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OPTIMAL STRATEGIES FOR REGIONAL
YIELD TESTS OFCULTIVARS
Ross S. Kingwell
Adviser,
Division of Agricultural Economics
and Marketing,
Department of Agriculture t
western AUstralia.
2
In the plant breeding programmes of many countries field assessment of
potential new cult1vars involves comparing their characteristics (for
example~ yield and disease resistance) to those of one or more standard
cult1vars. Cultivar comparison usually involves a series of field trials
replicated over sites and years. The usual aim of these trials is to
identify which potential new cultivars are genuinely superior to the
standard or convnonly grown cultivars. However. the very nature of both the
cultivars and the environments in which field testing ocCUrs commonly
introduces risks in selecting or identifying "trulY" superior cultiva.rs~
Cultivarsrarely perform uniformly across locations and years.
Consequently, the ranking ofcultivars 1s seldom the same at each location
or in each year. The interaction of cultivars with their test environment
(genotype x environment interaction) means that it is unlikely for superior
cultiVars to be identified on the bas.is of a single year's testing at a
sin91esite. Hence the question often arises; Over hoW many years,
locations and plot replications should the field testing of cultivars take
place before one lsreasonably sure that a ··truly" super10rcultivar has
been identified.
This question has almost solely concerned biologists and biometricians
(Sprague and Federer; Finney; Patterson ,!:It ali Talbot). rather than
agri.cultural economists. The work of the f\lrmer group, perhaps to be
expected, has involved analyses that ignore financial costs (Finney;
Patterson ~t ali Talbot), capture only some of the costs of field testing
(Spra9ueand Federer) or that consider mainly technical restrictions on the
cQmponentsof a field testing progranvne. None of the studies explicitly
accounts for the opportunity costs and actual costs of foresone cultivar
superiority.
As examples of suoh costs: (a) field test results may falsely indicate
anewcultivar is higher yielding than standard or conwnonlygrown
cultivars. Hence, when the new cult1var is recommended and .adopted,
farmers will likely forego some yield~ (b) field test results maY falsely
indicate a neW cultivar yields no more than the standard or commonly grown
cultivat"~h Fai lure to recommend and adopt this superior cultivar involves
an oppOrtunity cost of foregone yield.
In this article field testing for the purpose of identifying high yielding
cultivars 1.s examined. Adecis10n model that firstly accounts for costs
(including foregone yield) associetedwithfield testing and which secondly
identifies optimal field test strategies is described and applied. In the
f1rstsect1on the decision model is described. Then it is applied to a
case study of' wheat breeding in the south-east ·of western Australia. The
final section presents some caveats of the analysis and conSiders further
research issues.
3
Field Testing Model
The model described here focuses solely on field testing for yield and
1s couched in terms of a non-linear programning problem . The model assumes
the sole purpose of field testing is to identify if a potential new
cultivar, when grown at sites representative of some region, does in fact
on average out yield some standard cultivar(s).In the model other cultivar
characterist i cs (for example, baki ng qual i ty) are ignored.
The purpose of the model is to identify which testing st."atagy is optimal,
given that test costs and costs of incorrect decisions basad on test
results should be minimized, and that certain technical restrictions .may
apply to field testing. The objective fUnction of the model is to minimize
the combined costs of yield testing and wrong inferences about cultivar
Yields. Algebraically, the objective function is to
2
('1)
Minimize .£ = ~ +. I
(E[~~
1=1
IQJ
P[Tj. IDl) ,
where Q is the total cost of field testing, A is the direct cost of field
testing ·s given in equation (2). E[1; IQ.] is the expected revenue loss
associ'it r ,! with error type i given the actual yield difference between the
new and .. t ndard cult;vars is Rand P[li IQ] is the probabi lity of error
type igiven the yield difference Q. The direct cost of field testing, A,
comprises
(2)
A = pyr(n + s)fi. + PY!i +
t.z
where p, y and r are the number of places. years and plot replicates
respectively in the testing programme., nand s are the numbers of new
and standard cultivars in the testing prograJmle, !! and ~are the average
variable plot and site costs and finally, f is the fixed cost of the
progranroe.
