The Statistics of a Taste Test
Teacher Notes
Middle School (6-8)
Materials
One die for each group of 2 students
Paper towels
Foil to cover labels on the bottles
Small paper cups
Oyster crackers
Calculators
Student activity sheets
3 different brands of the same flavor of
soda (cola, lemon-lime, root beer)
Objectives
The students will:
determine the probability of each possible choice when all factors are
equal
collect data related to a taste test preference for different brands of the
same flavor of soda pop
organize data on a frequency table using fractions, decimals, and
percent
compare and contrast the taste test data with the probability data
perform and analyze data using a chi-squared probability test
Standards
CCSS.Math.Content.6.SP.A.1; CCSS.Math.Content.6.SP.A.2;
CCSS.Math.Content.6.SP.B.5; CCSS.Math.Content.6.SP.B.5a;
CCSS.Math.Content.6.SP.B.5b; CCSS.Math.Content.6.SP.B.5c;
CCSS.Math.Content.7.SP.A.1; CCSS.Math.Content.7.SP.C.6;
CCSS.Math.Content.7.SP.C.7a; CCSS.Math.Content.7.SP.C.7b;
CCSS.ELA-Literacy.RST.6-8.7; CCSS.ELA-Literacy.RST.6-8.3;
CCSS.ELA-Literacy.RST.6-8.4; LS1.D Information Processing;
References to Common Core are adapted from NGA Center/CCSSO © Copyright 2010. National Governors Association
Center for Best Practices and Council of Chief State School Officers. All rights reserved. References to Next Generation
Science Standards are adapted from NGSS. NGSS is a registered trademark of Achieve. Neither Achieve nor the lead states
and partners that developed the Next Generation Science Standards was involved in the production of, and does not endorse,
this product.
Extension:
TASTE BUD TALLY
How many taste buds
do you have? Can you
count them? Are you a
super taster? Let’s find
out!
Link:
http://www.bbc.co.uk/science/h
umanbody/body/articles/senses
/tongue_experiment.shtml
Introduction
Just like the other senses, different people have different levels of acuity for
their sense of taste. The taste buds on your tongue are the sensors that detect
specific molecules which are present in the food you consume, but your brain
must interpret the signals coming from the taste buds. So different levels of
taste acuity between people could result from physiological differences (i.e.
more or less taste buds are present on the tongue) or from “learning” (i.e. a
chef probably has a lot of experience in identifying many specific flavors,
Illinois Math and Science Academy
1
and distinguishing subtle changes of flavor). So, in a taste test like the one in
this activity, the first question to ask is, “can you distinguish three different
tastes?” You may have heard, for instance, that smokers have a diminished
sense of taste. Therefore, a smoker may not be able to tell that the three
different brands taste differently (i.e. that each has its own unique taste).
For those of us who can distinguish different tastes, we have the second
issue, “which taste do you prefer?” This is a very different issue, and is
probably pretty complex. In other words, a person’s taste preferences may be
the result of many different factors. For instance, maybe you grew up
drinking a certain brand of cola. Later on you have several choices, but you
stick with your old favorite because its taste has become your “ideal” version
of that product. Alternatively, maybe you’ve always had to settle for a
bargain brand of a given product. Suddenly you come into money and can
afford a more expensive brand. You taste it for the first time… but is it
better? Your brain may make you think there’s a difference even if your taste
buds can’t distinguish one.
Inquiry Overview
Meaningful data activities should include the formulation of the question, the
active collection of data, the organization, analysis and representation of the
data, and finally, reaching a conclusion based upon the data.
This lesson contains three activities. In the first activity the students collect
data to determine the mathematical probability of selecting one of three
choices when making random selections. This leads to the second activity in
which the students collect data to examine how an external factor such as
taste preference in a blind taste test may or may not show the same statistical
probability. The students then compare and contrast the two sets of data.
Finally, the students use the chi-squared goodness of fit test to analyze their
data.
Incorporated in this lesson are three mathematics concepts: 1) probability and
chance, 2) data collection and analysis, and 3) statistical analysis.
It should be noted that the understandings and strategies that are developed
as students work through the suggested tasks could be applied in a wide
variety of inquiry situations. Students should be made aware of the fact that
these processes of making sense of collected data not only apply to this
particular investigation but to other inquiries that demand similar decisions
regarding the significance of differences between collected data and expected
results.
