Types of Checks in Variety Trials One could be a long term check that is unchanged from year to year –serves to monitor experimental conditions from year.

Types of Checks in Variety Trials One could be a long term check that is unchanged from

year to year– serves to monitor experimental conditions from year to year– is a baseline against which to measure progress

Other checks may be included for different purposes– a “local” variety would be good if comparing diverse locations– might want a susceptible to get a baseline for disease

expression– a new variety could serve as the “best” current standard

Replication of Checks Because all new entries are compared to the

same checks, the checks should be replicated at a higher rate than any of the new entries– number of replications of a check should be the

square root of the number of new entries in the trial

– so if you had 100 new entries, you would need 10 replications of the check for each replication of the new entries.

rc=replications of checksr =replications of new entries

LSI t rc r MSE rcr /

Early Stage Yield Trials Seed is precious - in early stages, usually not enough to

replicate Could plant small plots (often single rows) and at regular

intervals plant a check– consider how many adjacent plots are likely to be grown under

uniform conditions, given the soil heterogeneity, and the sensitivity of the crop and response variables to environmental factors; plant a check at appropriate intervals

– could make subjective comparisons of new entries with nearest check

– alternatively, get an estimate of experimental error from the variation among the checks. Then compute an LSI to compare the yields of the new lines to the checks

LSI t rc 1 MSE rc /

Early Stage Yield Trials But there are disadvantages

– the checks are often systematically placed, so estimate of experimental error may not be valid

– no provision is made to adjust yields for differences in soil, etc.

Augmented Designs – An alternative

Introduced by Federer (1956)

Controls (check varieties) are replicated in a standard experimental design

New treatments (genotypes) are not replicated, or have fewer replicates than the checks – they augment the standard design

Augmented Designs - Advantages Provide an estimate of standard error that can be

used for comparisons– Among the new genotypes– Between new genotypes and check varieties

Observations on new genotypes can be adjusted for field heterogeneity (blocking)

Unreplicated designs can make good use of scarce resources

Fewer check plots are required than for designs with systematic repetition of a single check

Flexible – blocks can be of unequal size

Some Disadvantages Considerable resources are spent on production

and processing of control plots

Relatively few degrees of freedom for experimental error, which reduces the power to detect differences among treatments

Unreplicated experiments are inherently imprecise, no matter how sophisticated the design

Applications of Augmented Designs

Early stages in a breeding program– May be insufficient seed for replication– Using a single replication permits more genotypes to

be screened

Participatory plant breeding– Farmers may prefer to grow a single replication when

there are many genotypes to evaluate

Farming Systems Research– Want to evaluate promising genotypes (or other

technologies) in as many environments as possible

Augmented Design in an RBD

Area is divided into blocks – these are incomplete blocks because they contain only a subset of

the entries

Two or more check varieties are assigned at random to plots within the blocks– same check varieties appear in each block– little is lost if you want to place one check systematically - a block

marker

Most efficient when block size is constant

Checks are replicated, but new entries are not

So how many blocks? Need to have at least 10 degrees of freedom for error in

the ANOVA of checks

df for error = (r-1)(c-1)– c=number of different checks per block– r=number of blocks=number of replicates of a check

Minimum blocks would be r > [(10)/(c-1)] + 1

For example, with 4 checks

[(10)/(4-1)]+1=(10/3)+1=3.33+1=4.33 ~ 5

you would need 5 blocks

Each block has at least c+1 plots

Analysis Experimental error is estimated by treating the

checks as if they were treatments in a RBD

MSE is then used to construct standard errors for comparisons

_

Adjustments for block differences– based on difference between block check means and over-all

check mean* – Recall Yij = + Bi + Tj + eij

– ai = Xi - X– therefore iai = 0

*this calculation assumes that blocks are fixed effects(we will use this simplification to illustrate the concept)