Equation (1) may also be subject to several technical or logistic
restrict'tons such as
(3) pr(n + s) <= ~1
(4)
(5)
r(n
t
+ .s) <= !2 ,
n<=
~3
t
where!1 1s the total number of plots permissable 1n the program."I1e due to
staff and eqUipment limitations, !.2 is the number of plots permissable at
anyone s1teand ~3 is the maximum number of new cultivars that the testing
progranvne can accommodate.
Solving equation (1), subject to constraints (3) to (5), reveals .optimal
field test. strategies, in terms of the necessary numbers of years, sites
and plot replications, for various preconditions such assizes of Q,
4
tstlmating Probabilities of Decision Errors
Before applying the model, the probabilities of decision errors of types I
and II need to be estimated. The nature of type I and II errors and their
estimation can be illustrated by a Simple comparison of two cultivars using
independent, d1.fferently sized .samples and assuming unequal population
variances. The null and alternate hypotheses are
H1
Xi
) Xs
where Xi and Xs are the "true'l or population yields of the
new cultivar i and the standard cultivar s.
The test of the null hypothesis is based on the modified! statistic (~)
which is an approx.imat10n to Student's ~ (Steel and Torrie, p.l06). The
test of the alternate hypothesis, however, is based on the non-central In
statistic (Hays and Winkler). The test statistics, !at and !:n ' are random
variables whose values are sample dependent. Associated with the
distributions of ~ and tn are regions of rejection or critical regions
which define the ranges of !m and In that lead to rejection
of the null and alternate hypotheses respectively ..
Because the test statistics are sample dependent their decision rules are
not 8 guarantee of arriving at a correct decision. Two types of error
arise. A type I error occurs when the null hypothesis is true yet it is
rejected (cultivar it although the same or lower yielding than the standard
cultivar s,is accepted .as being higher yielding). A type II error occurs
when the alternate hypothesis is true yet it is rejected (cultivar i,
although higher yielding than the standard, is accepted as yielding the
same or less than the standard).
The probability of a type I error is the probability of rejecting
hypothesis when it is true. Commonly in agricultural experiments
probability is set in advanc~ at 0.05. Following Cochran, in the
cultivar case already outlined, the probability of a type I error
stated as
alpha = 0.05
= Px =x
i
s
[!m> QJ
the null
this
two
can be
where
and where !i and ~$ are the Student 1:.. values for pyr1 and pyrs degrees
of freedom and prObability of 0.05; p,y,ri and rs refer the numbers of
places, years and plot replicates for cultivars i and s respectively and
!;2and ~2 are sample variances for cultivars ; and s.
Calculation of the probability ofa type II error involves recourse to the
non-central t...stat1stic. The probabilities of t.n values are usually
5
tabled as functions of delta (the non-centrality parameter, see Johnson and
Katz. chp. 31) and the degrees of freedom (Neyman et all or as functions of
other factors that produce very close approximations to !n values
(Resnikoff and Lieberman, Locks et al, OWen). Recourse to the non-central
In. statistic causes estimation of type II error to depend on several
factors: (a) tha discrepancy between the null hypothesis and the true
relationship. The larger the discrepancy the smaller is the type II error.
(b) sample size. The larger the sample size (more sites, years and plot
replicates) the smaller is th~ error. (c) the standard deviation of the
difference in mean yields. The reliability of the estimate may be improved
by altering the mix of sites, years and replicates. (d) the level of
significance of the test of the null hypothesis. The larger alpha is the
smaller the type II error.
Unlike alpha (the probability of type I error) which tends to be set in
advance, the probab1"ity of a type II error is not pre-set. Rather it is
conditional on seve'al factors some of Which are interrelated. Hence,
calculating type] . error using known formulae (for example, Johnson and
Kotz) , gener.ates ,value uniquely associated with a particular set of
precondi.tions ($ .lch as the .size of alpha).
In applying the model described in equations (1) to (6) various sets of
preconditions were examined and the associated probabilities of type II
error were estimated using an accurate approximation method developed by
Hodges and Lehmann. The sets of preconditions were t 1n effect, different
field test strategies. For example, sample size was determined by the
number of cultivars. places, years and replicates to be considered and
these in turn affected the estimate of the standard deviation of the
difference inmaan yields of .a new and standard cultivars which in turn
affected the probability of type II error. These effects are described in
more detail below.
