This article throws light upon the five important experimental designs for plant breeding programmes. The designs are: 1. Simple Experimental Designs 2. Augmented Design-I 3. Completely Randomized Design 4. Randomized Complete Block Design 5. Split Plot Design.
Contents
1. Simple Experimental Designs:
The difference among experimental plots treated alike is called experimental error. This error is the main basis for deciding whether an observed difference is real or just due to chance. Thus, every experimental design must have provision to measure experimental error.
This calls for:
Replication:
In the same way, that at least 2 plots of the same variety are needed to determine the difference among plots treated alike, experimental error can be measured only if there are at-least, 2 plots planted to the same variety (or receiving the same treatment). Thus, replication is a must to obtain a measure of experimental error.
Identifying the optimum number of replications in an experimental design is often a difficult job, even though commonly 4 replications have become a standard norm. Diwakar and Oswalt (1992) at ICRISAT have compiled a manual on research planning and data handling and have dealt with several statistical issues related to day to day experiments by the breeders and agronomists.
As per this compilation quoting standard publications, two procedures can be used to determine the optimum number of replications. The first procedure is based on a simple formula, where CV and SEM are known.
In this situation, number of replications (N) is calculated by the following formula:
N = (CV/SEM)2
where,
N = Optimum number of replications
CV = Coefficient of variation (%)
SEM = Standard error of mean
For example, if CV is 12% and SEM is 6, then
N = (12/6)2 = 4
In case, when, CV and SEM are not known, which is often the case, then number of replications can be arrived at using the principle that in order to increase precision of the experiment, the error variance should be kept to the minimum. This is achieved by providing more degrees of freedom for the error variance.
In other words, a lower number of degrees of freedom for experimental error results in enlarged experimental error. Based on this principle, it is generally, agreed that number of degrees of freedom for error component of variance should not be less than 15 and not less than 10 in any case.
Randomization:
Randomization is required to avoid personal bias, i.e. varieties must be assigned to experimental plots in such a way, that a particular variety is not consistently favoured or handicapped. This can be achieved by randomly assigning varieties to the experimental plots.
Control of Error:
All possible means of minimising the experimental error constitute error control. This is achieved by blocking, proper plot technique and appropriate data analysis.
2. Augmented Design-I:
This design is commonly used to evaluate a large number of germplasm lines, where seed is in small quantity and other designs are not appropriate due to large number of entries. In this design whole experimental area is divided into N plots (N = number of test genotypes, v + number of checks, c which are repeated b times at regular intervals). Thus N = v + be
Total number of entries, e = V + C
Conceptually, this design has been explained by Federer (1956).
A worked example as illustrated by Sharma (1998) is as follows:
Statistical Analysis:
General correction factor (GCF)
3. Completely Randomized Design:
The simplest of all designs having a random arrangement is the completely randomized design. In this design, the treatments are randomly arranged over the whole of experimental material. No effort is made to restrict treatments to any portion of entire area, material or space.
This design is used when variation over all of the experimental material is relatively small like in laboratories/greenhouse studies. The number of replications may vary for each treatment, but for simplicity of analysis, it is desirable to adopt equal number of replications for each of the treatment.
This design is easy to layout and allows the maximum number of degrees of freedom for error sum of square and thus, increases efficiency of the design. However, it should be kept in mind that this design is usually suited for small number of treatments and for homogeneous experimental area.
A worked example taken from Federer (1955) with calculation details for easy understandability is given below:
The data provided includes 4 treatments (A, B, C, and D) each replicated 5 times, but with no restriction on placement of treatments in the experimental area.
The compiled data is as follows:
Since the calculated value of F is more than the table value of F at treatment and error degrees of freedom at 0.05 p, the treatment differences are significant.
Various statistics may be computed from the above analysis of variance table.
(i) The standard error of a single observation or the standard deviation (SD) = square root of error mean square = √s2 = 722.42 = 26.87
(ii) The standard error of a treatment mean = S x̅ = s/√r = √722.42/5 = 12.0
(iii) Standard error of difference between two means = s d̅= √2EMS/r =16.99
(iv) The least significant difference (LSD) = Standard error of difference between two means x t value at error degree of freedom = 16.99 X 2.12 = 36.0
(v) The coefficient of variation = (SD/Mean) x 100 = 26.87/84.75 = 0.317 = 31.7%
4. Randomized Complete Block Design:
This is one of the most commonly used designs in agricultural research, particularly in plant breeding programmes. Its primary distinguishing feature is the presence of blocks (replications) of equal size, each of which contains all the treatments.
The calculated F value is more than the table value at 4 and 12 degrees of freedom at P = 0.01. Therefore, difference between mean values of 5 varieties is highly significant.
5. Split Plot Design:
This is specifically, suited for a 2 factor experiment that has more treatments than can be accommodated by a complete block design. One of the factors is assigned to the main plot and the main plot is divided into subplots, to which, the second factor is assigned.
The precision of the subplot factor is improved. For an experiment, having a = 6 as the number of main plots b = 4 as the number of subplots and r = 3 as that of replications, the analysis of variance table is as follows:
For analysing the data following steps are observed:
Construction of Two-Way Tables of Totals:
First, a 2-way table of totals involving replication X factor A is constructed. Another 2-way table includes totals of factor A and B and A x B table is constructed. Various sums of squares are calculated in usual way.
Replication x Main Plot Analysis (R X A)
With a significant interaction, caution must be exercised when interpreting the results.
Standard Error of the Mean Difference for Each of the Four Types of Pair Comparisons in a Split-Plot Design:
