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Cold Breakfast Cereal Unit Cost and
Corresponding Ingredient Content
Introduction
Currently the United States is experiencing a less than perfect financial situation, where
economic hardships are encouraging consumers to give extra attention on spending habits.
Financial difficulties can be felt with almost every facet of daily living. The effects of a
lackluster national economy and the resulting consequences felt among families across the nation
have yielded in a heightened awareness of monetary value- many times the discussion of
economic deprivations arise first thing in the morning during breakfast. Morning conversations
regarding the distressed finances often stem from what is presented on the dining table.
Consumer food choices and its relationship with breakfast food spending can be expressed with a
myriad of selections and one the primary breakfast items found in virtually every house in the
nation is cold, ready-to-eat (RTE) cereal.
Available finances frequently dictate the decisions consumers make regarding cereal
selection. Pursuing personal flavor preferences while simultaneously adhering to a grocery
budget is not always an available consumer option for many households. By determining
whether a relationship exists between cold, RTE ingredients and unit price provides for a better
assessment as to which types of cereal are purchasable within the financial means of the
consumer.
Many cereal consumers have to forgo personal brand preferences in lieu for more
economical varieties of cereals with an implicit belief that a reduction in cereal unit cost has an
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inherent negative consequence in flavor and nutritional health benefits. Whether or not this is
true can be determined by assessing the nutritional value of the cereals; sugar content, for
example, where a greater amount of sugar found in a particular cereal corresponds to greater unit
cost of cold, RTE cereals. For consumers that are restricted to a limited income and are
constrained to a short list of cereal options, being aware of how cereal ingredients are related to
unit cost will aid determining if personal nutritional preferences are within personal economic
means.
By expressing how cereal ingredients are related to the unit price the consumer will be
better informed as to how to best maintain personal cereal flavor preferences within limited
monetary dispositions. Furthermore, additional insights can also be determined, such as: whether
or not traditional and healthier cereal varieties are cheaper or more expensive than cereals that
are comparatively laden with substantially greater amount of sugar. Ultimately, not only does
this research seek to determine the corresponding relationship between cold breakfast cereal unit
cost and ingredient content, but also facilitates in providing greater knowledge of which types of
cereals are available within specific monetary ranges. Providing cereal flavor preference while
simultaneously saving money and supplementing for additional expendable income not only
makes for a more satisfying breakfast experience (especially for households with many
dwellers), but also stimulates discretionary spending among consumers.
Literature Review
Breakfast choices, regarding RTE cereals, are responsible for a substantial part of both
personal and/or household monetary spending. RTE cereal is by far the most popular breakfast
food choice in the United States- beyond other breakfast foodstuffs, such as: bagels, quick
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breads, or eggs and toast (Gejdenson and Schumer 1999). The RTE cereal industry is a
metaphorical Goliath when compared to other breakfast food preparations. An average, RTE
cereal represents about two-thirds of all breakfast foods and consumers purchase more than a
billion units of RTE cereals annually (Gejdenson and Schumer 1999 and Gillespie 1995). When
combined, the total average of RTE cereal consumption per person equates to about 12 pounds
per year (Gejdenson and Schumer 1999).
RTE cereal consumers in the United States are responsible for creating a gargantuan
industry that yields sizable revenues within the breakfast foods market. It has been determined
that in 1987 the combined sales within the RTE cereal market were approximately $4 billion
(Levy 1987) and $9 billion in 2005 (Lee 2005 and Gejdenson and Schumer 1999). This rise in
gross sales is disproportionately large when compared to national inflation rates: 5.5% for 1980-
1989 and 3.0% for 1990-1999 (Metzen, S.R and Morgan, K.J. 1979). As the price of cold RTE
cereals increase in price over time the choices in product purchase will become more limited.
The importance in finding the best RTE cereal item selection within a monetary budget while
maintaining desired flavor, while simultaneously achieving superior nutritional benefits is
becoming a grocery shopping topic that is being discussed with greater frequency.
When identifying and categorizing the numerous kinds of cereals in the local supermarket
into subsets of levels of nutritional value in regards to price the Food and Drug Administration,
FDA, recommends cereals that are energy-dense and are made of whole-wheat or whole-wheat
bran provide are a primary component in satisfying daily nutritional values (Drewnowski and
Fulgoni 2008).
“To meet the FDA definition of “healthy” foods, the food had to
contain at least 10% of the RDI or the daily reference value (DRV)
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per reference amount of one or more of six nutrients: protein, fiber,
vitamins A and C, calcium, and iron; it also had to be low in fat
(<3 g), saturated fat (<1 g), cholesterol (<60 mg), and sodium
(<480 mg). Foods were disqualified from health claims if a
serving of food contained >13 g of fat, >4 g of saturated fat, >60
mg of cholesterol, or >480 mg of sodium.” (FDA 2002).