In practice, the field testing of cultivars rarely involves the comparison
of a single new cultivar with a standard. Usually several new cultivars
are compared to a standard cultivar. For any new cultivar nominated in
advance of any statistical examination of yields, Yi is an unbiased
estimator of xi. Following Finney, the distribution of Y1 ;s
and
(6)
where Yi is the mean of pyr plots of cultivar 1, Xi and Xs are the true
yielding capacities of cultivar i and the standard respectiVely, Ys is the
mean of pyrk plots of the standard and ve t vee 1l.ld vf are variance
components relating to environmental effects, cult1var x environment
interaction and residual error effects respectively. The Variance
components are generally defined by
Vp
(8)
ve
== - ....
Vy
Vpy
+-- + y
py
,
6
(9)
Ycp
"c.y VCpy
vce = _. + - . + P
Y
py
(10)
Vf
J
'Ie
=--rpy
where variance components are further disaggregsted into the components 'lip
'IVy ,Vpy ,v ep ,'Icy ,V epy and Yf whieh relate to variance associated with
places, years, place x Yearintersction, cultivar x place interaction,
cultivar x year interaction, cultivar x place x year interaction clOd
residual error respectively. Given that field testing of cultivars usually
fol' '\>/s some experimental design (for example, randomized blocks or Latin
squares) analys1sof variance can usually be applied to the field data to
generate estimates of these variance components. These variance components
di rectly af~'ect the variance of yield difference in equation (7). By
substitutinJl for various values of p,y,rand k in equations (1) to (10),
the impact (If various field test strategies on the estimate of the variance
of the yielc difference in equation (7) can be assessed and this in turn
affects theorobab11 ity of a type II error.
Estimating Costs of Decision Errors
The costs of type I and II decision errors crucially depend on the degree
to which the adoption response of farmers depends on results from cultivar
field trials.. Brennan and Cullis have examined regional adoption and
disadopti.on of wheat cultivars in Australia and found that relative yield
advantage. as recorded in field trials, was a significant explanator of
adOPtion response. Their approach was to fit inverse polynomia1s (t~elder)
to adoption and disadoptlon responses for many cultivars. The fitted
inverse polynomials were of form
(11)
P;y
= yliai + bi Y + el y2 ),
where PlY is the proportion of the total wheat area sown to cultivar i 1n
year y. .From equation (11), the year (Yim) in which Pim is maximized is
(12)
Vim
= (81/c1o.5),
and the maximum proportion of total wheat area in year Yim is
ValuesofPim and Vim were treated as observations of the dependent
variables Pm and Yro in regression analyses of adoption response. From
estimates of the expected values of Pm and Ym values of a, band c were
calcu'lated.
Following the predictton of adoption and disadoption response based on
fie1d tria.1 results, itisposs1ble to estimate the costE> of type I and
errors.. The cost pf type. II errors can be estimated by contrasting the
II
adopti.on response which would have occurred if field trial results truly
indicated yield relativities versus current adoption response (the decision
rule accompanying a type II error would be to not release the naw
cultivar)" The cost of type I errors can be estimated by contrast·ing
current adoption response to that associated with the wrong release of
an inferior cultivar .
lnthis paper, .although regression analysis was used in predicting adoption
and disadopt1on response, the form of the ana·lysis differed from that of
Brennan and Cullis.The approach Was firstly. to compare the yield
relatiVities of historical and current wheat cultivars using special field
trial data. Secondly, truncated binomial distributions were fitted to
adoption patterns of these cult1vars. Ttli rdly, feature.s of these
distributions were regressed 8gainstappropriate yield relativities of the
cultivars. Using the regression results, adoption patterns for cultivars
of known or hypothsticaly1eld superi.ority were predict$d~ Fourthly, the
adoption patterns were converted into wheat product.ion and revenue
estimates. The production and revenue estimates became the basis for
estimates of foregone yield and revenue respectively. These latter
estima.tes wefe the costs of type land II errors.
In the cassof a type I errQr it is probably sensible to not rely on the
regressionrelat1onships as accurate predictors of the adoption response of
the wrongly recommended i.nferiorcult1var t if only because it means
extrapolating from data on which the regression or curve,...f1tting is based.
