 3.168 Standard Deviation: .946Standard Deviation: .946

TWO SAMPLE T TEST (see previous equation and TWO SAMPLE T TEST (see previous equation and conditions that apply)conditions that apply)

(4.157-3.168)/((.497^2/15)+(.946^2/4))^.5(4.157-3.168)/((.497^2/15)+(.946^2/4))^.5t=2.02t=2.02tcdf (2.02,10^10, 3)tcdf (2.02,10^10, 3)p=.0683 p=.0683

Conclusion About Healthy Conclusion About Healthy BreakfastsBreakfasts

P=.0683P=.0683 Our data is not significant at the 5% alpha level; Our data is not significant at the 5% alpha level;

however, it is significant at the 10% alpha level.however, it is significant at the 10% alpha level. There is good, but not overwhelming, evidence There is good, but not overwhelming, evidence

to reject the null in favor of the alternative, to reject the null in favor of the alternative, stating that healthy breakfasts result in higher stating that healthy breakfasts result in higher GPAs.GPAs.

Our sample size for unhealthy breakfasts was Our sample size for unhealthy breakfasts was very small and may have resulted in some bias, very small and may have resulted in some bias, additional tests with a greater sample size will be additional tests with a greater sample size will be more helpful in establishing more solid statistical more helpful in establishing more solid statistical conclusions.conclusions.

Final ConclusionFinal Conclusion

Our data showed that those who eat Our data showed that those who eat breakfast do indeed have higher GPAs, breakfast do indeed have higher GPAs, and those who eat a healthier breakfast and those who eat a healthier breakfast have a slight edge over those who love have a slight edge over those who love starting their day with big bowls of sugar.starting their day with big bowls of sugar.

Therefore, it is advantageous to eat any Therefore, it is advantageous to eat any type of breakfast, because it helps you type of breakfast, because it helps you start your day and grades off right.start your day and grades off right.

MYTH: SKIPPING BREAKFAST DOES NOT AFFECT GPAMYTH: SKIPPING BREAKFAST DOES NOT AFFECT GPA