Six Sigma Case Studies with Minitab®

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 Figure5.7, and the dialog box shown in Figure5.11 opens.

Check the box for “Chi-Square analysis” 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5.12 is the result. Because the Pearson chi-square P-value (0.000) is less

than 0.05, there are signicant 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 Figure5.13.

Doing so opens the dialog box in Figure5.14. Select “View Probability” and

click on “OK”. This opens the dialog box shown in Figure5.15. 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 Figure5.16 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 Figure5.12), right-

click on the plot shown in Figure5.16 and select “Reference Lines” as shown

in Figure5.17. Doing so opens the dialog box shown in Figure5.18. Enter

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

shown in Figure5.19 is the result.

Now that it is clear that there are signicant 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 Figure5.5), 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.