61
5
Chi-Square Analysis to Verify
Quality of Candy Packets
This case study is about how chi-square analysis can be used in a Six Sigma
project to collect voice of the customer (VOC) data and then to verify if a
claim made about product quality is true.
Colorful Candy, Inc. makes colored chocolate candy and sells them in
packets that are claimed to contain 14% yellow candy, 13% red candy, 20%
orange candy, 24% blue candy, 16% green candy, and 13% purple candy. The
company wants to know whether the customers really care about the variety
of colors, and if so, whether the above claim of percentages is correct.
Section 5.1 gives a brief description of the dene phase. Section 5.2 explains
the measure phase. The analyze phase is illustrated in Section 5.3 with
detailed instructions for using Minitab
®
. Finally, the improve and control
phases are briey discussed in Section 5.4.
5.1 Define Phase
The company wants to ensure that customers are getting what they are
expecting regarding the percentages of different colors of candy in each
packet they are purchasing. However, before randomly selecting a packet
and testing it, the company executives decide to check whether customers
really care about the different colors.
5.2 Measure Phase
To gather the VOC data, a number of randomly selected customers in Boston,
Cleveland, New York City, San Francisco, and Chicago, are asked to rate on
a 17 scale, how important the variety of colors is to them, with 7 being
extremely important” and 1 being “not important at all”. The collected data
are in the CHAPTER_5_1.MTW worksheet (the worksheet is available at the
62 Six Sigma Case Studies with Minitab
®
publisher’s website; the data from the worksheet are also provided in the
Appendix). A part of the worksheet is shown in Figure5.1.
5.3 Analyze Phase
A bar chart is plotted for the data collected. Figure5.2 shows how to select
“Bar Chart. Doing so opens the dialog box shown in Figure5.3. Select “Values
from a table” from the drop-down menu, and select the “Stack” option under
One column of values. Click on “OK” and the dialog box shown in Figure5.4
opens. Select the “Observed” column for “Graph variables” and select “City”
and “Importance of Candy Color” for “Categorical variables for grouping”.
The bar chart shown in Figure5.5 is the result. Although it is clear from the
bar chart that customers in New York City seem to give a lot more importance
FIGURE 5.1
Data collected for importance given to candy color.
63Chi-Square Analysis to Verify Quality of Candy Packets
to candy color than those in the other cities, the company executives want to
perform a chi-square test of homogeneity to check whether the higher impor-
tance by customers in New York City is statistically signicant. Figure 5.6
shows how to select “Chi-Square”. Doing so will open the dialog box shown
in Figure5.7. Select “Importance of Candy Color” for “For rows” and “City”
for “For columns”. Select “Observed” for “Frequencies in” and check the box
for “Counts”. Click on “OK” and the output shown in Figure5.8 is the result.
The output shows how many customers were sampled in each of the cities and
how many customers gave what importance rating (1–7).
For expected values, click on “Chi-Square” in the dialog box shown in
Figure5.7, and the dialog box shown in Figure5.9 opens. Check the box for
“Expected cell counts” and click on “OK. It takes you back to the dialog box
shown in Figure5.7. Click on “OK” and the output shown in Figure5.10 is
the result.
FIGURE 5.2
Selection of “Bar Chart.
64 Six Sigma Case Studies with Minitab
®
FIGURE 5.3
Selection from options for bar chart.
FIGURE 5.4
Selection of variables for bar chart.
65Chi-Square Analysis to Verify Quality of Candy Packets
ChicagoSan
Francisco
New York
City
ClevelandBostonCity
1600
1400
1200
1000
800
600
400
200
0
Observed
1
2
3
4
5
6
7
Importance of
Candy Color
Chart of Observed
FIGURE 5.5
Bar chart.
FIGURE 5.6
Selection of chi-square test.

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