Cereal continues to be the dominant breakfast food and in regards to nutritional health is
also a major contributor. However, “In the years 2000 to 2004, Americans consumed 22.2
teaspoons of added sugar each day; this amount of sugar is equivalent to an excess 355 calories
daily” (Hetzler 2010). This excessive intake of sugar means that unneeded calories are
consumed, yielding in adverse health complications that may include: weight gain, diabetes
mellitus, and heart disease. Although consumers demand to have healthier cereal selections,
customers continue to purchase cereals that are greatly considered as sugary kids’ cereals- it can
be said that RTE cereal is experiencing a popularity comparable to that of fast food, such as
hamburgers and pizzas: RTE cereal is the new junk food.
According to Canstar Blue (2011), an Australian consumer review agency, 25% of cereal
consumers surveyed do not review nutritional information labelling prior to choosing a breakfast
cereal. In addition, 34% of participants didn’t rate low sugar content as a key consideration
when choosing a cereal. The percentage of RTE cereal purchasers are experiencing a nutrition-
taste tradeoff, where the growth of, “food processing sectors adept at producing foods [are]
aimed at the consumer’s palate” (Blaylock et al. 1999). RTE foods are becoming more
commonly found with the addition of fats, sweeteners and salt, all of which create for an
enhanced taste, but yield in negative health effects.
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Over the past few years, Public Health Authorities have become increasingly
concerned about the evolution of the nutritional quality of processed food products
(Combris, et al. 2010). Processed foods, such as RTE cereals, are a significant source of
dietary nutrition and highlight the necessity and feasibility of reformulation of many
foods that are more favorable in creating a healthier consumer. Furthermore, the cereal
consumer can be deceived by less-than honest promotions of beneficial nutrition from
manufacturers. Although a particular cereal may contain some or many of the ingredients
necessary to qualify as a healthy food, it could be not as nutritious as perceived. The
addition of refined sugars, fats, and other additives could potentially make what would be
popularly considered as healthy as the opposite. Cereal consumers must exercise
heightened visual awareness of possible misleading nutritional claims.
By the 1970’s research has shown that there was a relationship between the
consumption of insoluble dietary fiber and the incidence of colon cancer; continued
research provided evidence that fiber prevents cancer (Ippolito and Mathios 1990). This
scientific proof has provide cereal manufacturers to create RTE cereals that claim to have
nutritious levels of fiber and other healthy ingredients and could conceivably increase
sales as result of information about the health benefits claimed (Levy, A.S. and Stokes,
R.C. 1987).
“Many manufacturers try to entice you by promising their cereal
is "Made with Whole Grain." In fact, it might appear that those
rainbow-colored, sugar-coated rings are the nutritional equal of a
bran flake or shredded wheat, but it's not the case.” (Mclndoo
2010).
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Although there are numerous references that assess which ingredients are healthier than
others, the existence of a universal cereal nutrition categorization, in which RTE cereals that are
most nutritious and provide the most benefit for optimal health are compared to inferior products
that do not have such healthy components, does not exist. Despite research, there is no definite
government guidelines for sugar serving recommendations other than ‘use sparingly’, according
to the FDA, and a reasonable amount can be assigned by acknowledging previous studies
involving the measurement of sugar in RTE cereals.
Cereal consumers viewed RTE cereals that are high in fiber, protein, and minerals to be
healthy, in that a healthy cereal should contain low sugar, low levels of sodium or fat, whole
grain and/or 100% recommended daily allowance of vitamins. However, a general consensus
was made that healthy cereals are not was flavorful and do not provide a comparative tasty
experience when compared to much less healthy sugary cereals. Whether considered healthy or
not, the taste of the RTE cereal must be good enough to be willingly consumed (Lee and Lee
2006).
The importance of reading the nutrition label of the RTE cereal box and comparing which
ingredients are most beneficial may aid in detouring from front-of-the-box health benefits that
could be used to merely entice an uneducated consumer into making an impulse purchase at not
only the consequence of the customers’ health, but also the bottom dollar.
The most common concerns for RTE cereal customers are as follows
(Canstar Blue 2011):
• Too expensive
• Cereal goes soggy quickly
• High sugar content
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• Lack of nutritional value
• Value for money
Determining how RTE cereal ingredients correspond to superior nutritional levels and
price depends on which ingredients are responsible for categorizing cereal healthiness factor.
Although there is a proven relationship between the use of healthier food ingredients, such as
fiber, and the reduction of less healthy ingredients, such as sugar, salts, and fat, with the
prevention of diet related disorders, there are no definitive guidelines, provided by federal health
authorities, that dictate which cereals qualify as beneficial for dietary health. Therefore, the
application of previous studies related to the classification of RTE cereals according to
nutritional value must be observed.
