Split Plot Design: Basic Concept, Randomization, ANOVA, Solved Example and Demonstration in Agri Analyze

This blog is about Split plot design, randomization, ANOVA, solved example with steps and demonstration of split plot analysis in Agri Analyze platform. Quiz on split plot design is given below (Reading time 15min)

The split-plot design is commonly employed in factorial experiments. This design can integrate various other designs, such as completely randomized designs (CRD) and randomized complete block designs (RCBD). The fundamental principle involves dividing whole plots or whole units, to which levels of one or more factors are applied (main plots). These main-plots are then subjected to levels of one or more additional factors called sub plot. Consequently, each whole unit functions as a block for the treatments applied to the sub-units.

In a split-plot design, the precision in estimating the main plot factor's effect is reduced to enhance the precision of the sub-plot factor's effect. This design allows for more accurate measurement of the sub-plot factor's main effect and its interaction with the main plot factor compared to a randomized block design. However, the precision in measuring the main plot treatments (i.e., the levels of the main plot factor) is less than that achieved with RCBD.

Ideal applications of this design

A split-plot design is particularly advantageous when treatments associated with one or more factors necessitate larger experimental units than treatments for other factors. For instance, in a field experiment, factors such as methods of land preparation or irrigation application typically require large plots or experimental units. In contrast, another factor, like crop varieties, can be evaluated using smaller plots. The split-plot design ensures efficient resource utilization and enhances the precision of certain factor measurements, making it ideal for complex experimental setups with hierarchical treatment structures.

1. The split-plot design is also beneficial when incorporating an additional factor to broaden the scope of an experiment. For example, if the primary goal is to compare the effectiveness of various fungicides in protecting against disease infection, the experiment's scope can be expanded by including several crop varieties known to differ in disease resistance. In this setup, the varieties can be arranged in whole units, while the fungicide treatments (seed protectants) are applied to sub-units. This approach allows for a comprehensive analysis of both fungicide efficacy and varietal resistance within a single experimental framework, optimizing resource use and experimental precision.

Randomization and layout strategies for split-plot experiments

In a split-plot design, there are distinct randomization procedures for the main plots and sub-plots. Within each replication, main plot treatments are initially randomly allocated to the main plots. Subsequently, sub-plot treatments are randomly assigned within each main plot. This sequential randomization ensures independent and controlled assignment of treatments at both the main plot and sub-plot levels, maintaining the integrity and statistical validity of the experimental design.

Step 1: Partition the experimental area into "r" replications, each subdivided into "a" main plots.

Step 2: Randomly assign the treatment levels to the main plots within each replication independently.

Step 3: Partition each replication into "a" main plots, and within each main plot, partition into 'b' sub-plots. Randomly assign the levels of the sub-plot factors within each sub-plot.

Advantage of split plot design:

In a split-plot design, the effects of sub-plot treatments and their interactions with main plot treatments are tested with greater precision than the effects of the main plot treatments.

This design is more convenient for handling agricultural operations. When treatments such as irrigation, tillage, sowing dates, and other cultural practices are involved, these treatments can be assigned to the main plots.

Due to the combination of factors within the same experiment, this design incurs very little extra cost. Conducting separate experiments for each factor would be more expensive.

It saves experimental area and resources by devoting them only to the border rows in the main plot.

Disadvantage of split plot design

1. We lose precision for main plot treatments but gain precision for sub-plot treatments.

With the limitation of experimental area, the degrees of freedom for error often do not meet the minimum requirement of 12.

When missing plots occur, the analysis becomes more complicated.

EXAMPLE FOR SPLIT PLOT DESIGN

A split-plot design was used to investigate the effects of irrigation levels (main plot factor) and fertilizer types (sub-plot factor) on the yield of a particular crop. The experiment was conducted over four replicates (R1, R2, R3, R4).

