# Split Plot Design

The design in which the levels of one factor can be applied to large experimental units and the levels of other factors to the sub-units are known as “split plot design“.

A split plot experiment is a blocked experiment in which blocks serve as experimental units. After blocking the levels of other factors are randomly applied to large units within blocks, often called whole plots or main plots.

The split plot design are specifically suited for two factors designs that have more treatment to be accommodated by a complete block designs. In split plot design all the factors are not of equal importance. For example, in an experiment of varieties and fertilizers, the variety is less important and the fertilizer is more important.

In these design, the experimental units are divided into two parts, (i) Main plot and (ii) sub-plot. The levels of one factor are assigned at random to large experimental units (main plot) and the levels of the other (second) factor are applied at random the the sub-units (sub-plot) within the large experimental units. The sub-units are obtained by dividing the large experimental units.

Note that the assignment of a particular factor to either the main plot or to the subplot is extremely important, it is because the plot size and precision of measurement of the effects are not the same for both factors.

The sub-plot treatments are the combination of the levels of different factors.

The split plot design involves assigning the levels of one factor to main plots which may be arranged in a “CRD”, “RCBD” or “LSD”. The levels of the other factor are assigned to subplots within each main plot.

### Split Plot Design Layout Example

If there are 3 varieties and 3 fertilizers and we want more precision for fertilizers then with the RCBD with 3 replication, the varieties are assigned randomly to the main plots within 3 blocks using a separate randomization for each. Then the levels of the fertilizers are randomly assigned to the subplots within the main plots using a separate randomization in each main plot. The layout is

### Another Split Plot Design Example

Suppose we want to study the effects of two irrigation methods (factor 1) and two different fertilizer types (factor 2) on four different fields (“whole plots”). While a field can easily be split into two for the two different fertilizers, the field cannot easily be split into two for irrigation: One irrigation system normally covers a whole field and the systems are expensive to replace.

#### Advantages of Split Plot Design

• More Practical
Randomizing hard-to-change factors in groups, rather, than randomizing every run, is much less labor and time intensive.
• Pliable
Factors that naturally have large experimental units can be easily combined with factors having smaller experimental units.
• More powerful
Tests for the subplot effects from the easy-to-change factors generally have higher power due to partitioning the variance sources.
New treatments can be introduced to experiments that are already in progress.
• Cheaper to Run
In case of a CRD, implementing a new irrigation method for each subplot would be extremely expensive.
• More Efficient
Changing the hard-to-change factors causes more error (increased variance) than changing the easy-to-change factors a split-plot design is more precise (than a completely randomized run order) for the subplot factors, subplot by subplot interactions and subplot by whole-plot interactions.
• Efficient
More efficient statistically, with increased precision. It permits efficient application of factors that would be difficult to apply to small plots.
• Reduced Cost
They can reduce the cost and complexity of manipulating factors that are difficult or expensive to change.
• Precision
The overall precision of split-plot design relative to the randomized complete block design may be increased by designing the main plot treatment in a Latin square design or in an incomplete Latin square design.

#### Disadvantages of Split Plot Design

• Less powerful
Tests for the hard-to-change factors are less powerful, having a larger variance to test against and fewer changes to help overcome the larger error.
• Unfamiliar
Analysis requires specialized methods to cope with partitioned variance sources.
• Different
Hard-to-change (whole-plot) and easy-to-change (subplot) factor effects are tested against different estimated noise. This can result in large whole-plot effects not being statistically significant, whereas small subplot effects are significant even though they may not be practically important.
• Precision
Differential in the estimation of interaction and the main effects.
• Statistical Analysis
Complicated statistical analysis.
• Sources of Variation
They involve different sources of variation ad error for each factor.
• Missing Data
When missing data occurs, the analysis is more complex than for a randomized complete block design.
• Different treatment comparisons have different basic error variances which make the analysis more complex than with the randomized complete block design, especially if some unusual type of comparison is being made.

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