MINI PAPER
Candy Exercise –
Simple Data Analysis
by Bob Mitchell
While brainstorming ideas for the Kansas City AQC
division booth activity the Statistics Division officers
wanted to identify a hands-on activity whereby exhibit
hall visitors could participate in data generation and
analysis. The goal is to demonstrate the power of basic
statistical tools and Statistical Thinking in a fun,
entertaining manner – something that could be further
developed as a teacher lesson in the ‘Virtual Academy’
module of our re-designed website. The Virtual Academy
is an on-line e-Learning basic statistics-training tool
targeted for K-12 students. It is currently undergoing
dramatic changes to incorporate lots of motion,
animation, sounds, bright colors, etc. – tools to tickle the
senses of GenY future Statistics Division members.
Borrowing from the basic statistics module taught in Six
Sigma BB and GB training, we decided to demonstrate
Hypothesis testing, Signal-to-Noise ratios, and basic
quality tools to develop our process knowledge of candy
packaging. For example, known class exercises used in
some Six Sigma training involve studying bag fill weight
and color variation within and between Mars Inc.’s M&M
candy varieties (plain, peanut, almond, crispy, peanut
butter), or bag fill and flavor variation of Mars Inc.’s
Skittles (original fruit, tropical, wild berry, sour, mint).
One of the Statistics Division officers’ spouses owns a
candy store. Hearing about our search for a booth
activity, this spouse suggested that we examine the
hypothesis that people least like banana pieces of the five
Willy Wonka Runts flavors (cherry, strawberry, orange,
banana, watermelon). This candy storeowner orders by
bulk at the end of each month. It is her observation that
more people tend to remove the banana pieces before
their purchase; at the end of the month she has a
disproportionate amount of yellow Runts remaining in the
bin.
Two different hypotheses were developed for our Kansas
City AQC booth activity:
Null hypothesis Ho#1:
People like all Runts flavors equally;
No preference: Red = Pink = Orange = Yellow = Green
Null hypothesis Ho#2:
Bag fill process (by weight) is stable;
Short-term: Bag 1 = Bag 2 = Bag 3
Long-term: Lot 1 = Lot 2 = Lot 3
The ASQ Inspection Division provided the calibrated
electronic scale.
Exercise details:
1. Booth visitor selects and weighs a bag of Runts candies
2. Booth visitor opens the bag, sorts the candy by color
(flavor)
3. Booth visitor tastes each flavor
4. Record bag weight and color count by box# and bag.
5. Record individual flavor preference.
6. Recorded nominal empty bag weight
7. Recorded nominal candy weight by color
Data:
The Runts exercise data were analyzed in Minitab.
In order to promote discovery and learning we are
providing this Minitab workbook for download
from the Statistics Division website
http://www.asqstatdiv.org/documents/special/runts.xls.
We invite and encourage you to analyze the data and
offer your insights by posting your analysis and
conclusions to the Runts Discussion Page that
we created on the Statistics Division website
http://www.asqstatdiv.org/discussiongroups.htm.
Sample data set:
Bag
Full
Bag
Red
Empty
Blue
Orange Yellow
Pink
Green
Total
Preference
Box
60.1
55.7
57.8
60.5
56.0
53.1
59.4
57.9
58.0
57.1
1.4
1.4
*
*
*
*
*
*
*
*
10
4
2
3
2
6
2
4
5
5
6
7
11
11
14
11
6
15
10
13
9
13
16
15
14
11
11
11
15
17
9
8
2
4
6
1
5
5
5
0
43
45
48
49
45
44
44
48
48
49
orange
yellow
red
orange
red
orange
red
red
yellow
red
1
1
1
1
1
1
1
1
1
1
7
3
7
4
4
11
11
7
4
4
2
10
10
12
5
4
9
6
9
10
Continued on page 15
16
ASQ STATISTICS DIVISION NEWSLETTER, Vol. 21, No. 3
CANDY EXERCISE – SIMPLE DATA ANALYSIS
Continued from page 14
Summary data:
Color
Flavor
Red Cherry
Blue Raspberry
OrangeOrange
Yellow Banana
Pink Strawberry
Green Watermelon
Rule of Thumb: “When p-value is low, Ho must go”.
