types of checks in variety trials one could be a long term check that is unchanged from year to year...
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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