estimating yields

8/2/2019 Estimating Yields

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T e c h n i c a l B r i e fE s t i m a t i n g V i n e y a r d Y i e l d s : I n t r o d u c t i o nt o a S i m p l e , T w o - S t e p M e t h o dJ . A . W O L P E R T TM a n d E . P . V I L A S 2

Tec hn ic a l B r ie fs a re p res en ted under t he aus p ic es o f t he Am er i c an Soc ie t y f o r Eno logy and V i t i c u lt u re Tec hn ic a lP ro jec t s Com m i t tee . The a r t i c l es a re no t nec es s ar i l y o r i g ina l r es earc h bu t t ec hn ic a l papers on eno logy o rv i t ic u l t u re c on ta in ing i n fo rm at ion tha t m ay no t be genera l l y k nown to the i ndus t r y . Tec hn ic a l B r ie fs a re approv edfo r pub l i c a t ion by the ed i t o r s and a re no t s ub jec t t o t he no rm a l p eer r ev iew p roc es s .V i t i c u lt u r i s ts and v in tne rs m us t hav e a c c ura te es t im a tes o f v iney ard y ie lds i n o rde r to m a k e the nec e s s ary p lansfo r a v in tage . How ev er , e s t im a t ing y ie lds i s d if f ic u l t bec aus e o f i nheren t v a r iab i li t y fr om v ine to v ine and b loc kto b lock . Var iab i l it y c an be ac c oun ted fo r by us ing p rope r s am p l ing m ethods an d s am p le s i z e c a lc u la t i ons . Thepurpos e o f th i s a r t ic l e i s t o b r i e f ly r ev iew s om e a s pec ts o f s am p l ing and to p res en t a c om puta t i ona l l y s im p le ,two-s tep m ethod fo r y ie ld es t im a t ion .KEY W OR DS: s am p l ing , y ie ld es t im a t ion , s ta t i s ti c s

A r e v i e w : A successful sampling plan is one whichachieves the maximum information at or below thedesired cost. Toward this end, samplers must decidehow much error in the estim ate can be tolerated, or howlittle can be afforded, and the sample sizes required tostay within th at error. The required sample size (n) canbe calculated as:Equa t ion 1 . n = ( t 2 ) ( s 2 )C L 2

where t = value from Student's t tables (6) and deter-mines the probability tha t a sample m ean will be withinthe confidence limits from the population mean; s =population standard deviation, estimated either fromprior knowledge of the va riability of the population orfrom an initial small sample; and CL = the confidencelimits, i . e . , the maximum sample error from the truepopulation mean that the sampler will tolerate at agiven probability.As an alternative, the standard deviation can bereplace d wi th the coefficient of vari atio n (CV), which isthe s tand ard deviation (s) expressed as a percent of the

mean ( ~ ) :Equa t ion 2 . c v

When the CV is substituted for the st anda rd devia-tion in the sample size equat ion (Equa tion 1), confidencelimits are expressed as a percent of the mea n and arereferred to as percent error (PE):

n = ( t 2 ) ( C V 2 )p E 2

1Department of Vit iculture and Enology, University of Cali fornia, Davis, CA 95616 -8749.*Author to whom cor respondence shou ld be addressed.Manuscr ip t submi t ted fo r pub l ica t ion 21 June 1991.Copyr igh t 1992 by the Amer ican Soc ie ty fo r Eno logy and V i t i cu ltu re . A l l r igh ts reserved.