Steps in the Analysis Construct a two way table of check variety x block

means

Compute the grand mean and the mean of the checks in each block

Compute the block adjustment as

Adjust yields of new selections as

Complete a standard ANOVA (RBD) using check yields

ij ij iY Y a^

i ia X X

ANOVA

Source df SS MS

Total rc-1 SSTot =

Blocks r-1 SSR =

Checks c-1 SSC =

Error (r-1)(c-1) SSE = SSTot - SSR - SSC MSE=SSE/dfE

2i j ijY Y

2iit Y Y

2jjr Y Y

Standard Errors Difference between two check varieties

Difference between adjusted means of two selections in the same block

Difference between adjusted means of two selections in different blocks

Difference between adjusted selection and check mean

c=number of different checks per blockr=number of blocks=number of replicates of a check

Numerical Example Testing 30 new selections using 3 checks

Number of blocks:– ((10)/(c-1))+1 = (10/2)+1 = 6

Number of selections per block:– 30/6 = 5– Randomly assign selections to blocks

Total number of plots– (5+3)*6=48

Field Layout

I II III IV V VI

C1 C1 C1 C1 C1 C1

V14 C2 V18 V9 V2 V29

V26 V4 V27 V6 V21 V7

C2 V15 C2 C2 C3 C2

V17 V30 V25 C3 C2 V1

C3 V3 V28 V20 V10 C3

V22 C3 V5 V11 V8 V12

V13 V24 C3 V23 V16 V19

C1 is placed systematically first in each block as a “marker”

RBD analysis of check means

Source df SS MS

Total 17 7,899,564

Blocks 5 6,986,486

Checks 2 20,051

Error 10 911,027 91,103

estimate of experimental error to be used in LSI computation

Yields, Totals, and Means of ChecksVariety I II III IV V VI Mean

C1 2972 3122 2260 3348 1315 3538 2759

C2 2592 3023 2918 2940 1398 3483 2726

C3 2608 2477 3107 2850 1625 3400 2678

Mean 2724 2874 2762 3046 1446 3474 2721

Adjust 3 153 41 325 1275 753

se difference between 2 adj means of selections in different blocks

=

se difference between adjusted selection mean and check=

t value has (r-1)(c-1) = 10 df

-

A Comparison Statistic Because we are looking for those that exceed the

check, we compute LSI– 1-tailed t with 10 df at α=5% = 1.812– LSI = (1.812) ((6+1)(3+1)(91103)/(6*3) =

1.812*376=681

Any adjusted selection greater than– 2759+681=3440 significantly outyields C1– 2726+681=3407 significantly outyields C2– 2678+681=3359 significantly outyields C3

Selection Adj Yield Selection Adj Yield Selection Adj Yield

11 3055 Cimmaron 2726 13 238821 2963 22 2702 20 23453 2902 Waha 2678 2 2330

19 2890 24 2630 15 23244 2865 17 2569 1 2260

26 2852 10 2568 29 216227 2816 18 2562 5 202430 2802 8 2528 9 194325 2784 7 2512 28 186216 2770 23 2445 6 1823

Stork 2759 14 2402 12 1632

( )( )( / ( *vcs r c MSE rc (( )( ) ) /1 1 6 1 3 1 91103) 6 3) 376

The standard error of the difference between adjusted selection yield and a check mean

Compute the LSI using a 1-tailed t and 10 degrees of freedom (MSE)

Stork 2759+681 3440Cimmaron 2726+681 3407Waha 2678+681 3359

Interpretation Although the adjusted yield of 10 of the new

selections was greater than the yield of the highest check, C1, none of the yields was significantly higher than any of the check means

Variations in Augmented Designs New treatments may be considered to be fixed or

random effects– best to use mixed model procedures for analysis

Can adjust for two sources of heterogeneity using rows and columns

Modified designs use systematic placement of controls

Factorials and split-plots can be used

Partially replicated (p-rep) augmented designs use entries rather than checks to estimate error and make adjustments for field effects