Previous research (namely Consumer Report’s Consumer Union, Cereal Food
Advertising to Children and Teens Score, and the United Kingdom Food Standards Agency
Nutrient Profiling Model), although fundamentally different in ultimate objective share
similarities in the analysis of cereal nutritional comparison. The similarities found between these
studies measure the following variables: sugar, sodium, and dietary fiber content. These
variables will be used in this report’s analysis of cereals and its respective healthiness in regards
to price. Furthermore, an additional common trait found throughout these studies was the
predominance of sugary cereals and the association with higher cereal prices; this trend however,
was not thoroughly assessed with other divisions or categories of cereals according to nutritional
content, but rather other elements, such as advertising and marketing.
Variables including cereal item price and nutritional content will be compared, where a
relationship will be determined that will suggest that when greater quantities of refined sugar is
founded per serving of a particular cereals divided into nutritional health categories the price will
increase.
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Null Hypothesis: H0: There is no relationship between the price of ready-to-eat cereal and its
ingredients.
Alternate Hypothesis: H1: As the quantity of unhealthy ingredients increases per serving of
ready-to-eat cereal, the cost price of the cereal item will also increase.
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Data and Method
The data acquired for this research was primarily compiled from the Wal-Mart website,
where recent prices and nutrition information was gathered from the grocery shopping
portal. The usefulness of this data was helpful in that the listed prices were uniform across
the nation, with the differed option to shop locally via the online portal. From this website
the necessary variables were identified to determine whether or not there is a correlation
between the RTE cereal ingredients and its price.
Dependent Variable: Cost of cereal
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Independent Variables: Calories per serving, Amounts of sugar, dietary fiber, and sodium.
Although the Wal-Mart website is very informative in providing detailed nutrition
information, as well as the item price, the website fails to provide for a uniform standard that
creates for a consistent serving size for all RTE cereals. Furthermore, the identifying
classifications of which cereals fall into particular health categories was a responsibility for
the researcher, as Wal-Mart did not provide such information.
Searching for a nutritional categorical cereal standard for both dependent and
independent variable required additional research among academic journals and consumer
review agencies. In regards to the dependent variable, the division of cereal prices per
package was determined on two primary factors. The first being that all cereals researched
on the Wal-Mart web page were not on sale or temporary shoppers’ special. Furthermore,
only common package sizes were selected; value-size or economical bargains were forgone
as the product promotion could adversely affect the results of the research.
Searching for a method to divide RTE cereal product prices was aided by the research
methods employed by Lee and Lee’s 2006 work, Consumer Insights on Healthy Breakfast
Cereal. In this report the authors segmented the prices of RTE cereals into three ranges:
low, medium, and high. The respective prices were: $2-2.99 for low, $3-3.99 for medium,
and $4+ for high priced RTE cereals. As Wal-Mart did not have such a wide plethora of
varied priced cereals, a slight adjustment was made so as to better address the prices
provided in the Wal-Mart website. The divisions of price ranges are as follows: $0-1.99 for
low, $2-2.99 for medium, and $3+ for high. However, although a new range in price
schematics was established, its relevance to nutrition was irrelevant unless the package
prices of each cereal was converted to make a standard measure of value by dividing the
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package price of the cereal
In regards to independent variables, a similar strategy was employed, as with the
dependent variable where additional research reports that addressed similar topics and
methods as this report were used. For designating sugar, fiber, and sodium levels the
official website for Consumer Reports, Union Reports, was accessed. Within this website it
was determined that dividing sugar, fiber, and sodium ingredients were each divided into
low and high ranges, where the break point for each of the mention independent variables
are 5, 5, and 0.140 grams respectively.
Yet, like the dilemma with the dependent variable, where the assessment of nutrition and
its placement in its respective ranges are not practiced with a universal set range while
adhering to the serving size. It could be very well possible that a particular cereal could out-
perform another brand due to having a different serving size. Therefore, in order to make
for a leveled ground for all cereals, sugar, fiber, and sodium content was calculated by its
serving size in grams, then divided by the how many grams constitute the serving size of
each cereal.
The division of each independent variable foodstuff was made into 2 categories of high
and low content after assessing its nutritional food stuff-serving size ratio. Superior content
for fiber was awarded with a number 1 for containing more than 5 grams of dietary fiber, but
the inverse was given for the sugar and sodium, as elevated intake of these ingredients are
inherently detrimental to dietary health. A score of 1 for sugar yields less than 5 grams per
serving and a score of 1 for sodium yields less than 0.140 grams per serving. The same
method was employed for determining the caloric ratio of each RTE cereal by dividing the
number of calories per serving by the serving size in grams.