Main Plot Factor (A - Irrigation Levels):

A1: Low Irrigation

A2: Medium Irrigation

A3: High Irrigation

Sub-Plot Factor (B - Fertilizer Types):

B1: Organic Fertilizer

B2: Inorganic Fertilizer

B3: Mixed Fertilizer

Data:

Treatments	R1	R2	R3	R4
A1B1	386	396	298	387
A1B2	496	549	469	513
A1B3	476	492	436	476
A2B1	376	406	280	347
A2B2	480	540	436	500
A2B3	455	512	398	468
A3B1	355	388	201	337
A3B2	446	533	413	482
A3B3	433	482	334	435

Solution:

Treatments	R1	R2	R3	R4	Treatment total	Treatment means
A1B1	386	396	298	387	1467	366.75
A1B2	496	549	469	513	2027	506.75
A1B3	476	492	436	476	1880	470.00
A2B1	376	406	280	347	1409	352.25
A2B2	480	540	436	500	1956	489.00
A2B3	455	512	398	468	1833	458.25
A3B1	355	388	201	337	1281	320.25
A3B2	446	533	413	482	1874	468.50
A3B3	433	482	334	435	1684	421.00
Total	3903	4298	3265	3945	15411

A x B table:

	B1	B2	B3	Total A
A1	1467	2027	1880	5374
A2	1409	1956	1833	5198
A3	1281	1874	1684	4839
Total B	4157	5857	5397

Main factor (A) x Replication table:

	R1	R2	R3	R4
A1	1358	1437	1203	1376
A2	1311	1458	1114	1315
A3	1234	1403	948	1254

Calculation of Degrees of Freedom

Replication DF = r – 1 = 4 – 1 = 3

Main Plot DF = A – 1 = 3 – 1 = 2

Error a DF = (r-1)*(A-1) = 6

Sub Plot DF = B – 1 = 3 – 1 = 2

Interaction DF = (A-1) * (B-1) = 4

Error b DF = A*(r-1)*(B-1) = 18

Total DF = A*B*r – 1 = 35

The Mean Square for different component is obtained by dividing SS with DF for respective component

Calculated F value for different ANOVA components

Replication Cal F = Replication MS / Error a MS = 28.12

Main Plot A Cal F = Main Plot A MS / Error a MS = 8.48

Sub Plot B Cal F = Sub Plot B MS / Error b MS = 186.61

Interaction Cal F = Interaction MS / Error b MS = 0.22

Final ANOVA Table for Crop Yield Analysis Using Split-Plot Design with Irrigation (Main Plot Factor) and Fertilizer (Sub Plot Factor) Treatments:

SV	DF	SS	MS	CAL F	Table F 5%	Table F 1%
Replication	3	61636.97	20545.66	28.12	3.16	8.49
Main Plot A	2	12391.17	6195.58	8.48	5.14	10.92
Error (a)	6	4382.61	730.44	-	-	-
Sub Plot B	2	128866.67	64433.33	186.61	3.55	6.01
Interaction	4	304.17	76.04	0.22	2.93	4.58
Error (b)	18	6215.17	345.29	-	-	-
Total	35	213796.75	-	-	-	-

Conclusion:

· The calculated F-value (28.12) is much greater than the critical F-values at both 5% (3.16) and 1% (8.49) significance levels. Therefore, there is strong evidence to suggest that there are significant differences between the replicates.

· The calculated F-value (8.48) for main factor exceeds the critical F-value 5% (5.14) significance levels. This indicates that there are significant differences among the irrigation level.

· The calculated F-value (186.61) for sub factor exceeds the critical F-value at 1% (6.01) significance level. This indicates that there is highly significant variation among level of fertilizer.

· The calculated F-value (0.22) for interaction between main factor and sub factor (A x B) which is less than critical F-value at 5% (2.93) significance level. This indicate that there is non-significant interaction between irrigation and fertilizer.

· For the irrigation, highest yield was observed for A1 and A2 were found statistically at par with it based on critical difference.

· For the fertilizer, highest yield was observed for B2 and none of the level of fertilizer at par with it based on critical difference.

For the interaction (A x B), highest yield was observed for A1 x B2 and A2 x B2 were found statistically at par with it.

Steps to perform analysis of split plot design in Agri Analyze

Step 1: To create a CSV file with columns for replication, main factor (A), sub factor (B) and Yield. Link of the data

Step 2: Go with Agri Analyze site. https://agrianalyze.com/Default.aspx

Step 3: Click on ANALYTICAL TOOL

Step 4: Click on DESIGN OF EXPERIMENT

Step 5: Click on SPLIT PLOT DESIGN ANALYSIS

Step 6: Click on SPLIT PLOT 1,1 (SPLIT PLOT) ANALYSIS

Step 7: Select CSV file.

Step 8: Select replication, main factor (A), sub factor (B) and dependent variable (Yield).

Step 9: Select a test for multiple comparisons, such as the Least Significant Difference (LSD) test, to determine significant differences among groups. Same as for Duncan’s New Multiple Range Test (DNMRT), Tukey’s HSD Test.