Augmented design in R studio

1. Background 

Augmented designs was put forth by Federer in 1956 where controls (check varieties) are replicated in a standard experimental design. New treatments (genotypes) are not replicated or may have few replicates than the check varieties. 

2. Reasons of using 

A. Seeds, land and other resources are limited and the researcher wants to evaluate many genotypes as much as possible. And he can evaluate selection in subsequent season

B. There is difficulty to maintain homogeneous blocks in comparing different genotypes. This method provides a mechanism to adjust field variation. 

C. It is suitable for participatory plant breeding as a farmer may not be able to accommodate many replication so, he may prefer to grow genotypes with single replication (among many genotypes). 

3. Advantages of this design

A. Allows to evaluate more genotypes in many environment as it uses unreplicated design. It makes good use of scarce resources. 

B. The number of check plots are less than the designs that use systematic repetition .

C. It provides standard error estimates that can be used in comparing among and between new genotypes and check varieties. 

D. It is flexible as the block can be of unequal size.

4. Disadvantages of this design

A. Less degree of freedom for experimental error. 

B. As the design is unreplicated, it is  inherently less precise. 

5. Statistical model 

6. Field plan for augmented design

A. Sufficient number of check varieties and replicates  are to be included for providing good estimates of experimental error and detecting differences among varieties.

B. Blocks should be arranged along field gradient for maximizing variation among blocks and minimizing variation within blocks. 

C. Each of the checks should be assigned randomly at each block.

D. The new entries (genotypes) should be assigned randomly at remaining plots.

7. Format of design

In the figure, C1,C2 and C3 are check varieties. They are to be assigned randomly in each block. The remaining plots are to be used in random placing of other genotypes.

ANOVA

Source of these contents: Kling, J. n.d. Introduction to augmented design. Oregon State University. Available: https://pbgworks.org/sites/pbgworks.org/files/AugmentedDesignsFINAL.pdf

Further readings:
https://ecommons.cornell.edu/bitstream/handle/1813/32572/BU-480-M.pdf?sequence=1
https://ecommons.cornell.edu/bitstream/handle/1813/32841/BU-74-M.pdf?sequence=1&isAllowed=y
https://www.bioversityinternational.org/fileadmin/_migrated/uploads/tx_news/Data_analysis_manual_for_coconut_researchers_1291.pdf

8. Analysis in R studio 

During data entry in excel, assign block in the first column, followed by entries (treatment) and other variables to be tested. 

File used: aug.xlsx  (Note : Output is marked in blue color) 

https://drive.google.com/file/d/10VhW5R2FUFt2MJb4ps_fSP39CEdcYTSE/view?usp=sharing

A. Import the data set in R studio

B. Attach the dataset and change block and genotypes as factor ( see previous blogs) 

> attach(aug)

C. Select agricolae package 

> library(agricolae)

D. Run following commands ( based on your choice for mean separation) 

> out<-DAU.test(aug$block,aug$trt,aug$yield,method = "tukey",console = TRUE) or

> out<-DAU.test(aug$block,aug$trt,aug$yield,method = "lsd",console = TRUE)

ANALYSIS DAU:  aug$yield 

Class level information

Block:  I II III

Trt  :  1 10 11 12 13 14 15 16 17 18 19 2 20 21 22 23 24 25 26 27 28 29 3 30 31 32 33 34 35 36 37 38 39 4 40 41 42 43 44 45 5 6 7 8 9 A B C

Number of observations:  54 

ANOVA, Treatment Adjusted

Analysis of Variance Table

Response: aug$yield

                                                Df        Sum Sq       Mean Sq        F value      Pr(>F)    

block.unadj                              2          1.966          0.9829                      

trt.adj                                     47         88.656        1.8863         188.63       5.815e-05 ***

Control                                    2          18.620         9.3100        931.00       4.595e-06 ***

Control + control.VS.aug.     45         70.036          1.5563       155.63       8.544e-05 ***

Residuals                                 4           0.040          0.0100                      

---

Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

ANOVA, Block Adjusted

Analysis of Variance Table

Response: aug$yield

                                         Df       Sum Sq        Mean Sq         F value        Pr(>F)    

trt.unadj                            47        90.602           1.928                       

block.adj                            2           0.020           0.010            1.000      0.4444444    

Control                              2          18.620          9.310           931.000   4.595e-06 ***

Augmented                      44          33.878          0.770            76.995    0.0003461 ***

Control vs augmented       1          38.104         38.104        3810.387   4.125e-07 ***

Residuals                           4              0.040        0.010                       

---

Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

coefficient of variation: 0.8 %

aug$yield Means: 12.61167 

Critical Differences (Between)

                                                                              Std Error Diff.

Two Control Treatments                                          0.08164966

Two Augmented Treatments (Same Block)              0.14142136

Two Augmented Treatments(Different Blocks)         0.16329932

A Augmented Treatment and A Control Treatment      0.12472191

Treatments with the same letter are not significantly different.

   aug$yield  groups

29 16.433333       a

45 15.333333      ab

34 14.433333      bc

23 14.233333      bc

8  13.833333      cd

37 13.733333      cd

38 13.633333     cde

9  13.633333    cdef

41 13.533333   cdefg

24 13.533333  cdefgh

13 13.433333 cdefghi

20 13.433333 cdefghi

25 13.433333 cdefghi

18 13.333333 cdefghi

4  13.233333 cdefghi

17 13.133333 defghij

C  12.766667  efghij

12 12.733333  efghij

3  12.733333  efghij

36 12.733333 efghijk

33 12.633333 efghijk

42 12.633333 efghijk

44 12.633333 efghijk

7  12.633333 efghijk

27 12.633333 efghijk

10 12.533333  eghijk

11 12.533333  eghijk

15 12.533333  eghijk

2  12.533333  eghijk

32 12.533333  fghijk

39 12.533333   ghijk

40 12.533333   ghijk

43 12.533333   ghijk

22 12.533333   ghijk

28 12.533333   ghijk

5  12.463333   ghijk

14 12.433333   ghijk

31 12.433333    hijk

35 12.433333    hijk

16 12.433333     ijk

19 12.433333     ijk

21 12.433333     ijk

26 12.433333     ijk

30 12.333333     ijk

1  12.033333      jk

6  11.533333       k

B   9.766667       l

A   9.666667       l

Comparison between treatments means

<<< to see the objects: comparison and means  >>>

> plot(out)