# Split-Plot Design: Examples & Design Layout

## What is Split-Plot Design

A split-plot design is a special form of factorial design when there are two treatment factors and either the effects of one factor are likely to be substantially larger than the other or one factor involves operations such as mechanical cultivation that cannot be easily applied to a small plot.

It can be arranged in randomized blocks, in Latin squares, or in any other suitable design. But, generally, RBD is preferred.

## Choice of Main Plot and Sub-Plot Design

#### Degree of precision

For a greater degree of precision for factor B than A, assign factor B to the subplot and Factor A to the main plot.

#### The relative size of the main effects

If the main effect of one factor (factor B) is expected to be much larger and easier to detect than that of the other factor(factor A), Factor B can be assigned to the main plot and factor A to the subplot.

For eg, in a fertilizer X variety experiment, the researcher may assign variety to the subplot and fertilizer to the main plot because he/she expects the fertilizer effect to be much larger than the varietal effect.

## Management Practices

The cultural practices required by a factor may dictate the use of large plots. For practical feasibility, such a factor may be assigned to the main plot. For e.g. water management and variety, it may be desirable to assign water management to the main plot and varieties as subplots.

The chief practical advantage of this design is that it enables to include a factor that requires a relatively large amount of materials and another factor that requires only a small amount of materials to be combined in the same experiment.

## Randomization & Layout

There are two separate randomization processes in a split-plot design. One for the main plot and another for the subplot.

In each replication (block), main plot treatments are fist randomly assigned to the main plots followed by a random assignment of the subplot treatments within each main plot.

In a split-plot design, one of the factors is assigned to the main plot. The assigned factor is called the main plot factor. The main plot is divided into subplots to which the second factor, called the subplots factor, is assigned. Thus, each main plot becomes a block for the subplot treatments (i.e. the levels of the subplot factor).

Suppose there are r blocks(replications), each block is divided into p whole plots, and each whole plot is divided into q subplots. Within each block, the p levels of factor A are allocated at random to the p whole plots and within each whole plot, the q levels of factor B are allocated at random to the q subplots.