Also, in practice farmers through their own trial sowings and from those on
neighbouring farms.• would fairly quickly discern acultivar t s yield
inferiority. Hence, usually one would expect type I .costs to be relatively
small. For a type II error however, fanners have no access to the rejected
cultivar and sornayunknowingly forego a yield advantage over .many years.
Hence, type II errors are potentially more costly.
Application of the Hodel
The modal was applied toy; e 1d testing of wheat cult ivars in the south-east
of Western Australia. To Simplify theapp11cation, the technicalaod
logistlc restrictions of equations (3) to (5) were assumed to not apply.
Hence, the application involved estimating the var10usparameters in
equations (1) and (2), setting preconditions and then, by calculation,
finding Wllich values of P,Y and renabled £to be minimized in equation
(1) ..
Firstly, values for !!, g. and t in equation (2) were obtained from staff
administering the cultivar field tria1s. These values are given in Table 1
and. together with various values of p, y and r, provide values forA in
equation (1).
Crable 1 about her'e)
.secondly, data wereco'llected on the yield performance of a set of wheat
cult'ivarsgrown in the same cultivar trials at four sites over four years
in, the south-east of Western Austral ia. An ana lysis of var'iance of these
data provided estimates of yield variance components given in Table 2.
8
(Table 2 about here)
n (7). Also
The variance components in Table 1 sUbstitute 1ntoe quatio
(1) to (10) to
ns
uat1o
intoeq
tuted
substi
are
various values ,ofp,Y ,r and k
te of the
estima
the
on
gies
strate
test
fie.ld
s
variou
of
.
show the impact
of the
tes
estima
The
(7).
variance of the yield difference in equation
type II
of
bility
proba
the
affect
turn
in
ence
variancaof the yield differ
in
error
1.I
error. A150 affecting the probab'11 ity and cost of 3)type
such .as the level of
equation (1) are various preconditions (see Table
ence (Q) and the
differ
yield
actual
likely
the
alpha, thewheatpr1ce,
tivars a
discount rate.. To calcul ate the effect of Ron the adoption ofcul
regression approach previously described was applied.
equation (1) reveals
Given apart icu1a rset of preconditions, minimizingprogram
me associated with
trial
eld
costf1
the .chara cteris tics of the leastpreconditions are
and
tics
cteris
chara
vne
progran
Suoh
s.
those precondition
given in Table 3.
(Table 3 about here)
sets of preconditions,
A consis tent result in Table 3 is that across all ates.
Given the size of
least""cost field trial programmes include 3 replic effect
s) in Table 2,
plot
es
includ
va (the estimate of p-Qolederror which
finding in
usual
a
is
nd
such a ne1)d for repl1c at1oh is not surpri.tJins;a
..
kes)
Kalts1
~,
(Finne~
s
system
studie s of agricu ltural trial
s ,Whenever yield
Another result is that, in the 9~ 'fen sets of precon dition
a then a
15ks/h
to
equal
or
tnan
less
bb
to
ed
differences (Q)ar e expect
3 replic ates is
testin g programme of at least 4 sites, 4 years and
edly high (~ 175
expect
are
nces
differe
yield
when
er,
Howev
necessary..
although a few
mte,
prograr
g
kg/ha) there is no uniform 1east cost testin
trends emerge.
ranges
Firstl y, when the real discount rate is 10 percent then in the given
t
withou
almost
mt3
program
g
3
testin
of wheat price and alpha, the least- cost
t
highas
the
at
ly,
Second
..
est1ng
yieldt
of
years
3
exception only includes
lly
genera
is
sites
test
level of yield difference (200 kg/ha) the number of
reduced to 3 sites .
tics of leastAt the higher discount rate (20%) trends Hl the chara cteris values of
higher
the
At
clear.
less
cost yield testin g progra nJnesa re
of years of yield
alpha., wheat pr1ce and Yield difference, thanumber
3 years. In
casas
testin g falls to .2 years and 1n almost all other mes ~'isross
various
program
cost
least~
summarY, th$ chara cteris tics of
(b) never
ates.
replic
3
least
eat
inolud
always
(a)
to:
are
preconditions
g
testin
e
involv
al1y
(c)usu
rely on single year or s1ngl esita testin g .
under
gh
althou
sites,
4
over
g
testin
e
requir
y
over 3 years and (d) usuall
some oircumstances testin g over 30r 2 sites is possible.