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Equa t ion 3 .For many field sampling applications, 99 percentprobability is considered unnecessarily strict or need-lessly wasteful while 90 percent or less is generally tooimprecise. A PE of five percent of the mea n w ith 95percent probability is generally considered to be a

desirable target.For small samp les, we cannot e nter a t value into thesample size equation because it is dependent on theunknown sample size. Iterative methods have beensugges ted for the solution of small sa mple n, but Table1 provides a reliable solution at the 95 percent confi-dence level (5).T w o - s t e p m e t h o d f o r e s t i m a t i n g v i n e y a r dy i e l d s : Vineyard yields can be esti mated if one knowsboth the avera ge num ber of clusters per vine andaverage cluster weight. Knowing the numb er of vinesper acre, total fruit weight is an easy calculation. Forgreatest efficiency the two measurements are taken at

different times of the year. Step 1: Cluster numb er isdetermined on a vine-by-vine basis before bloom whenclusters are more easily visible. Step 2: Cluster weightsare dete rmined on a shoot-by-shoot basis near veraisonwhen cluster weights have stabilized.The sampling methods present ed call for completelyrandom sampling, i . e . , for probabilities to be precise,each individual in the population must have an equalchance of being selected. Unbiased rando m samplingcan be achieved using tables of rando m n umbers foundin most statistics texts or generated by computer pro-grams. However, for practicality most viticulturistswould probably opt for some regular systematic sam-pling plan such as every so many vines in every so man y

r O W S .

S t e p 1. C l u s t e r c o u n t s a m p l e s : To estimat e aver-age per-vine cluster counts we assume tha t ent ire vineswill be the sampling unit. Counts made by the autho rsin wine grape vineyards have had CV percentagesranging from 15 to 37 (data not presented), but good

A m . J . E n o l . V i t i c . , V o l . 4 3 , N o . 4 , 1 9 9 2


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V I N E Y A R D Y I E L D S m 3 8 5

T a b l e 1 . S a m p l e s i z e s r e q u i r e d f o r e s t im a t e d c o e f f ic i e n t s o f v a r i a t io n ( C V ) to e n s u r e p r e s c r i b e d a l l o w a b l e p e r c e n t a g e s a m p l i n g e r r o r s ( P E )( 9 5 p e r c e n t c o n f i d e n c e l e v e l) . 1S a m p l e S a m p l e S a m p l e S a m p l e S a m p l e S a m p l e S a m p l e S a m p l e

size: size: size: size: size: size: size: size:C V P E = 1 P E = 3 P E = 5 P E = 1 0 P E = 1 5 P E = 2 0 P E = 2 5 P E = 50

P ercen t p ercen t p ercen t p ercen t p ercen t p ercen t p ercen t p ercen t p ercen t1 7 3 3 2 2 2 2 22 18 5 3 3 3 2 2 23 38 7 4 3 3 3 3 24 64 10 5 3 3 3 3 25 99 14 7 4 3 3 3 26 141 18 9 4 3 3 3 37 191 24 11 5 4 3 3 38 249 30 13 5 4 3 3 39 3 1 4 3 8 1 5 6 4 4 3 3

10 387 46 18 7 5 4 3 311 468 55 22 8 5 4 4 31 2 5 5 6 6 4 2 5 9 5 4 4 31 3 6 5 2 7 5 2 9 9 6 5 4 314 756 87 33 11 6 5 4 31 5 8 6 7 9 9 3 8 1 2 7 5 4 316 986 112 42 13 7 5 5 31 7 1 1 1 3 1 2 6 4 7 1 4 8 6 5 318 1248 141 53 15 9 6 5 319 1390 157 58 17 9 6 5 320 1539 174 64 18 10 7 5 3212 22 32 42 52 62 72 82 93 0313 23 33 43 53 63 73 83 94 0414 24 34 44 54 64 74 84 95 0