Ind
Weight
Box1
Freq
Box2
Freq
Box3
Freq
Box4
Freq
Flavor
Total
Flavor
Preference
1.24
1.20
1.10
1.30
1.07
1.80
140
102
223
154
274
124
195
219
157
96
197
126
195
198
216
98
177
107
174
145
239
98
242
107
704
664
835
446
890
464
19
11
14
25
13
6
NOTE 1: We have a 6th color (flavor): blue raspberry.
Wonka recently introduced “Chewy” Runts
candies, and launched a new flavor with the
chewy product line.
NOTE 2: Unlike M&Ms and Skittles, Runts candies have
distinct shapes. Each color/flavor/shape has its
own weight distribution.
P = 0 therefore reject the null hypothesis that there is no
flavor preference. In fact, the data suggest that people
might actually prefer the banana flavor (Observed >
Expected)!
This is opposite from the store owner’s casual
observation. I am reminded by a quote from Don
Wheeler, “All data out of context are meaningless”. The
storeowner stocks Runts original (hard) candy; the AQC
booth activity used Runts “chewy” variety. While
consumers may prefer the banana flavor, feedback
suggests that the banana-flavored pieces in the original
Runts are so much harder than the other flavors. Is it this
hardness characteristic that people dislike? (I sense
another study). Green (watermelon) appears to be the
least preferred variety of chewy Runts.
Analysis of Means for Color Preference
0.03
Data Analysis:
Flavor Preference
Use Chi-Square to test Independence
Chi-Square Test: Flavor Sum, Flavor Preference
Expected counts are printed below observed counts
Color/Total
2.6SL=0.2689
0.2
P=0.1667
0.1
-2.6SL-0.06448
Flavor
Cherry
Sum
704
707.45
Preference
19 (Obs)
15.55 (Exp)
Total
723
Subgroup
Color
Raspberry
664
660.48
11 (Obs)
14.52 (Exp)
675
Orange
835
830.74
14 (Obs)
18.26 (Exp)
849
Banana
446
460.87
25 (Obs)
10.13 (Exp)
471
Strawberry
890
883.58
13 (Obs)
19.42 (Exp)
903
Watermelon
464
459.89
6 (Obs)
10.11 (Exp)
470
Total
4003
88
4091
1
2
Yellow
Red
3
Orange
4
Pink
5
Blue
6
Green
Overall 0.05 probability level used
Interesting side point: Though this study indicates that
people may prefer the chewy banana flavor, it has the
lowest frequency from Wonka…
Chi-Sq = 0.017 + 0.764 +
0.019 + 0.853 +
0.022 + 0.995 +
0.480 + 21.820 +
0.047 + 2.125 +
0.037 + 1.671 = 28.849
DF = 5, P-Value = 0.000
Continued on page 16
ASQ STATISTICS DIVISION NEWSLETTER, Vol. 21, No. 3
17
CANDY EXERCISE – SIMPLE DATA ANALYSIS
Continued from page 15
I and MR Chart for Bag Weight
Use ANOVA to test differences by box (22 bags per box)
One-way ANOVA: Bag Wt. (Lot 3014TL2) versus Box
MS
2.86
2.81
F
1.02
P
0.388
Mean=56.61
55
LCL=51.41
50
Subgroup 0
Individual 95% CIs For Mean
Based on Pooled StDev
Box
N
Mean
StDev -----+---------+---------+---------+1
22 56.886
1.890
(-----------*-----------)
2
22 56.945
1.676
(-----------*-----------)
3
22 56.255
1.796 (-----------*----------)
4
22 56.336
1.272 (-----------*-----------)
-----+---------+---------+---------+Pooled StDev =1.675
55.80
56.40
57.00
57.60
10
20
30
40
50
60
7
6
5
4
3
2
1
0
70
80
90
1
UCL=6.388
R=1.955
LCL=0
Another look at the same data, but segregated by box
shows a somewhat different story:
I and MR Chart for Bag Weight by Box
Individual Value
P-value > 0.05; cannot reject the null hypothesis that bag
weights are the same.