Table Sare presented
The costs of the least- cost field trial programmes asin alpha
decreases so the
that
in Table 4.. The result s in Table 4 indicate
is due to
This
ses.
increa
mes
program
g
present value cost .of the testin
se in the
increa
an
with
ated
associ
being
alpha
in
ion
reduct
firstl Y,the
9
probabi11tyof type II errors and secondly. due, to the relatively greater
expense of typelI errors relative to type I errors (see the footnote to
Table 4) ..
(Tabla 4 about hare)
Although results in Table 4 suggGst that relaXing of the significance level
(that is., la.rgeralphas) in comparisons of cultivar yie.lds reduces test
~O$.ts. in practice such actions will incur additional costs not included
here.. For ex.wnple, a m.arked relaxation of .alphaw111 increase the
probability or lower yield1ng cultivars being released to farmers. Even if
the on...farm costs of fanners initially trying and subsequent.ly rejecting
such cul,tivarsis relatively small , the organisation recomnendingthe
cultivars w111 likely lose soma of their credibility causing farmers· to be
mere cautious 1n their adoption of even truly higher yie1ding cultivars
recOll1mended by the.organisation. A lesser rats of adoption of such higher
yielding cultlvars w111obviously involve .significant costs of foregone
yield. Further., the organisation's .cereal bree.ding activity may suffer if
'its funding source. is by plant. variety rights or industry funds; in
Australia the latter'sallQcat10nis influenced by the credibility growers
attach to the Qrganisation.. Such a reduction in breed1ngeffort may cause
the rataofinctease in wheat yield on farms to be less than m19htoccur if
breed1ogafforts were not curtailed~ However, nonethe less the results do
suggest. thAt strict adherence to low alpha levels, say 0.05 or less, is not
warranted in the fieldt.rial progratl1nes considered here because of the
costs incurred by such strategies.
Resu1t,s in Table 4 also $howthat as. the l1kelyyield difference (Q)
increases so the costs aftesting deer(!8se. The reason for this inverse
relationship 1s due to the impact ofy1eld differences on beta values. Ths
larger the yield difference the smaller is the,probabil ityof a type II
error and 'in general the reducti.on in this probabili.ty more than offsets
the cost increasing effect of the larger yield difference.
Other results in Table 4 are that as the price of wheat decreases or as the
discot,mtrate 1ncrel'ses, then the cost of least cost testing decreases.
ln~ r;ffeet oftt.efal1 in the wheat price is s1m~ly to make the cost of
decision error, less and thereby reduce the combined cost Qf decision
errorssnd fie·ld t~ial costs.
Conclusions
This paper describes a model that identifies the cost and characteristics
of least-cost field trial progranvnes for yield tests of wheat cult1vars 1n
a region of Western Australia. The least-cost progrSfM\SS developedalway.s
involve at least 2 years of testing (conrnonly 3 year test1ngis selected),
usually over 3 or 4 sites and always with at least 3 rep.licates. The cost
of anyprogranrne depends mainly on the pteconditions set for the model.
Fc~ .Bxample, if thepr1ce of wheat decrea.sescr real discount rates
increaSe then the cost of least-cost testing t4-aoreases. Further, if
cultiVars within the progranvne are likely to be .at least moderately higher
yie.1dingthan the standard cultivar (for example. higher yielding by at
least 150 ks/ha) then the costs of testing decrease relative to the case
where only small yield differences are expected.. Also if theground$ for
10
accepting&.. cultivaras higher yielding than the standard are relaxed (for
Qxarnpliil, alpha is set at 0.1 rather than 0.05) then the cost of 1east-cost
programmes falls.
References
Brennan, J.P. and B.. R. Cullis. "Estimating the Adoption and
01sadopt1onof Wheat Cultivars." A Paper presented to the
31st Annual Conference of the Australian Agricultural
Economics .society, Univ. of Adelai.de, South Australis,
February, 1981 .
F1nneY)O.J •. °The Replicat'ion of Variety Trials". Siom.