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In order to make for a more simplistic perspective of which cereals are healthy and those
that are not, it was agreed that by collapsing the identifiers of determining nutritional quality
in regards to the independent variables. Creating a nutritional index by combining the three
foodstuffs (sugar, fiber, and sodium) ratios into a binomial representation aids in reducing
potential misinterpretation of what constitutes a healthy or less healthy cereal item purchase.
Should any cereal fulfill in obtaining a nutritional index of 3 means that it has score of
superior healthiness by minimizing the levels of sugar and sodium in each cereal serving,
while elevating the presence of fiber. A score of 2 could be a superior result of two out of
three foodstuffs, a score of 1 would result in only one superior foodstuff result meeting the
nutritional criteria, and a score of 0 would yield the least healthy of cereal selections, where
it does not meet any of the minimum requirements to be considered healthy. The path to
collapsing the independent variable data continues by further condensing the identity of
what is a healthy cereal choice by combining nutrition factor scores 3 or 2 were translated
into scores of 1 and nutritional scores of 1 or 0 were translated in scores of 0; thus, making
the nutritional index a nominal index.
The methods chosen to assess the data are as follows:
1. Hypothesis testing with Samples: This testing method was selected as a primary
model due to its popular use among social scientists. Not only is the data to be assessed in
respects to formulated hypotheses, but is to be a determining factor in identifying the
strength of relationships between the dependent and independent variables through statistical
inference. A clear assumption can be made as whether the provided information is strong
enough to definitively reject or not reject the null hypothesis, where no relationships can be
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determined.
2. Contingency table with Chi-Square Test: Assuming that there is no relationship
between the dependent and independent variables determines whether any apparent
relationship obtained in a sample cross-tabulation is attributable to chance. As the Chi-
square statistic is acquired, it can be assessed that as the deviation between observed and
expected frequencies increases as does the inference that a relationship does exist between
studied variables. Furthermore, the calculation of the Chi-square statistic also determines a
precise degree of confidence acknowledging the degree of the relationship between
variables.
3. Regression Analysis: As the data provided are interval-level data, the decision to
chose regression analysis for determining the relationship between dependent and
independent variables is obvious, as the statistical relationship focuses on the value of the
independent variable so as to estimate the value of the dependent variable.
A linear regression model will be employed so as to reveal both the direction and
strength of association between cereal ingredients and product price. In addition, an
ANOVA data output will also evaluate any potential the amount of error present in the
model and to detail the proportion of variance between variables, with the application of an
F-statistic. Beta weights, which include R-squared values, will aid in assessing any change
in price due to foodstuff modification. The Durbin-Watson measure will monitor the
possibility of multicolliniarity found among independent variables and finally, the
hypothesis will be again acknowledged by studying p-value measures.
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Analysis and Results
1. Hypothesis Testing with Samples:
Step 1: Estimate the population mean. The population mean would be the average of the
price of cereal for every cereal name.
MeanPop
: $0.28
Step 2: Estimate the population standard deviation. S = $0.10
Step 3: Calculate the standard error of the mean. Divide the population standard
deviation by the square root of the total number found within the sample
population.
s.e. = s / (square root 93) = 0.10 / 9.64 = 0.01
Table 1. Calculations for Two Different Sample
Sizes
Experimental Sample Control Sample Total Population
Less Healthy Healthy Both
N 74 19 93
Means $0.27 $0.34 $0.28
S 0.09 0.13 0.10
s.e. 0.01 0.03 0.01
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Step 4: Test the hypothesis. Find the difference between the sample mean and the
population mean divided by the population standard deviation.
t-score = (Population mean- Sample mean) / standard error of the mean
= (0.27 – 0.28) / 0.01 = 1
df = n-1 = 74 – 1 = 73
A t-score of 1 assessed with a level of significance of 0.05, with 73 degrees of freedom,
yields a distribution value of 1.645; thus, tcalc
= 1 and t∝
= 1.645. Looking up a t-score of 1 in the
t-table (df=73), the probability of a sample of 74 with a mean of $0.27 is less than 0.1
Step 5: Accept or Reject null hypothesis.
As the t-alpha value is greater than the t-calculated score, it can be determined that the
null hypothesis cannot be rejected, or in other words, the research hypothesis cannot be accepted.
As more than 90% of increased cereal prices in relation to added sugar are due to chance.
T-test Assuming Proportions
Step 1: Experimental: p1= 74/93 = 0.796
S1= sqrt(p(1-p))= sqrt(0.796(1-0.796))= 0.403
Control: p2= 19/93 = 0.204
S2= sqrt(p(1-p))= sqrt(0.204(1-0.204))= 0.403
Step 2: Calculate s.e for both groups
Experimental: s1/sqrt(n1)= 0.403/sqrt(74)= 0.0468
Control: s2/sqt(n2)= 0.403/sqrt(19)= 0.0924
Step 3: Calculate overall s.e.d= sqrt(0.0468^2 + 0.0924^2)= 0.1035
Step 4: Convert the difference between groups in a t-score with df= infinity as the
number of cases exceeds 30.
