The table below shows the quantity of watches made by a company for different plant layout and shift times.
Weekly quantity of wrist watches produced in a factory |
|||
Shifts (hours) |
|||
Layout |
6 |
8 |
12 |
1 |
300 |
400 |
900 |
350 |
350 |
950 |
|
450 |
490 |
850 |
|
330 |
500 |
800 |
|
2 |
80 |
250 |
500 |
100 |
300 |
450 |
|
60 |
190 |
550 |
|
150 |
240 |
600 |
|
3 |
700 |
800 |
1200 |
600 |
900 |
1800 |
|
750 |
680 |
2000 |
|
800 |
720 |
2200 |
i) The output of two-way ANOVA is:
Anova: Two-Factor With Replication | ||||||
SUMMARY | 6 | 8 | 12 | Total | ||
1 | ||||||
Count | 4 | 4 | 4 | 12 | ||
Sum | 1430 | 1740 | 3500 | 6670 | ||
Average | 357.5 | 435 | 875 | 555.8333 | ||
Variance | 4225 | 5233.333 | 4166.667 | 60371.97 | ||
2 | ||||||
Count | 4 | 4 | 4 | 12 | ||
Sum | 390 | 980 | 2100 | 3470 | ||
Average | 97.5 | 245 | 525 | 289.1667 | ||
Variance | 1491.667 | 2033.333 | 4166.667 | 36390.15 | ||
3 | ||||||
Count | 4 | 4 | 4 | 12 | ||
Sum | 2850 | 3100 | 7200 | 13150 | ||
Average | 712.5 | 775 | 1800 | 1095.833 | ||
Variance | 7291.667 | 9433.333 | 186666.7 | 326644.7 | ||
Total | ||||||
Count | 12 | 12 | 12 | |||
Sum | 4670 | 5820 | 12800 | |||
Average | 389.1667 | 485 | 1066.667 | |||
Variance | 72862.88 | 56990.91 | 368787.9 | |||
ANOVA | ||||||
Source of Variation | SS | df | MS | F | P-value | F crit |
Sample | 4053689 | 2 | 2026844 | 81.17901 | 3.8E-12 | 3.354131 |
Columns | 3226106 | 2 | 1613053 | 64.60586 | 5.11E-11 | 3.354131 |
Interaction | 757244.4 | 4 | 189311.1 | 7.582273 | 0.000313 | 2.727765 |
Within | 674125 | 27 | 24967.59 | |||
Total | 8711164 | 35 |
The p-value of the interaction is 0.000313. As the p-value<0.05, it means that the interaction between layout and shift hours is significant. This means that the production of a particular layout depends on the levels of shift hours as well.
ii) The interaction plot between layout and shifts can be made from the "average" data. The plot is:
The table below shows the quantity of watches made by a company for different plant layout...
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