20(1964):1-15.
Hays, W.L. and R.. L. Winkler .. StatisticS Vol 1: Probability
Inference and DeciSion. Holt, Rinehart and W1nstor} Incorp.,
New York, USA.
Hodges, J .. L., and E.L .. Lehmann .. "A Compact Table for Power of the
1-1est/' Annal. Math. stat •.39(1968): 1629-1631 .•
Johnson, N.L. and $. Kott. continuous UnivariatE:) Distributions-2.
Houghton Mifflin Company," Boston, USA.
Kaltsikes,P.J~
uGenotype-Environment Interaction Variances in
Yield Tria.l$ of Fall Rye. to Can. J. Plant Sci •.50(1970)t71.... S0.
Kingwe.ll. R.S. Economically OPtimal strate.9ies for Regional Yield
Tests of Cultivars. Unpublished H.Sc. thesis, Univ. Qf
Western Australia t Nedlands, WA, 1987 .
Locks, M.O. t AleXander, N.J. and B.. J. Byar!j. "New Tables of the
Non-Central S-Distribution.·\ Report ARL6j-19(1963) t WrightPatterson A1r Force Base .
Nelder.J",A. uInverse Polynom1als,8 Useful Group. of Multi-Factor
RE)spond Functions. "Siom. 22(1966): 128-141 ..
Neyman, \ t Iwaszkiewicz, K. and S,. Kolodziejczyk. "Statistical
problems in Agricultural Experimentation." J. Royal stat.
Soc., Series B. 2(1935):107-180.
Owen, 0 .. ,8. itA Survey of Properties
and Appl ications of the NonCentral t-Distrtbution. u Technomet. 10(1968):445-478.
PatiJ.f.son, H.O., Silv.ey, Vq Talbot.M~ and S. T.C. Weatherup •
.tV.ariab111ty of Yields of Cereal Varieties in UK Tria1s. J.
Agricl! Sci. Carob. 89(1977):239-245.
to
Resn1koff,G.J .. and G.J. Lieperlltan. Tables of the. Non-Central
Distribution ...stanford Univ.ersity Press, Stanford, USA.
~­
11
..iteel,R.G.O. and J .. H. Torria .. Principles and Procedures of
Statistics: a B10metrical ApprQach 2nd. Ed. McGraw-Hill
Kogskusha Incorp.) Tokyo, Japan.
Sprasue,G.F. and W.T .. Federer. uA Cotnparison of Variance
Components in Corn Yield Trials:!I Error. Year x Variety,
Location x Variet.y and Variety Components. Agron. J .•
It
43(1951):535-541.
Talbot, M. ··Yield Variability of Crop Varieties in the U.. K.
Agrie. Sci~ 102(1984):31S-321~
il
J.
12
1 Patterson ~t a1 and Talbotimpl1c1tly recognize the importance
of such costs in their concepts of critical difference and
acceptance regions.
2 .Ingeneral the calculation of Sy - Y depends on whether (a) the
i
s
two populations have a common variance, (b) the COfMlOn or
individual variances are known or estimated, (e) the two
samples are of the same size and (d) yie1d observations are
paired.
S Kingwel1 (1981) has also considered the impact of downward or
upw.ard trends in the wheat price on the characteristics of leastr ' c o s t field trial programmes.
~.
[
r
,~
K~
[
[,
~.
13
Table 1:
Field Trial Operating Costs
Cost Item
Unit
Average plot
c~st (8)
Average site
cost (G)
Fixed cost (F)
$/plot
8.98
$/site
782
$/year
2843
a
Cost
a All costs are in constant 1986 dollar terms.
Table 2:
Estimates of Vield Variance Components in the
Wheatbelt of Western Australia
Sl~~th-east
---~-~-------~-------~-----~~---~-~--------~~~--~-,~----~-~----~-~--~--
Source of
variation
df
SS
MS
MS
a
VR
symbol
F ratio
probab.