Activity One:
 A MATHEMATICAL SIMULATION
Explain to the students that they will be working in pairs to collect data for a
mathematical simulation of a taste test involving three different kinds of soft
Illinois Math and Science Academy
2
drink—A, B, and C. You may want to display the 3 bottles for the taste test
(see below) with the labels hidden by having foil wrapped around them.
http://www.roll-diceonline.com/
By rolling one die the students will be simulating the taste test as follows:
 If the die lands of a 1 or 2, students will
assume that Drink A is chosen.
 If the die lands of a 3 or 4, students will
assume that Drink B is chosen.
 If the die lands of a 5 or 6, students will
assume that Drink C is chosen.
Ask the students what the theoretical probability would be for A, B and C
(when rolling one die, the theoretical probability of obtaining a 1 or 2 is ⅓ or
33⅓%, of obtaining a 3 or a 4 is ⅓ or 33⅓%, and of obtaining a 5 or a 6 is ⅓
or 33⅓%).
The ability to generalize the results of this experiment is dependent on
collecting sufficient data. It is best to have the largest amount of data
possible so that experimental probability begins to approach what should
theoretically occur through mathematical probabilities. In an effort to
approach the theoretical probability, each student pair will roll the die 48
times and record the rolls in the frequency table on the student sheet. The
data collected by each pair of students is then entered on the Class Analysis
Table and a mean found for each of the possibilities.
Discussion of Probability Data
After the students have calculated the mean for each of the possibilities,
engage them in a discussion of the results.
Ask the students to compare their individual results with the class results.
Which most closely resembles the theoretical probabilities?
How can they explain their observations?
While individual group results may not approach the theoretical probabilities,
when all of the group results are averaged, the results should be about ⅓ or
33⅓% for each.
Activity Two:
 THE TASTE TEST
Obtain one bottle each of three different brands of the same flavor soft drink
(e.g., cola). Wrap each bottle with aluminum foil to hide the label. Using a
permanent marker, label each one either “A”, “B” or “C”.
Set out the crackers, three small paper cups for each student, and three
different brands of the same kind of soft drink ready to pour. The soft drinks
Illinois Math and Science Academy
3
may be chilled or at room temperature, but no ice. You may want to pre-pour
the soft drinks in labeled cups. Paper towels, a pail or sink in which to spill
unwanted soda, and a waste basket should be nearby.
Be careful of
gluten allergy.
Discuss with the students what they know about taste tests.
 What might be the purpose for doing a taste test?
 How might they used by industry?
 Do they think that they are an effective way to gather information
about a product?
 Have any of them have ever participated in a taste test? If so, did they
learn the results?
Explain to the students that each of them will sample three different brands
of the same flavor of soft drink. Between each sample, they are to take a bite
of the cracker to “clear their palate”. They may also choose to cleanse their
palates with water.
Emphasize that students should not make any motions or grimaces as
they taste and should silently record their vote, so that they do not
influence the vote of any other member(s) of the class.
http://www.polleverywher
e.com/
After they have tasted all of the samples, they are to decide which they prefer
and record their choice on the ballot provided. The ballots should then be
collected and the results recorded for the class to see so that the students can
complete Our Taste Test Frequency Table and answer the questions below
the table.
Discussion of Taste Test Data
When the students have finished discussing the results in their small group,
have them share their answers with the entire class. Depending on the brands
you use there may or may not be a clear favorite, so continue the discussion
by asking the students to consider whether or not the results of the test might
be considered significant by the company conducting the test.
Ask the students to discuss the meaning of significant results. Have them
consider the size of the sample group.
 How did the individual die rolling data compare with the class
results?
It is important for the students to realize that the term “significant” is
imprecise unless it is defined with a specific mathematical description.
Activity Three:
 CHI-SQUARED ANALYSIS
Illinois Math and Science Academy
4
The soft drink industry might be interested in performing an analysis using
an α, “alpha” level of 0.05 to see whether participants have a preference of
soft drink. (A step-by-step sample example is explained below).
The following hypothesis will be tested.
Participants show no preference in the soft drinks. (Null-Notation H0)
Participants show preference in the soft drinks. (Alternative-Notation H1
First, take the data that was generated from the taste test and place it into the
chi-squared analysis table.
Chi-Squared Analysis Table (Sample of headings)
Choice
Observed Expected
(O-E)2
Frequency Frequency
E
For this “sample” calculation A, B, C, D will be used as choice values.
The observed frequency values ( O ) are the data that was collected as part of
the taste test itself.
For example, if 100 people were sampled and there were 4 choices (A, B, C,
and D) and each person got one “vote”---- a sample observed frequency
count might look like the following:
28 votes for A, 12 votes for B, 35 votes for C and 25 votes for D;
28+12+35+25=100 votes total.
