Strip Plot Design Lecture - 51

 

Strip Plot Design 

Lecture - 51

Introduction 

The strip plot design is a suitable design for two-factor experiments like split plot design. In split plot design, the second factor is nested within the whole plot, and both factors are completely crossed. But in strip plot design, the experimental material is divided into horizontal (rows) and vertically (columns) strips and assigned two factors in such a manner that one level of factor A is assigned to each row and one level of factor B is assigned to each column.

The strip plot design is also considered a special type of factorial. The first factor is called the vertical factor, and the second factor is called the horizontal factor. The strip plot design is sometimes split block design and used when

1.      Both factors required large experimental units, or

2. The interaction factor is more important than individual factors.

In strip plot design, factor A is applied to whole plots like the usual split-plot designs, but factor B is also applied to strips, which are actually a new set of whole plots orthogonal to the original plots used for factor A. 

Layout of Strip Plot Design

Let us have two factors A with three levels (a0, a1, a3) and factor B with four levels (b0, b1, b2, b3) and use three replications.

The layout of the above strip experiment is explained below:

Step 1: Divide the experimental material into two blocks.

Replication 1

Replication 2

Step 2: Now divide each replication into 3 horizontal plots and assign factor A levels randomly.

Step 3: Now divide the same replication (replication 1) into 4 vertical factors and assign factor B levels randomly.

Repeat the same procedure for other replications.

Statistical model

Let Yijk be the response of j^th level of factor A and k^th level of factor B in the i^th replicate, then it can be represented by the following linear statistical model.

Yijk = μ + ρi + αj + (ρα)ij + βk + (ρβ)ik + (αβ)jk + ϵijk

i=1,2,...,r. 

j = 1, 2,..., a.

 k = 1, 2, ..., b

Where:

(ρα)ij, (ρβ)ik, and ϵijk are error components and independently normally distributed with zero mean and standard deviation σa, σb, σϵ.

Statistical Analysis

Let Yijk be the response of j^th level of factor A, k^th level of factor B in the i^th replicated. Let j = 2 and k = 3.

The data that can be obtained is tabulated as:

The above result can be expressed in terms of Y’s as:

Vertical Strip Analysis:

AR:

Horizontal Strip Analysis:

B R:

Interaction (A x B) Analysis:

ANOVA Table:

Interpretation

First test the AB interaction:

If the interaction AB is significant, the main effects have no meaning if they are significant.

If the interaction AB is non-significant, then look at the significance of main effects and summarize in the one-way tables of the means for factors with significant main effects.

Example

Suppose an experiment was conducted by using a strip plot design with the following details.

A1, A2 are horizontal levels of factor A, and B1, B2, and B3 are vertical levels of factor B. There were 5 replicates, and the data of yield in kg/ha is as follows:

Test the following hypotheses at 5%:

i. There is no significant difference between the main effects of factor A.

ii. There is no significant difference between the main effects of factor B.

iii. There is no interaction between A & B.

Solution:

Vertical Analysis:

Horizontal Analysis

Interaction of (A X B) analysis:

ANOVA Table:

Remarks:

The factor B is significant.

Advantages:

i. Strip plot design permits efficient application of factors that would be difficult to apply to small experimental units.

ii. Each factor and their interaction effects are compared with their associated mean squares of error.

Disadvantages:

i. Differential in precision in the estimation of interaction and the main effects.

Difference between Split Plot & Strip Plot Design

No.	Split Plot	Strip Plot
i	One factor is assigned to the main plot, and a second factor is assigned to the subplot.	Both factors are assigned to the whole plot.
ii	The second factor is nested with a whole plot factor.	The plot is divided vertically and horizontally.
iii.	Ability to accommodate the third factor when the experiment is in progress.	Have not the ability to introduce another factor when the experiment is in progress.

• Read More: Introduction to Statistics