🧣 Other Designs

Layout, Statistical Analysis, Pros & Cons, Applications

Split Plot Design (SPD) ^{NABARD Mains 2020}

In field experiments certain factors may require larger plots than for others. For example, experiments on irrigation, tillage, etc. requires larger areas. On the other hand, experiments on fertilizers, etc. may not require larger areas.
To accommodate factors which require different sizes of experimental plots in the same experiment, split plot design has been evolved.
In this design, larger plots are taken for the factor which requires larger plots. Next each of the larger plots is split into smaller plots to accommodate the other factor. The different treatments are allotted at random to their respective plots. Such arrangement is called split plot design.
In split plot design the larger plots are called main plots and smaller plots within the larger plots are called as sub plots.
The factor levels allotted to the main plots are main plot treatments and the factor levels allotted to sub plots are called as sub plot treatments.

👉🏻 This design used under following condition:

When factors of the different nature are to be tested in same experiment that is level of one factor require larger area as compared to other factor e.g. Depth of ploughing and nitrogen level, date of sowing and varieties, varieties and nitrogen level, irrigation level and varieties.
When all factors aren’t important.
When all the levels of one factor produce larger differences as compared with the levels of other factors.
When we want to study one factor with higher precision as compared to other factor and take it in sub plots (Smaller Plot).

The analysis of variance will have two parts, which correspond to the main plots and sub-plots.
For the main plot analysis, replication X main plot treatments table is formed. From this two-way table sum of squares for replication, main plot treatments and error (a) are computed. For the analysis of sub-plot treatments, main plot X sub-plot treatments table is formed.
From this table the sums of squares for sub-plot treatments and interaction between main plot and sub-plot treatments are computed.
Error (b) sum of squares is found out by residual method. The analysis of variance table for a split plot design with m main plot treatments and s sub-plot treatments is given below.
Analysis of variance for split plot with factor A with m levels in main plots and factor B with s levels in sub-plots will be as follows:

This design is used when both the factors require relatively large area.
This design is also known as split block design. When there are two factors in an experiment and both the factors require large plot sizes it is difficult to carry out the experiment in split plot design. Also, the precision for measuring the interaction effect between the two factors is higher than that for measuring the main effect of either one of the two factors. Strip plot design is suitable for such experiments.
In strip plot design each block or replication is divided into number of vertical and horizontal strips depending on the levels of the respective factors.

The plot size for the treatments allotted in vertical strips will not be equal when compared to the treatments allotted in horizontal strips
In this design there are three plot sizes.
- Vertical strip plot for the first factor – vertical factor
- Horizontal strip plot for the second factor – horizontal factor
- Interaction plot for the interaction between 2 factors
The vertical strip and the horizontal strip are always perpendicular to each other.
The interaction plot is the smallest and provides information on the interaction of the 2 factors.
Thus, we say that interaction is tested with more precision in strip plot design.

The analysis is carried out in 3 parts.
- Vertical strip analysis
- Horizontal strip analysis
- Interaction analysis
Suppose that A and B are the vertical and horizontal strips respectively. The following two-way tables, viz., A X Rep table, B X Rep table and A X B table are formed. From A X Rep table, SS for Rep, A and Error (a) are computed. From B X Rep table, SS for B and Error (b) are computed. From A X B table, A X B SS is calculated.
When there are r replications, a level for factor A and b levels for factor B, then the ANOVA table is