Help - Augmented Designs

Overview

Block designs are useful in experiments requiring eliminations of heterogeneity in one or two directions. Randomized block design or any such design becomes inadequate or inefficient under the following two conditions:

  1. When seeds of test genotypes are small in quantity so that replications are not possible.
  2. When large numbers of germplasm collections are to be evaluated; limited facility of uniform land becomes a bottleneck.

Such a huge collection cannot be accommodated in Randomized Block Design (RBD) as soil heterogeneity becomes unmanageable. In the absence of error term (error variance) in the ANOVA (Analysis of Variance), without replications, tests of significance cannot be applied. However, both these problems can be surmounted by employing Augmented Design.

Introduction

These types of situations came to be known to Federer around 1955 in screening new strains of sugarcane and soil fumigants used in pineapples. New designs known as Augmented (Hoonuiaku) designs were introduced by Federer (1956) to fill a need arising in screening new strains of sugarcane based on agronomic characters other than yield.

Federer (1956, 1961) provided the analysis, randomization procedure, and construction of these designs by adding new treatments to the blocks of RCB design and balanced lattice designs in control treatments. Augmented design eliminating heterogeneity in one direction is called augmented block design, while those eliminating heterogeneity in two directions are called augmented row-column designs.

Models Proposed by Federer

Federer (1956) proposed three models:

  1. Augmented Completely Randomized Design (Augmented Design I).
  2. Augmented Randomized Complete Block Design (Augmented Design II).
  3. Augmented Latin Square Design (Augmented Design III).

Test Treatments with Single Replication

a. Augmented Design I

When the number of seeds is a limitation, this type of design is most suited. In this design, the whole experimental area is divided into N plots (where N is equal to the number of test genotypes (V) + number of checks (C), which are standard varieties or hybrids of known performance) repeated b times, i.e., N = V + bC; and total number of entries, e = V + C. All the N plots are allotted randomly for all V and C, the latter repeated b times. Blocks are not marked at all.

b. Augmented Design II

Augmented designs have several advantages over randomized complete block design such as:

  1. More than one control treatment is included.
  2. Standard error of differences between new treatments is available.
  3. Using the survivors of previous screening stage as the control is a device for testing the survivors at the same time that a new set of genotypes is being screened.
  4. Fewer cycles of selection are needed than for the standard method.

This is a slightly modified version of Augmented Design I, where instead of repeating all the checks b times throughout the field, the whole field is divided distinctly into b-blocks. Then randomization is done such that all the checks and a part of test genotypes fall only once in each block. Thus, the total number of plots (N) remains the same as in Design I (if the same number of V and C are used) but the number of plots in each block is variable.

Field Plan and Randomization

An illustration using the example given in Augmented Design I, i.e., V = 8 (V1 to V8), C = 4 (C1 to C4), b = 3, e = 12, and N = 20. Now divide the whole experimental field into (b = 3) distinct blocks:

  1. Block 1, consisting of (say) 7 plots (C1 to C4 + V1, V4, and V8).
  2. Block 2, comprising (say) 6 plots (C1 to C4 + V2 and V3).
  3. Block 3, encompassing (say) 7 plots (C1 to C4 + V5, V6, and V7).

So as to construct a relatively homogeneous stratification of area in each block. The number of test varieties falling in each block are n = 3, 2, and 3, respectively. For random allocation of these treatments in the experiment, proceed as follows:

Data Arrangement for Analysis Using Online Tool

The blocks must be coded as 1, 2, and 3, controls must be coded as C1, C2, C3, and C4, and the entries/varieties must be coded as V1, V2, V3, …, V8. Now enter these codes in MS Excel as per the following criteria:

  1. In the first column, the codes of the block number.
  2. In the second column, the codes of controls/checks (C1, C2, …) and entries/varieties (V1, V2, …).
  3. In the third column, enter the observed value of control or variety.

Example Data from an Augmented Block Design

Consider the field layout of Augmented Design II. The observed data is given in the table:

Blocks Experimental units
1 N8 (74), C3 (78), C4 (78), N3 (70), C1 (83), C2 (77), N7 (75)
2 C4 (91), C2 (81), C1 (79), C3 (81), N1 (79), N5 (78)
3 N4 (96), C3 (87), C1 (92), N2 (89), C4 (81), C2 (79), N6 (82)

Arrange the data as given below in Excel or any text editor:

1    C1    83
1    C2    77
1    C3    78
1    C4    78
1    V3    70
1    V7    75
1    V8    74
2    C1    79
2    C2    81
2    C3    81
2    C4    91
2    V1    79
2    V5    78
3    C1    92
3    C2    79
3    C3    87
3    C4    81
3    V4    96
3    V2    89
3    V6    82

Copy the data and paste it in the text area provided in the data entry interface. Also, enter the character name in the text area for character name as shown below:

Press Enter and data will be analyzed, and results will be displayed on a separate web page.

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