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. r c =replications of checks r =replications of new entries   LSI t rcrc rMSErcrrcr   /

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 rcrc 1MSErcrc   /

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 Y ij =  + B i + T j + e ij –a i = X i - X –therefore  i a i = 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 i Y Y a ^  i i a X X  

ANOVA SourcedfSSMS Totalrc-1SSTot = Blocksr-1SSR = Checksc-1SSC = Error(r-1)(c-1)SSE = SSTot - SSR - SSC MSE=SSE/dfE

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 block r=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 IIIIIIIVVVI C1C1C1C1C1C1 V14C2V18V9V2V29 V26V4V27V6V21V7 C2V15C2C2C3C2 V17V30V25C3C2V1 C3V3V28V20V10C3 V22C3V5V11V8V12 V13V24C3V23V16V19 C1 is placed systematically first in each block as a “marker”

RBD analysis of check means SourcedfSSMS Total177,899,564 Blocks56,986,486 Checks220,051 Error10911,02791,103 estimate of experimental error to be used in LSI computation

Yields, Totals, and Means of Checks VarietyIIIIIIIVVVIMean C C C Mean Adjust 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% = –LSI = (1.812) ((6+1)(3+1)(91103)/(6*3) = 1.812*376=681 Any adjusted selection greater than – =3440 significantly outyields C1 – =3407 significantly outyields C2 – =3359 significantly outyields C3

SelectionAdj YieldSelectionAdj YieldSelectionAdj Yield Cimmaron Waha Stork  ()( /(* vc s rcMSErc  (()())/ )63)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 Cimmaron Waha

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