169 7 191 71 20 11 7 6 41 8 6 2 2 1 0 7 7 2 2 1 1 8 6 42 0 3 5 2 2 9 8 4 2 3 1 2 8 6 42 2 1 6 2 4 9 9 1 2 5 1 3 9 7 42 4 0 4 2 7 0 9 9 2 7 1 4 9 7 4260 0 291 10 7 29 15 9 7 4280 3 314 115 31 15 10 7 430 15 338 123 33 16 11 8 43234 362 132 35 17 11 8 43460 387 141 38 18 12 9 4369 4 413 151 40 19 12 9 43 3 9 6 4 4 0 1 6 0 4 2 2 0 1 3 9 54 1 8 6 4 6 8 1 7 0 4 5 2 2 1 3 1 0 54 4 4 4 4 9 6 1 8 1 4 7 2 3 1 4 1 0 5470 9 526 191 50 24 15 11 54981 556 20 2 53 25 15 11 55 2 6 2 5 8 7 2 1 3 5 6 2 6 1 6 1 1 55 5 5 0 6 1 9 2 2 5 5 8 2 8 1 7 1 2 55 8 4 6 6 5 2 2 3 7 6 1 2 9 1 8 1 2 56 1 4 9 6 8 6 2 4 9 6 4 3 0 1 8 1 3 56 4 6 0 7 2 0 26 1 6 8 3 2 1 9 1 3 66 7 7 9 7 5 6 2 7 4 7 1 3 3 2 0 1 4 67 1 0 6 7 9 2 2 8 7 7 4 3 5 2 1 1 4 67 4 4 0 8 2 9 3 0 0 7 7 3 6 2 2 1 5 67 7 8 2 8 6 7 3 1 4 8 1 3 8 2 2 1 5 68 1 3 1 9 0 6 3 2 8 8 4 3 9 2 3 1 6 68 4 8 9 9 4 6 3 4 2 8 8 4 1 2 4 1 7 68 8 5 3 9 8 6 3 5 7 9 1 4 2 2 5 1 7 79 2 2 6 1 0 2 8 3 7 2 9 5 4 4 2 6 1 8 79 6 0 6 1 0 7 0 3 8 7 9 9 4 6 2 7 1 8 7

A m . J . E n o l . V i ti c ., V o l . 4 3 , N o . 4 , 1 9 9 2


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3 8 6 - W O L P E R T a nd V I L A S

T ab le 1 . Con t .S a m p l e S a m p l e S a m p l e S a m p l e S a m p l e S a m p l e S a m p l e S a m p l e

size: size: size: size: size: size: size: size:C V P E = 1 P E = 3 P E = 5 P E = 1 0 P E = 1 5 P E = 2 0 P E = 2 5 P E = 50

