Basic Concept, Randomization, ANOVA, Solved Example and Demonstration in Agri Analyze

        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.

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:

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.

Agri Analyze is the tool that helps researchers to perform analysis of design of experiments online.

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.

Step 10: After submit
download analysis report. 

Output of the Analysis

Link of the Output Report

Link of the Split Plot Quiz

REFERENCES

Gomez, K. A., & Gomez, A. A. (1984). Statistical
Procedures for Agricultural Research. John wiley & sons. 50-67.

This Blog is written by

Darshan Kothiya

MSc Scholar 

Department of Agricultural Statistics

Anand Agricultural University