(p1-p2) /s.e.d= (0.403-0.403) / 0.1035= 0
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A conclusion can be made that the t-calculated statistic found in step 4 (t= 0) does not
exceed 1.282, the t-score associated with the 0.10 level of significance.
Step 5: A probability greater than 0.10 is not good enough to reject the null hypothesis;
the result suggests that there is a greater than 0.10 probability that the null
hypothesis is correct- 90% chance that ingredients have
relationship with cereal price. It can be concluded that the experimental
group, less healthy cereals that many contain elevated levels of sugar and
sodium, with diminished levels of dietary fiber, did not yield an increase in
cereal cost. Therefore, the null hypothesis cannot be rejected: There
is no relationship between the price of ready- to-eat cereal and its
ingredients.
2. Contingency Tables with Chi-Square Test
Step1: Determine the dependent and independent variables, as noted in the research
hypothesis- As the quantity of sugar and other unhealthy ingredients
increases per serving of ready-to-eat cereal, the cost price of the cereal item will also
increase.
The dependent
variable would be
the price and the
independent
variables will be
the
nutritional value of the cereals as calculated by
Table 3. Percent Distribution for
Data:
Relationship Between Nutrition Level
and Price
Nutrition, %
Price, % Low High
Low 13.51 5.26
Medium 40.54 21.05
High 45.95 73.68
Total 100.00 100.00
Table 4. Hypothetical No-
Relationship
Cross-Tabulation for Chi-Square
Nutrition, %
Price, % Low High
Low 11.83 11.83
Medium 36.56 36.56
High 51.61 51.61
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creating a collapsed frequency of four possible nutritional categories to 2.
Step 2, 3: Calculate percentages within the variables and ccompute expected frequencies.
Step 4: Compare the value of Chi-Square computed for the actual cross-tabulation with
the appropriate value of Chi-square tabulated in the table of theoretical
values. Degrees of freedom equal (3-1) x (2-1) = 2
Chi-square computed= 135.55
Table 5. Calculations for Expected Frequencies and Chi-Square
Price Nutrition Lev. Obs Freq. Exp Freq. (Obs-Exp)^2/Exp
Low Low 10=.1183*74 8.75 0.18
Low High 1=.3656*74 27.05 25.09
Medium Low 30=.5161*74 38.19 1.76
Medium High 4=.1183*19 2.25 1.37
High Low 34=.3656*19 6.95 105.36
High High 14=.5161*19 9.81 1.79
Total 93 93.00 135.55 =Chi-Square
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Chi-Square tabulated= p<0.005 = 10.60
There is a probability of 1% that in the long run, an inference will be made that a
relationship will be made that exists in the population when in fact it does not. According to the
decision rule, where if the calculated Chi-square value is greater than the tabulated value for Chi-
square, while considering degrees of freedom, then the null hypothesis must be rejected, or the
null hypothesis cannot be accepted. Therefore, the null hypothesis that claims that there is no
relationship between the cost of cereal and its ingredients must be rejected or the experimental
hypothesis that claims that a relationship does exist must be accepted.
Nominal Measure of Association Based on Chi-Square: Cramer’s V:
V= sqrt(chi-square/(mN)) where m= # of columns – 1= 2
N= size of sample= 93
=sqrt(135.55/(2*93) =sqrt(135.55/186) =0.854
Like all measures of association for nominal-level variable, Cramer’s V is always a
positive number. The measure ranges from 0, indicating no relationship between variables, to
1.0+, indicating a perfect relationship.
3. Regression Analysis
Table 6. Variables and Descriptive Statistics
Variable Mean Std. Deviation N= Obs
PricePS 0.2803 0.10504 93
NutritionIndex 0.2043 0.40538 93
Sugar 0.2648 0.11905 93
Fiber 0.0759 0.0762 93
Sodium 0.0047 0.00239 93
Calories 3.6948 0.37218 93
Table 7. Regression Coefficients
Model B, Coefficients: y- t Sig.
PricePS 0.67 3.985 0
NutritionIndex -0.061 -1.643 0.104
Sugar -0.24 -2.442 0.017
Fiber -0.1 -0.509 0.612
Sodium -23.497 -4.019 0
Calories -0.053 -1.373 0.173
* Dependent Variable: PricePS
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Table 8. Model Summary
R2
Adjusted R2
Std. Error of the Durbin-Watson Std. Error of the ANOVA F-score
0.233 0.217 0.189 1.286 0.09457 5.301
Predictors: (Constant), Calories, Sodium, Sugar, Fiber, Nutrition Index
*Dependent Variable: PricePS
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Step 1-7: Calculate slope and intercepts, note appendix for table calculations.
