An Intuitive Graphical Approach to Understanding the Split-Plot Experiment

Figures & data

Table 1. A replicated 3-level design for paper manufacturing example

Replicate
	1	1	2	1	3	2	2	3	3
Prep Method	2	3	2	1	2	1	3	3	1
Tensile Strength	38.75	31	37.25	34.5	39.5	35.25	37.5	33.25	37.25

Figure 1. Experimental error representation CRD (a). Experimental error representation for SPD[CRD,RCBD] (b).

Table 2. Analysis of Variance for the CRD in Table 1.

Source	DF	SS	MS	F	Prob>F
Prep Method	2	32.097	16.048	3.384	0.1038
Error	6	28.458	4.743
C.Total	8	60.555

Table 3. RCBD for the 3-level Paper Manufacturing Example

Day
Prep Method Tensile Strength	1			2			3
	1	3	2	2	3	1	1	2	3
	34.5	31	38.75	37.25	33.25	35.25	37.25	39.5	37.5

Table 4. Analysis of Variance Table for RCBD Analysis of Data in Table 3.

Source	DF	SS	MS	F	Prob>F
Prep Method	2	32.097	16.048	7.078	0.0485
Day	2	19.389	9.694
Error	4	9.09	2.267
C.Total	8	60.555

Figure 2: Experimental error representation for RCBD (a). Whole-plot experimental error and whole-plot treatment effect representation for SPD[RCBD,RCBD] (b).

Table 5: Randomization of the Whole-Plot Factor Prep Method Replicated Three Times.

Replication
Prep Method	1	1	2	1	3	2	3	2	3
	2	1	1	3	1	2	2	3	3

Table 6: Randomization of the SPD[CRD,RCBD] in Prep Method and Temp

Replication
Prep Method	1	1	2	1	3	2	3	2	3
	2	1	1	3	1	2	2	3	3
Temp	275	200	275	200	275	275	200	200	225
	250	225	250	225	250	200	250	250	250
	225	275	225	250	200	225	225	275	200
	200	250	200	275	225	250	275	225	275

Table 7: Analysis of variance for SPD[CRD,RCBD]

Source	DF	SS	MS	F	Prob>F
Prep Method	2	128.39	64.19	3.38	0.1038
Reps (Prep Method) Whole-plot Error	6	113.83	18.97	.	.
Temp	3	434.08	144.69	36.43	< 0.0001
Prep Method x Temp	6	75.17	12.53	3.15	0.0271
Sub-plot Error	18	71.50	3.97	.	.

Table 8: Randomization of the SPD[RCBD,RCBD] in Prep Method and Temp

Day 1				Day 2			Day 3
Prep Method	2	3	1	1	3	2	3	1	2
Temp	275(42)	200(29)	275(36)	200(28)	275(40)	275(40)	200(32)	200(31)	225(40)
	250(38)	225(26)	250(37)	225(32)	250(32)	200(31)	250(39)	250(41)	250(39)
	225(41)	275(36)	225(35)	250(40)	200(31)	225(36)	225(34)	275(40)	200(35)
	200(34)	250(33)	200(30)	275(41)	225(30)	250(42)	275(45)	225(37)	275(44)

Table 9: Analysis of variance for the SPD[RCBD,RCBD] case

Source	DF	SS	MS	F	Prob>F
Day	2	77.56	38.78	.	.
Prep Method	2	128.39	64.19	7.08	0.0485
Reps (Prep Method) Whole-plot Error	4	36.28	9.07	.	.
Temp	3	434.08	144.69	36.43	< 0.0001
Prep Method x Temp	6	75.17	12.53	3.15	0.0271
Sub-plot Error	18	71.50	3.97	.	.

Table 10: Sub-Plot Structure for one Prep Method

Batch Number Nested within Prep Method (Blocking variable at the Sub-Plot Level)
	1				2				3
Temp	200	225	250	275	200	225	250	275	200	225	250	275

Figure 3: Replication(Block) by Temp interaction for Prep Method 1 (3a). Replication(Block) by Temp interaction for Prep Method 2 (3b). Replication(Block) by Temp interaction for Prep Method 3 (3c).