P e r c e n t p e r c e n t p e r c e n t p e r c e n t p e r c e n t p e r c e n t p e r c e n t p e r c e n t p e r c e n t5 1 9 9 9 4 1 1 1 3 4 0 3 1 0 3 4 7 2 8 1 9 75 2 1 0 3 9 0 1 1 5 7 4 1 8 1 0 7 4 9 2 9 2 0 753 10 793 120 2 435 111 51 30 20 754 1120 4 1248 451 115 53 31 21 75 5 1 1 6 2 3 1 2 9 4 4 6 8 1 1 9 5 5 3 2 2 2 85 6 1 2 0 5 0 1 3 4 1 4 8 5 1 2 3 5 6 3 3 2 2 85 7 1 2 4 8 4 1 3 9 0 5 0 2 1 2 8 5 8 3 4 2 3 85 8 1 2 9 2 5 1 4 3 9 5 2 0 1 3 2 6 0 3 5 2 4 85 9 1 3 3 7 5 1 4 8 9 5 3 8 1 3 7 6 2 3 6 2 4 86 0 1 3 8 3 2 1 5 3 9 5 5 6 1 4 1 6 4 3 8 2 5 96 1 1 4 2 9 7 1 5 9 1 5 7 5 1 4 6 6 6 3 9 2 6 96 2 1 4 7 6 9 1 6 4 4 5 9 4 1 5 1 6 9 4 0 2 7 96 3 1 5 2 4 9 1 6 9 7 6 1 3 1 5 5 7 1 4 1 2 7 96 4 1 5 7 3 7 1 7 5 1 6 3 2 1 6 0 7 3 4 2 2 8 96 5 1 6 2 3 3 1 8 0 6 6 5 2 1 6 5 7 5 4 4 2 9 96 6 1 6 7 3 6 1 8 6 2 6 7 2 1 7 0 7 7 4 5 3 0 1 06 7 1 7 2 4 7 1 9 1 9 6 9 3 1 7 5 8 0 4 6 3 1 1 06 8 1 7 7 6 5 1 9 7 7 7 1 3 1 8 1 8 2 4 7 3 1 1 06 9 1 8 2 9 2 2 0 3 5 7 3 4 1 8 6 8 4 4 9 3 2 1 07 0 1 8 8 2 6 2 0 9 4 7 5 6 1 9 1 8 7 5 0 3 3 1 17 1 1 9 3 6 7 2 1 5 5 7 7 7 1 9 7 8 9 5 1 3 4 1 17 2 1 9 9 1 7 2 2 1 6 7 9 9 2 0 2 9 1 5 3 3 5 1 17 3 2 0 4 7 4 2 2 7 7 8 2 2 2 0 8 9 4 5 4 3 6 1 17 4 2 1 0 3 8 2 3 4 0 8 4 4 2 1 3 9 6 5 6 3 7 1 17 5 2 1 6 1 1 2 4 0 4 8 6 7 2 1 9 9 9 5 7 3 8 1 27 6 2 2 1 9 1 2 4 6 8 8 9 0 2 2 5 1 0 2 5 8 3 8 1 27 7 2 2 7 7 8 2 5 3 4 9 1 4 2 3 1 1 0 4 6 0 3 9 1 27 8 2 3 3 7 4 2 6 0 0 9 3 8 2 3 7 1 0 7 6 1 4 0 1 27 9 2 3 9 7 7 2 6 6 7 9 6 2 2 4 3 1 0 9 6 3 4 1 1 38 0 2 4 5 8 8 2 7 3 5 9 8 6 2 4 9 1 1 2 6 4 4 2 1 38 1 2 5 2 0 6 2 8 0 3 1 01 1 2 5 5 1 1 5 6 6 4 3 1 38 2 2 5 8 3 2 2 8 7 3 1 0 3 6 2 6 1 1 1 8 6 8 4 4 1 38 3 2 6 4 6 6 2 9 4 3 1 0 61 2 6 8 1 2 1 6 9 4 5 1 48 4 2 7 1 0 8 3 0 1 5 1 0 8 7 2 7 4 1 2 3 7 1 4 6 1 48 5 2 7 7 5 7 3 0 8 7 1 1 1 3 3 8 0 1 2 6 7 2 4 7 1 48 6 2 8 4 1 4 3 1 6 0 1 1 3 9 2 8 7 1 2 9 7 4 4 8 1 48 7 2 9 0 7 8 3 2 3 4 1 1 6 6 2 9 4 1 3 2 7 6 4 9 1 58 8 2 9 7 5 1 3 3 0 8 1 1 9 3 3 0 0 1 3 5 7 7 51 1 58 9 3 0 4 31 3 3 8 4 1 2 2 0 3 0 7 1 3 8 7 9 5 2 1 59 0 3 1 1 1 8 3 4 6 0 1 2 4 8 3 1 4 1 4 1 8 1 5 3 1 59 1 3 1 8 1 3 3 5 3 7 1 2 7 5 3 2 1 1 4 4 8 2 5 4 1 69 2 3 2 5 1 6 3 6 1 6 1 3 0 3 3 2 8 1 4 7 8 4 5 5 1 69 3 3 3 2 2 7 3 6 9 4 1 3 3 2 3 3 5 1 51 8 6 5 6 1 69 4 3 3 9 4 5 3 7 7 4 1 3 61 3 4 2 1 5 4 8 8 5 7 1 79 5 3 4 6 7 1 3 8 5 5 1 3 9 0 3 5 0 1 5 7 9 0 5 8 1 79 6 3 5 4 0 5 3 9 3 6 1 4 1 9 3 5 7 1 6 0 9 1 6 0 1 79 7 3 6 1 4 6 4 0 1 9 1 4 4 9 3 6 4 1 6 4 9 3 61 1 79 8 3 6 8 9 6 4 1 0 2 1 4 7 9 3 7 2 1 6 7 9 5 6 2 1 89 9 3 7 6 5 2 4 1 8 6 1 5 0 9 3 7 9 1 7 0 9 7 6 3 1 8