Step 8: Y-hat = a + b1X1 + b2X2 + b3X3 + b4X4 + b5X5 + e
=0.67 + 1.06 X1 – 0.12X2 – 0.02X3 + 0.00X4 + 0.16X5 + e
Table 9. Regression intercepts and slopes
Intercepts a Slopes b a * b
a1 -0.0919b1 1.0566 -0.0971
a2 0.3b2 -0.12081 -0.0362
a3 0.07764b3 -0.01831 -0.0014
a4 0.00461b4 0.00025 0.0000
a5 3.65461b5 0.15604 0.5703
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Step 9: Calculate: standard error of the estimate, coefficient of determination, and
standard error of the slope- assess measures of goodness. Note
appendix for calculations.
Table 10. Measures of Goodness
Std. Er. Est. Coef. Det. Std.Err,b
Sy|x r^2 sb
Y1 0.395 0.0725 0.3983
Y2 0.12 0.2074 0.0901
Y3 0.077 0.0031 0.054
Y4 0.002 0 0.0016
Y5 0.375 0 0.2391
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Discussion and Further Analysis
The results found with the provided data made for less than perfect results, where
conflicts in the relationships between the dependent and independent variables were evident.
Initial hypothesis tests have found that inferior t-test scores for both the initial calculations and
later another t-test with assuming proportions with a control variable comprised of foodstuffs
other than sugar, i.e. fiber and sodium. Thus, it can be determined that there is a low likelihood
of these foodstuffs influencing the individual prices of RTE cereals.
The great majority of the relationship between the dependent and independent variables
are left to chance, as the correlation strength between these variables determined by t-test has
shown to be weak, with scores falling below the 0.10 probability on the t-distribution table with
infinite degrees of freedom. Therefore, provided the processed data and the dismal result
compared with the t-scores yield in the rejection of the alternate hypothesis and the refusal the
reject the null hypothesis.
Null Hypothesis: H0: There is no relationship between the price of ready-to-eat cereal
and its ingredients.
Alternate Hypothesis: H1: As the quantity of unhealthy ingredients increases per serving
of ready-to-eat cereal, the cost price of the cereal item will also increase.
More interestingly, the second method, contingency table with applied chi-square test,
used to assess the possible relationship between cereal ingredients and the respective price
yielded a result that provided for a strong possibility for a relationship between the dependent
and independent variables. According to the contingency data, it can be noted that the
percentage relationship between nutrition level and price per serving demonstrates a strong
relationship with high nutrition and high prices, however, chi-squared analysis proves that the
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relationship between cereal cost and nutrition have alternate results. Chi-square testing has
demonstrated a relationship between moderately price RTE cereals and low nutritional health.
The compared value of the calculated chi-square value to that of the tabulated score
favors the calculated score, about 136 v. 11. As the calculated value of chi-square is much
greater than its tabulated counter-part, there is a probability of 1% that in the long run, an
inference will be made that a relationship will be made that exists in the population when in fact
it does not. This means that despite having a very sizable calculated chi-square statistic, it could
misrepresent the data in misidentifying particular independent variables’ potential weight to
influence the cereal price.
Indeed, this is true as with Cramer’s V, the calculated chi-square statistic is again proven
that a relationship between dependent and independent variables exists, however pinpointing the
origin of relationship when compared to contingency tables is not as specific. However, the
resulting score for Cramer’s V was 0.854; as this number more closely approaches 1, the
stronger the possibility of inter-variable action, where the independent variables, such as sugar,
fiber, or sodium content determines the strength of its relationship with cereal price. The null
hypothesis, as stated in the beginning of this document, is rejected- a relationship between
independent variable or variables do exist.
In regards to linear regression, the results were not favorable and will provide much
opportunity for improvement. The relationship between cereal price and constituting ingredients
are very small, despite numerous evaluations and measures. In researching for a commonality
between ingredients and cost this report has yielded confronting analyses that prove that this
report has many flaws that need to be addressed.
Measures of goodness of fit are primary tools in evaluating data and explaining
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correlation and variance. The first measure of goodness of fit is the standard error of the
estimate; this measures the amount of error when predicting Y, when given X. A well-designed
statistical analysis can accurately estimate Y hat variation with a predicted value of Y. However,
prevalence in the amount of errors undermines the center hypothetical topic, that the ingredients
of a cereal dictate the cost of the item. Similarly, when comparing the coefficients of
determination also stresses that the ratio of experimental variance to total variance in Y. Due to
the provided data the coefficient of determination fails to acknowledge the reduction of error be
using the regression line to the total error guessing the mean. Furthermore, a seemingly small r-
square value prevents a relationship from being observed; the r-square rating totaled only about
0.3- as smaller ranks are deemed more likely to fail in gaining strong, reciprocal dependent-
independent relationship.