The expected frequency values ( E ) are the data that is expected if assumed
an equal distribution of data.
For example, if 100 people were sampled and each person got one “vote” and
there were 4 choices (A, B, C, and D) each choice would have an equal
number of votes, for example 100 ÷ 4 or 25 votes. Thus, if you add them 25
+ 25 + 25 + 25 = 100 votes total.
Analysis Table (Sample based on 4 choices with a total of 100 votes)
Choice
Observed Expected
(O-E)2
(e.g. A,B,C,D) Frequency Frequency
E
A
28
25
B
12
25
C
35
25
D
25
25
Illinois Math and Science Academy
5
Use the formula ((O-E)2/E)) to calculate a chi-squared value for each choice.
Next, sum all chi-squared values to calculate an overall chi-squared test
value. Set this value aside for now.
http://graphpad.com/quic
kcalcs/
Discussion
Point:
What about
significant
digits?
∑
Analysis Table (Sample based on 4 choices with a total of 100 votes)
Choice
Observed Expected
(O-E)2
(e.g. A,B,C,D)
Frequency Frequency
E
A
28
25
(28-25)2 = 0.36
25
B
12
25
(12-25)2
= 6.76
25
C
35
25
(35-25)2
=4
25
D
25
25
(25-25)2
=0
25
TOTAL
100
100
∑=11.12
STATISTICAL SIGNIFICANCE CALCULATION
Now, to find if the data has statistical significance one would need to
compare the test chi-squared value to a table of chi-squared probabilities.
First, find the degrees of freedom. Take the number of sample choices and
subtract one. These values are located on the left side of the data table in the
first column (see chi-squared table).
Degrees of Freedom formula: n-1=df
Using our sample example we get: 4-1=3
df=3
Move across the degrees of freedom row until you find your calculated chisquared value. You may not find your exact calculated value. If the exact
value isn’t there just pick the value that is closest to your calculated value.
Follow that value up the column and choose the corresponding alpha level.
Our sample chi-squared test value was 11.12
The value that is closest is 0.01
Illinois Math and Science Academy
6
In our example 0.01 <0.05, therefore we can conclude that there is a
preference in soft drink selection.
Chi-squared Table (Sample table of probability values)
α-level
Degrees 0.750
0.500
0.100
0.050
of
Freedom
1
0.102
0.455
2.71
3.84
2
0.575
1.39
4.61
5.99
3
1.21
2.37
6.25
7.81
4
1.92
3.36
7.78
9.49
5
2.67
4.35
9.24
11.1
0.025
0.010
5.02
7.38
9.35
11.1
12.8
6.63
9.21
11.3
13.3
15.1
Snap shot of Table:T5 Upper α Probability Points of χ2 Distribution (pgs. 360-361), Sensory
Evaluation Techniques 3rd Edition, Meilgaard, Civille, Carr
Report and discuss findings as a class.
 What was the significance of doing the chi-squared test?
Conclusion: Debriefing questions for all three activities
As you debrief the activities in this lesson
 Review the differences and similarities among them.
 Discuss why the probability simulation and the taste test were both
done.
 Review the meaning of significant results and why it would be
important to the company making the soft drink.
 Discuss the significance of doing the chi-squared analysis.
Culminating Activity:
 DESIGN YOUR OWN TASTE TEST
EXTENSIONS
1. Are you a super taster? http://barbstuckey.com/
2. Host a discussion about designing a sensory experiment.
a. A suggested question might be: What do test designers need to
take into consideration? Record ideas for the class to see and
then “cluster” ideas into categories
Facility conditions (testing room, testing location, testing climate,
testing booths, computers for recording selections etc…)
Illinois Math and Science Academy
7
Product conditions (temperature of soda, labeling, randomize
sampling order etc…)
People (Pre-survey for liking, reduce conversations-bias, training
panelists etc…)
Other testing possibilities (attribute, degree of liking, etc…)
