Question

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

1. What are the effects of layout and shift hours on quantity of watches produced? Explain your answer using the p-values.
2. Plot an Interaction plot between layout and shifts.

Answer 1

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:

Interaction Plot 2000 1800 1600 1400 1200 1000 Layout 1 800 Layout 2 600 Layout 3 400 200 0 6-hour 8-hour 12-hour Shifts Production