The coefficient of determination’s r-square rating prevents this project from identifying
price-ingredient relationships. Perhaps, an adjusted r-square measurement would provide for a
more accurate picture of the explanatory power of this model by adjusting for the presence of
partial slopes with insignificant values. After running the data through SPSS, the adjusted r-
square was 0.217- lower than the original r-square value. When the adjusted r-square value is
greater than the r-square the statistical significance it can be determined that the data model does
not much statistical significance and has possibly has significant partial slopes. It can be
assumed that by either acknowledging the common r-square or the adjusted modification, the
data presented does not matter the experimental hypothesis. In fact, this project’s r-square values
can assume that the relationship between cereal cost and its ingredients only comprise about 30%
of correlation; therefore, it can be determined that about 70% of cereal prices are governed by
chance and the ingredients have little responsibility in the overall cost for a box of RTE cereal.
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The third measurement of goodness of fit, standard error of the slope, explains variance
as a percentage and much like the previous tools of statistical measurement has demonstrated
that with its low numbers of coefficiency the data provided and the method it was studied yielded
in scores close to zero, indicating that the likelihood of a relationship between dependent and
independent variables to be very small. In addition, standard of error scores that hover around
the zero mark exhibit insignificant slopes and often are found to have reduced r-square values,
thus inclining the message that the choice in independent variables were in poor in an attempt to
convey a relationship with unit cost of RTE cereals. The measurements of goodness of fit have
all reached the same conclusion that small numerical coefficients are not conducive in creating
strong relations between the variable provided.
In an effort to continue to assess the dearth of potentially valuable and useful data and
affiliated relations between dependent and independent variables more statistical diagnoses were
undertaken. Testing for multicollinearity identifies an important assumption when creating
linear relationships, where variables can be identified and determined if it shares a linear path
with another variable. The presence of inflated and inconsistent standard error of the estimate
statistics is a trademark of multicollinearity. Also, multicollinearity can also be pinpointed by
linear equations that yield in high adjusted r-squares with insignificant slope coefficients- the
closer the r-square value is to one, the more likely that multicollinearity is a problem. Although
the coefficient statistics have provided for less than streamlined and perfect relationships that
ideally correspond to each other, the prevalence of multicollinearity is present, but not
devastating.
Yet another test to demonstrate the relationship between the provided variables is the F-
statistic. This measurement assesses whether partial slope coefficients for all the independent
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variables should be identified and taken as a group and are equaled to zero. Should most or all of
the slope coefficients in a multiple regression lack explanatory power, the F-statistic will be low.
Conversely, a larger F-statistic is more likely to identify one or more of independent variables as
statistically significant. The F-statistic produced by SPSS has yielded in a small number, 5.301.
Just like how small slope values correspond to diminished variable relationships, a small F-score
is also an indicator of increased multicollinearity. Compared to larger F-scores, such as 50,
which indicates that there is almost, if not any, chance that all the partial slopes are equal to zero.
The F-statistic provided in this report indicates that the possibility of the independent variables
being too closely related is strong and the prevalence of multicollinearity to be unavoidable.
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COLD CEREAL PRICES AND INGREDIENT CONTENT
Chart 1: Price v. Ingredients
0
0.1
0.2
0.3
0.4
0.5
0.6
0.00 0.20 0.40 0.60 0.80
Foodstuffs (g)
PricePerServing
Sugar Rat.
Fiber Rat.
Salt Rat.
Cal. Rat.
Linear (Sugar Rat.)
Linear (Fiber Rat.)
Linear (Salt Rat.)
Linear (Cal. Rat.)
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COLD CEREAL PRICES AND INGREDIENT CONTENT
Another concern that needs to be brought to attention is the possibility of autocorrelation,
or the assumption that errors are not correlated. Although correlated errors are predominantly an
issue that is usually found in time series analyses, the problem with autocorrelation is that the
standard errors of the slopes are not given enough attention. Statistical mistakes could
potentially result in slopes that may appear to be significant, when in fact, they are not. To test
for the possibility of autocorrelation the Durbin-Watson statistic will be used. By counting the
number of independent variables and the number of observations or cases within a study an
assessment can be made as to how error positively or negatively affects the null and
experimental hypotheses.
SPSS has provided this study with a Durbin-Watson score of 1.286. Upon reception of
this score a Durbin-Watson table aids in guiding that score within an upper and lower range.
Should the lower limit be less than 4, the perfect positive autocorrelation, and less than the
Durbin-Watson value one must reject the proposed null hypothesis with negative autocorrelation.
