66 Six Sigma Case Studies with Minitab

®

FIGURE 5.7

Creation of contingency table for chi-square analysis.

Tabulated statistics: Importance of Candy Color, City

Using frequencies in Observed

Rows: Importance of Candy Color Columns: City

New York San

Boston Chicago Cleveland City Francisco All

1 92 29 38 53 62 274

2 63 58 46 36 70 273

3 98 100 82 41 125 446

4 480 478 326 263 486 2033

5 315 250 364 196 348 1473

6 257 203 405 304 252 1421

7 197 197 274 642 210 1520

All 1502 1315 1535 1535 1553 7440

Cell Contents: Count

FIGURE 5.8

Observed data.

67Chi-Square Analysis to Verify Quality of Candy Packets

FIGURE 5.9

Selection of “Expected cell counts” option.

Tabulated statistics: Importance of Candy Color, City

Using frequencies in Observed

Rows: Importance of Candy Color Columns: City

New York San

Boston Chicago Cleveland City Francisco All

1 92 29 38 53 62 274

55.3 48.4 56.5 56.5 57.2 274.0

2 63 58 46 36 70 273

55.1 48.3 56.3 56.3 57.0 273.0

3 98 100 82 41 125 446

90.0 78.8 92.0 92.0 93.1 446.0

4 480 478 326 263 486 2033

410.4 359.3 419.4 419.4 424.4 2033.0

5 315 250 364 196 348 1473

297.4 260.3 303.9 303.9 307.5 1473.0

6 257 203 405 304 252 1421

286.9 251.2 293.2 293.2 296.6 1421.0

7 197 197 274 642 210 1520

306.9 268.7 313.6 313.6 317.3 1520.0

All 1502 1315 1535 1535 1553 7440

1502.0 1315.0 1535.0 1535.0 1553.0 7440.0

Cell Contents: Count

Expected count

FIGURE 5.10

Observed data and expected data.

68 Six Sigma Case Studies with Minitab

®

For the P-value of the chi-square analysis, click on “Chi-Square” in the dia-

log box shown in Figure5.7, and the dialog box shown in Figure5.11 opens.

Check the box for “Chi-Square analysis” and click on “OK”. It takes you back

to the dialog box shown in Figure5.7. Click on “OK” and the output shown in

Figure5.12 is the result. Because the Pearson chi-square P-value (0.000) is less

than 0.05, there are signicant differences among the ratings given by cus-

tomers in the various cities. In order to view the chi-square probability dis-

tribution plot, select “Probability Distribution Plot” as shown in Figure5.13.

Doing so opens the dialog box in Figure5.14. Select “View Probability” and

click on “OK”. This opens the dialog box shown in Figure5.15. Select “Chi-

Square” from the drop-down menu for “Distribution” and enter “24” for

“Degrees of freedom” [The degrees of freedom are (number of ratings – 1)

* (number of cities – 1) = (7 – 1) * (5 – 1) = 6 * 4 = 24]. Click on “OK” and the

probability distribution plot shown in Figure5.16 is the result. Notice that

36.42 is the critical value of the chi-square characteristic. In order to add a

reference for the Pearson chi-square of 802.637 (refer to Figure5.12), right-

click on the plot shown in Figure5.16 and select “Reference Lines” as shown

in Figure5.17. Doing so opens the dialog box shown in Figure5.18. Enter

“802.637” for “Show reference lines at X values” and click on “OK”. The plot

shown in Figure5.19 is the result.

Now that it is clear that there are signicant differences among the ratings

given by customers in the various cities and that New York City seems to give

a lot more importance to candy color than the other cities (see Figure5.5), the

company wants to check whether its claim of the following percentages in a

packet are correct: 14% yellow candy, 13% red candy, 20% orange candy, 24%

blue candy, 16% green candy, and 13% purple candy. To this end, a packet

of candy is randomly selected, and the number of candies of each color is

counted. The collected data are in the CHAPTER_5_2.MTW worksheet (the

FIGURE 5.11

Selection of “Chi-Square analysis” option.

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