3. Discuss ideas on reducing variability
Repeat experiment
Increase sample size
Train panelists
4. Compare nutrition labels (calories, carbohydrates, sodium, etc…).
http://www.socrative.com/
FUN TRIVIA
 What year was Barq’s rootbeer introduced? 1898
 What year was A&W rootbeer introduced? 1919
 What year was MUG rootbeer introduced? 1940
http://sodas.findthebest.com/compare/104-411/A-And-W-Root-Beer-vsBarq-s-Root-Beer
Illinois Math and Science Academy
8
BALLOTS FOR TASTE TEST
A B C
A B C
A B C
A B C
A B C
A B C
A B C
A B C
A B C
A B C
A B C
A B C
A B C
A B C
A B C
A B C
A B C
A B C
A B C
A B C
A B C
A B C
A B C
A B C
Illinois Math and Science Academy
9
CLASS ANALYSIS TABLE OF PROBABILITY SIMULATION
GROUP
%A
(1 or 2)
%B
(3 or 4)
%C
(5 or 6)
1
2
3
4
5
6
7
8
9
10
11
12
13
MEAN
TRANSPARENCY MASTER
Illinois Math and Science Academy
10
A MATHEMATICAL SIMULATION
Page 1 of 2
Look at the 3 containers of soda pop that are on display. Their labels have been covered but
they are all the same “flavor” or kind—just different brands. Let’s assume that every one of
them has the exact same taste. If there was a blind taste test to find a “favorite” do you think
that there would be much difference between the number of people choosing each of the
flavors? If we assume each of the different brands taste the same, we can also assume that
people will randomly choose A, B or C as their favorite.
The theoretical probability for each drink being randomly selected can be calculated. Drink A
has a 1 in 3 chance of being selected.
What is its theoretical probability of being selected?____________
What is the theoretical probability of Drink B being selected?___________
What is the theoretical probability of Drink C being selected?___________
A mathematical simulation can show the “results” for a taste test in which all of the flavors
are exactly the same and random choices are made by the taste testers.
Here’s how it works…
You and a partner will be roll one die 48 times and tally each roll in the table below.
If you roll a 1 or a 2, you will consider that Drink A was chosen as a favorite.
If you roll a 3 or a 4, you will consider that Drink B was chosen as a favorite.
If you roll a 5 or a 6, you will consider that Drink C was chosen as a favorite.
The results are not based on a taste preference, but are random—by chance.
Our Probability Simulation Frequency Table
Choices
Tally
Frequency
Ratio
Decimal
Percent
A (1 or 2)
B (3 or 4)
C (5 or 6)
TOTAL
When you complete your Probability Simulation Frequency Table, fill in your percentages in
the Class Data Table overhead. Then copy the other group’s data and determine the class
mean or average for each choice.
Illinois Math and Science Academy
11
A MATHEMATICAL SIMULATION
Page 2 of 2
CLASS ANALYSIS TABLE OF PROBABILITY SIMULATION
GROUP
%A
(1 or 2)
%B
(3 or 4)
%C
(5 or 6)
1
2
3
4
5
6
7
8
9
10
11
12
13
MEAN
How do your individual percentages compare with the mean class percentages? How can you
explain any differences?
Illinois Math and Science Academy
12
THE TASTE TEST
Page 1 of 1
When shopping in a mall, have you ever been asked to take a survey or a taste test? A
company conducting the test wants to know if their brand is more popular than the other
choices. But what does this actually mean? How much more popular is it? Is there a way to
find out just how much more popular one brand is than another? Who might be interested in
this type of statistical data?
You will be conducting a real taste test and by doing an analysis of the results of this tests and
the mathematical simulation you have done, perhaps it can be determined if one of the soda
pop samples was really much more popular than the other two!
OUR TASTE TEST FREQUENCY TABLE
Choices
Tally
Frequency
Ratio
Decimal
Percent
A
B
C
TOTAL
From the data in the above table does it appear that one of the brands of soda pop is much
more popular that the other two? Do you think that the data you collected is “significant”?
Discuss these questions with your group and write your answers below.
How does the actual data from the taste test compare with the mathematical simulation data?
What are some of the reasons that the the data may not be similar?
Illinois Math and Science Academy
13
STATISTICAL ANALYSIS: CHI-SQUARED ANALYSIS
Page 1 of 1
Chi-square analysis is used to test the “goodness of fit” between the observed and expected
data.
Hypothesis:___________________________________________________
Procedure:
Fill in the observed frequency values (i.e. Tally Numbers ) in the table below.
Determine the expected frequency values (i.e. Theoretical Probability) for the observed data.
Calculate each chi-squared value using the formula:
Sum the chi-squared values and calculate a total.
∑
CHI-SQUARED ANALYSIS TABLE
Choices
Observed Frequency
Expected Frequency
(Observed-Expected)2
Expected
A
B
C
TOTAL
Determine the degrees of freedom. df
, where n is the number of choices.
Using Table T5, locate the value closest to your chi-squared total value on the degrees of
freedom row. Follow up the column to find the alpha value.
State your conclusion.
Illinois Math and Science Academy
14
DESIGN YOUR OWN: TASTE TEST
Extended Exploration: What might you do to design your own taste test?
What questions need to be asked and answered?
Illinois Math and Science Academy
15