On the other hand, a lower limit score that outperforms both the Durbin-Watson score and is
greater than zero forces the researcher to reject the null hypothesis with positive autocorrelation.
The provided Durbin-Watson score of 1.286 is smaller than, the upper and lower limits, 1.776
and 1.542, provided in the statistical table. Therefore, it can be determined, that the null
hypothesis must be rejected and that the research has a propensity for greater positive
autocorrelation.
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COLD CEREAL PRICES AND INGREDIENT CONTENT
Conclusion
The experimental hypothesis that a relationship, or relationships, exists between
the contents of RTE cereals and its respective price cannot be completely determined.
Although chi-square testing has revealed a relationship between moderately price RTE
cereals and low nutritional health from its ingredients, alternative assumptions can be
made. Furthermore, a graphic analysis visually demonstrates that a relationship
between a couple independent variables and the dependent variable does exist. It can be
observed that sugary cereals have achieved the title as most expensive RTE cereal and
that as less sugar is found within the ingredients, the product price of the cereal goes up
as well. This negatively reciprocal relationship is noted, however, the weight that
should be placed on the reliability of this observation is not definitive. Likewise, a
slight positive relationship can be noted with the presence of fiber, where increased
prevalence of this product in RTE cereals yields in a positive correlation- the price
increased with more dietary fiber found in the cereal. Yet, like with the sugar example
just mentioned, these trends are not to be trusted as they are highly variable and more
closely resembles a heteroskedastic representation that is heavily loaded with outliers,
potential errors in data acquisition, and disagreeable independent variables.
In order to improve upon this research model it is advisable that additional
considerations be addressed, so as to aid in the elimination of collinear trends and
prevent autocorrelation, while seeking more advantageous independent variables that
also contribute in identifying additional routes to positively influence the dependent
variable. Additional variables that could be responsible for varying the price of a box of
cereal may include a multitude of variables.
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COLD CEREAL PRICES AND INGREDIENT CONTENT
Conclusion
The experimental hypothesis that a relationship, or relationships, exists between
the contents of RTE cereals and its respective price cannot be completely determined.
Although chi-square testing has revealed a relationship between moderately price RTE
cereals and low nutritional health from its ingredients, alternative assumptions can be
made. Furthermore, a graphic analysis visually demonstrates that a relationship
between a couple independent variables and the dependent variable does exist. It can be
observed that sugary cereals have achieved the title as most expensive RTE cereal and
that as less sugar is found within the ingredients, the product price of the cereal goes up
as well. This negatively reciprocal relationship is noted, however, the weight that
should be placed on the reliability of this observation is not definitive. Likewise, a
slight positive relationship can be noted with the presence of fiber, where increased
prevalence of this product in RTE cereals yields in a positive correlation- the price
increased with more dietary fiber found in the cereal. Yet, like with the sugar example
just mentioned, these trends are not to be trusted as they are highly variable and more
closely resembles a heteroskedastic representation that is heavily loaded with outliers,
potential errors in data acquisition, and disagreeable independent variables.
In order to improve upon this research model it is advisable that additional
considerations be addressed, so as to aid in the elimination of collinear trends and
prevent autocorrelation, while seeking more advantageous independent variables that
also contribute in identifying additional routes to positively influence the dependent
variable. Additional variables that could be responsible for varying the price of a box of
cereal may include a multitude of variables.
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COLD CEREAL PRICES AND INGREDIENT CONTENT
When purchasing RTE cereal the time of the year could dictate eating frequency
and choice of product. It can be assumed that more cold cereal is consumed during
warm seasons, however, that is to be assessed. Additionally, a factor that is probably
more important than the ingredients of the cereal itself is the advertising and marketing
that promotes that particular product. Initial research for this project revealed that the
cereal industry is governed by public awareness and the ability to coax shoppers into
purchasing particular cereal items is paramount. The amount of revenue that is invested
in the marketing and promotion of RTE cereals are more than any other industry, as
noted on a blog from the Consumer Reports website. Frequently, the influence of
advertising on purchase power transcends personal necessity. Those that are more
susceptible to being influenced by such campaigns could have a strong influence on the
overall pricing schematics of RTE cereals. Additionally, those that could be identified,
as potential marketing targets are also additional independent variables, as age and
gender probably also dictate how cereals are manufactured and sold. In searching for
the relationship between cereal ingredients and cost, comparing product prices across
multiple grocers would also aid the production of better results and more distinctive
variable relations. Although the cereal industry may seem benign in its operations,
however, manufacturers may attempt to sell unhealthy selections under the guise of
something more nutritiously beneficial. Ultimately, it is up to the consumer to make the
best decisions when purchasing their favorite cereals, be it because of any reason from
health preference to financial fastidiousness.
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