Boxplots of Bag Wt. by Box
(means are indicated by solid circles)
62
61
60
64
62
60
58
56
54
52
50
1
58
57
56
55
54
7
6
5
4
3
2
1
0
2
3
4
UCL=60.10
Mean=56.34
LCL=52.57
Subgroup 0
59
Moving Range
Bag Wt Lot 301 4TL2
UCL=61.81
60
Moving Range
Analysis of Variance for Bag Wt.
Source
DF
SS
Box
3
8.58
Error
84
235.73
Total
87
244.31
Individual Value
Bag Fill Consistency
10
20
1
30
2
40
50
60
70
3
80
90
4
1
UCL=4.621
R=1.414
LCL=0
4
3
2
52
1
53
The bag fill weights appear statistically equivalent; but is
the process variation over time?
It is theorized on our part that total bag weight is
affected by flavor (shape, weight) distribution. So what is
the relative color /flavor distribution by box?
P=chart of Color Distribution
Stratified by “Box”
Red
1
2
3
4
UCL=0.3462
0.4
0.3
Color/Total
The caution here is that we do not know the order of bag
fill at the candy manufacturer. The time series order
presented below is the order of booth visitor. Control
limits that define the true bag fill process natural variation
may very well be quite different; but our observation tells
us that the bag weight is rather consistent, bag to bag.
0.2
P=0.1731
0.1
LCL=3.47E-05
0.0
0
10
20
30
40 50
Packet
60
70
80
90
Continued on page 17
18
ASQ STATISTICS DIVISION NEWSLETTER, Vol. 21, No. 3
CANDY EXERCISE – SIMPLE DATA ANALYSIS
Continued from page 16
P=chart of Color Distribution
Stratified by “Box”
P=chart of Color Distribution
Stratified by “Box”
Blue
1
2
Pink
3
4
1
2
3
4
0.5
0.4
UCL=0.4364
0.2
P=0.1443
Color/Total
UCL=0.3050
0.3
Color/Total
0.4
0.3
P=0.2408
0.2
0.1
0.1
0.0
LCL=0
0
10
20
30
40 50
Packet
60
70
80
LCL=0.04519
0.0
90
0
10
20
30
0.5
70
80
90
Green
Orange
2
60
P=chart of Color Distribution
Stratified by “Box”
P=chart of Color Distribution
Stratified by “Box”
1
40 50
Packet
3
1
4
3
4
0.3
UCL=0.4326
0.4
2
P=0.2378
0.2
Color/Total
Color/Total
UCL=0.2476
0.3
0.2
0.1
P=0.1065
0.1
LCL=0.04304
0.0
0.0
0
10
20
30
40 50
Packet
60
70
80
LCL=0
0
90
P=chart of Color Distribution
Stratified by “Box”
10
20
30
40 50
Packet
60
70
80
90
Control Chart of Average Weight per Piece
(Stratified by Box)
Yellow
1
2
3
4
1.5
1
2
3
4
0.3
1.4
UCL=1.387
0.2
0.1
P=0.09751
Total Weight
Color/Total
UCL=0.2332
1.3
Mean=1.235
1.2
1.1
0.0
LCL=0
0
10
20
30
40 50
Packet
60
70
80
90
LCL=1.082
1.0
0
10
20
30
40 50
Bag #
60
70
80
90
The chart above, “Average Weight per Piece” gives us
some insight that bag fill variation is controlled by the
relative frequencies of Runt color.
Continued on page 18
ASQ STATISTICS DIVISION NEWSLETTER, Vol. 21, No. 3
19
CANDY EXERCISE – SIMPLE DATA ANALYSIS
Continued from page 17
Conclusion
Our intention for the AQC booth activity was to
demonstrate the applicability of basic statistics and quality
tools in everyday activities. Our hope is that this brief,
fun look at passive data analysis will motivate the use of
graphical displays of data towards deeper process
understanding and discovery. Our plan is to continue
development of the Virtual Academy to present statistics
in a fun and stimulating learning environment to K-12
education.
20
To be certain, we could have launched into more
sophisticated statistical data analysis, but that was not our
goal. Again, you are invited to download the dataset and
post your analysis and conclusions on the Discussion
Page we have provided on the Statistics Division website
(www.asqstatdiv.org).
ASQ STATISTICS DIVISION NEWSLETTER, Vol. 21, No. 3