1 0 0 3 8 4 1 7 4 2 7 1 1 5 3 9 3 8 7 1 7 4 9 9 6 4 1 81 R e p r i n te d w i t h p e r m i s s i o n f r o m F o r e s t S c i e n c e , p u b l i s h e d b y t h e S o c i e t y o f A m e r i c a n F o r e s t e rs , 5 4 0 0 G r o s v e n o r L a n e , B e t h e s d a , M D 2 0 8 1 4 - 2 1 9 8 . ( 5 )

A m . J . E n o l . V i t ic . , V o l . 4 3 , N o . 4 , 1 9 9 2


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estimates can be assured in vineyards using Stein's twosample method (7). By Stein's method, the requiredsample size is estima ted from the CV of an initial smallrandom sample. The sample CV can be easily calculatedin the vineyard using an inexpensive, hand-held calcu-lator with a standard deviation key.For most agricultural applications, an initial samplesize can be dependab le if it is about 10, or per hap s even

as small as 5, if the population is normally distri buted(4). Using the stan dard deviation and the mean of a 10-vine sample, the CV is calculated according to Equation2. The CV is first located in the left-most column of Table1 and the required sample size is found under thedesired P E column. For exampl e, if the CV is 25 percen tand a PE of 5 percent is desired, Table 1 calls for asample size of 99. If 10 vines were init ially counted, anadditional 89 vines must be counted to achieve therequired 99 total. If the counts are accurate, the m eanof all 99 vines should be wit hin about 5 perc ent of thetrue mean of the population (vineyard) at the 95 percentprobability level. There is no need to recalculate a newsample size using the combined samples.If experience shows tha t r equired sample sizes areusually larger than some number, say 20, the firstsample size should be increased to tha t n umbe r to giveeven more reliability to the two-sample method.S t e p 2 . S a m p l i n g f o r c l u s t e r w e i g h t : Clustersamples will likely be taken sometime after veraison. Itis not easy to relocate the specific vines use d for clustercounts so, for simplicity, cluster samples can be takenrandoml y throug hout the vineyard, relying on the judg-ment of the sampler. Unbiased sampling is not alwaysachievable, but one method is to reach blindly into avine, contact a shoot and remove all the clusters fromthe shoot. Repeat this shoot selection from vines se-

lected either casually or systematically, or selectedusing random numb er tables until the first sample of 10or more cluste rs has b een collected. This shoot sampli ngmethod should ensure that samples contain a propor-tionate nu mber of basal and second clusters. The samestatistical analyses can be applied to the weights ofrandom clusters as were applied to vine counts. Eachcluster must be weighed individually, and the me an a ndstandard deviation calculated. Samples taken from anumb er of wine grape vineyards had m ean clusterweights ranging from 0.2 to 0.5 lb. with standarddeviations between 0.08 and 0.3 lb. A vineyard with acluster weight sta nda rd deviation of 0.15 and a mean of0.4 lb. will have a calculated CV of about 38 percent.Using this figure for an example, Tabl e 1 indicat es th at,for a desired PE of 5 percent, a total sampl e of 225clusters must be sampled, i.e., 215 in addition to theinitial 10. Of course, it is not necess ary to individu allyweigh the additional 215 clusters to calculate the mean;one weight of the combined cluster s will suffice.

