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. Is there any layout and/or shifts that maximizes production? Explain your answer
2. In your own words, give the difference between a one-way ANOVA and a two-way ANOVA
3. Use Minitab or Microsoft Excel.

Answer 1

Let's do the two-way ANOVA in excel. Enter the data in excel as follows. Then go to Data -> Data analysis -> two-way anova with replication and enter the following:

The output is:

Anova: Two-Factor With Replication
SUMMARY	Shift 6	Shift 8	Shift 12	Total
Layout 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
Layout 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
Layout 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
Layout	4053689	2	2026844	81.17901	3.8E-12	3.354131
Shifts	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

If we take a look at the p-value column, we can see that that there is a significant difference in mean production between layout and shifts. Also, there is a significant interaction effect between both the variables. Hence, we can find out a layout & shift in which maximizes production. Let's take a look at each table for different layouts and observe the row which tells us the averages (marked in italics), we can see that the highest average is of Layout 3 and Shift with 12 hours having an average of 1800 (marked in bold).

Hence, layout and shift which maximizes production is Layout 3 and shift with 12 hours.

2. The difference between a one-way anova and two-way anova is that the former has only one independent variable and the latter has two or more independent variables. In this case, we have two independent variables, Layout and Shift, hence this is a two-way ANOVA. If there was only one independent variable, Shifts or Layout, it would have been a one-way ANOVA.