~------~---~---~~--~~------------------~------------~------~-----~--
Year(y)
Place(p)
YXP
Reps in y & P
CUl t.1var(c)
YX c
P Xc
PX YXc
residual
Grand Total
47854552
33648984
40698352
3420444
3
2778109
9
2194130
9
605758
3002208
27
96
1535528
191 135738080
3
3
9
32
15951518
11216328
4522.039
106889
926036
243792
6730t,
111193
15995
Vy
vp
Vpy
Vc
Vcy
vcp
Vcpy
ve
149.2
104.9
42.3
<0.001
<0 .. 001
<0.001
57.9
15.2
4.2
7.0
<0.001
<0.001
<0.001
<0.001
~~~~~~--~~-~-~--~--~~-------------~---~---~~~--~~-------,--------------~
a These are the same variance components and symbols as given in
equations (8) to (10)!!
14
Table .3: Characterist,ics of Least-Cost Field Trial Programmes
a
b
for Various Preconditions.
_ _ ... _ ...... _
...._ _ _... _ ... _ ..... _ _ ,..., _ _ _ .... _ _ _ _ ~ _ _ _ _
. _ _. __ _ _ _ _ _ _ _ _ _ _ _ _ _ _ .... _ _ ...-r
OR Wheat Alpha
price
(%) ($/t)
----------Vield difference(kg/ha)-------25 50 15 100 125 150 175 200
---~~~~-~--~---~------~~----------~-~~---~~--------~~--------
10 130
0.1
0.05
0.025
0 .. 01
115
20 130
115
0.1
0.05
0.025
0.01
0.1
0.05
0.025
0.01
0.1
0.05
0 •. 025
0.01
443
443
443
443
443
41
443
443
443
443
443
443
443
443
443
443
443
443
443
443
443
443
443
443
443
443
443
443
443
443
443
443
443
443
443
443
443
443
443
443
443
443
443
443
443
443
443
443
443
443
443
443
443
443
443
443
343
443
443
443
343
443
443
443
433
443
443
443
433
343
443
443
433
343
343
443
.;:3.3
433
343
443
433
343
433
433
433
343
433
433
333
433
433
433
333
333
33.3
433
433
333
333
433
3~3
433
423 42.3
333 423
333 333
433 243
333 423
433 333 423
433 333 333
4.33 433 243
433
433
433
343
433
433
433
~-~---~-~---~----~-~~-~--~~-------~-~-----~---~----~---~~-
a Theprogramrnes are denoted by figures such as 443 where the first
digit (4) refers to the number of trial sites, the second digit (4)
refers to the number of years .and the last digit (3) refers to the
number of plot, replicates"
b The precondit.ions relate to values ·of alpha, the discount rate,
wheat price and likely yield difference..,
15
Table 4: The Cost of Least-Cost Yield Testing Programmes
a
($m)
~~----------------~--~------------------------------------~---~-
DR Wheat
Alpha
price
(~)
($/t)
------------Vield d1fference(kg/ha)---------75 100
125
25
150
175
200
50
~-~---------~~------------~-----~~-----------~--~-------------
10 130
115
20
130
115
0.1
0.05
0.01
0.1
0.05
0.01
0.1
0.05
0.01
0.1
0.05
0 .• 01
1.92
2.38
3.04
1,,72
2.12
2.71
0.93
1.14
1.44
0.84
1.02
1.29
1.21
1.96
3.97
1.09
2.85
4 .. 79
0.60
0.92
1.79
0.54
0.83
1.61
0.32
0.53
1.65
0.31
0.49
1.48
0.21
0.29
0.75
0.20
0.28
0.68
0.21
0.20
0.34
0.21
0.20
0.32
0.15
0.16
0.21
0.15
0.16
0.21
0.13
0.16
0.22
0.13
0.16
0.22
0.10
0.12
0.17
0.10
0.12
0.16
0 .. 11
0.14
0.17
0.11
0.14
0.16
0.09
0.11
0.11
0.08
0.11
0.11
0.11
0.11
0.14
0.11
0.11
0.14
0.08
0.09
0.11
0.08
0.09
0.11
0.08
0.08
0.11
0.08
0.08
0.11
0.06
0.06
0.09
0.06
0.06
0.09
----------~----------------------~-------~--,----------------~
a These costs are in present value 1986 dollar terms and assume it is
reasonable to attribute no cost to type I decision errors because
of farmers' likely quick rejection of such lower yielding and
wrongly recommended cult1vars.