It should be noted tha t differences between sampleweight and final harvest weight can contribute majorerror to crop predictin g (1). These differences c an be dueto crop dehydration, raisining, sunburn, etc.

E s t i m a t e d T o t a l V i n e y a r d Y i e ld : The averageyield per vine is calculated simply by multiplying themean cluster count by the mea n cluster weight. A meancluster count of 75 clusters per vine and a mean clusterweigh t of 0.3 lb will give an avera ge yield of 22.5 lb pervine plus or minus the percent error.Percent error of the average yield depends on itsstandard deviation which is calculated by entering the

means and sta ndar d deviations of the cluster countsand weig hts into a varianc e of products equa tion (3).c v , = V c v ,

When we did the calculations, the resulti ng error aver-aged seven percen t, a loss of two percent from our targ etof five percen t err or a t the 95 percent confidence leveldemonstrating that some loss of sampling precisionshould be expected when sample me asu reme nts such asweights and counts are multiplied.Total vineyard yield is estimate d by multiplying theaverage vine yield by the num ber of vines in the vine-yard. If the vine count is accurat e, th e PE of total yield

will be equi valen t to the PE of vine yield.C o n s e q u e n c e o f v i n e y a r d s iz e: Although largevineyards may be more variable than small vineyards,due to increased va riability of the site or in culturalpractices, the fact remain s th at calculated sample sizesto achieve a PE a re a function of CV not popul ation size.The exception to this rule occurs when five to 10 perc entor more of a population is sampled, in which casestatisticians recommend that the finite population cor-rection (FPC) be applied (2). It is very unlikely thatvineyards will ever be sampled intensely enough torequire the FPC and most samplers would avoid apply-ing the FPC to keep the samp ling equation simple. The

consequence of not applying the FPC when recom-mended is tha t the s tand ard deviation of the samplemean will be over-estimated, and calculated samplesizes will be somewhat larger than needed.Vine yard s wit h a CV of 20 percent will require thesame sample size, 64, to achieve five percent error with95 percent confidence whether the vineyards are fiveacres or 20 or 60. However, total tonnage being greaterin large vineyards, total tonnage error will be greaterand the vi ticulturist may choose to vary sampling inten-sity according to vineyard size in order to equalize thetotal tonnage error.F l e x i b i l i t y o f c h o i c e s : While an error no largerth an five perce nt of the m ean with 95 percen t confi-dence would be desirable, samplers may find it neces-sary to reduce sample sizes and accept less precision,such as 10 percent error r ath er t han 5 percent, in orderto cover many vineyard blocks while keeping costswithin a prescribed budget. This decision can be madefor each viney ard block dependin g on factors such as theimportance of the estim ate and the vineyar d size.

L i t e r a t u r e C i t e d1. Ca in , M ., and N. Ciancio . Foreca st ing the Ca l i fo rn ia grape crop.Ca l i fo rn ia Crop and L ivestoc k Repor t ing Serv ice Pub l ica t ion . 21 pp. (1978) .



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2. Cochran , W. G. Samp l ing techniques (3rd ed. ). 428 pp. John Wi ley andSons, New York (1977) .3. G oodm an, L. A. On the exact var iance of products . J . Am er ican Stat .Assoc. 55:708-13 (1960) .4. S ampford, M. R. An int roduct ion to samp l ing theory wi th appl icat ionsto agr iculture. 292 pp. Ol iver and Boyd, Ltd. , Edinburgh a nd Lond on (1962) .

5. Stauf fer , H. B. A sample s ize table for fores t sampl ing. Fores t Sc i .28 : 777-84 (1982).6. Steel , R. G. D. , and J . H. Torr ie. Pr inc ip les and pro cedure s of s tat is t ics(2nd ed. ) . 633 pp. McGraw-Hi l l , New York (1980) .7. Ste in, C. A two-sample tes t for a l inear hypothes is whose power isindependent of the var iance. Annals Math. Stat . 16:243-58 (1945) .


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