DETERMINATION OF OPTIMUM SAMPLE SIZE FOR MEASURING THE CONTRIBUTING CHARACTERS OF BOTTLE GOURD

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1 ISSN Bagladesh J. Agrl. Res. 40(4): , December 015 DETERMINATION OF OPTIMUM SAMPLE SIZE FOR MEASURING THE CONTRIBUTING CHARACTERS OF BOTTLE GOURD N. MOHAMMAD 1, M. S. ISLAM, K. S. RAHMAN 3 M. M. RAHMAN 4 AND S. NASRIN 5 Abstract To mrove effcec collectg data from feld exermet o frut attrbutes of bottle gourd (Lau), the samle sze was studed for samle sze at Olerculture Dvso, Hortculture Research Cetre (HRC) of Bagladesh Agrcultural Research Isttute (BARI) Gazur durg The treatmets/varetes were LS , LS , LS 117-F-1, LS 117-A- ad BARI Lau-3. Frut legth, breadth ad weght of bottle gourd (Lau) data were collected from the exermetal lot. The data were used to desg otmum samlg la from eual umber of observatos er cell. The observato o frut legth (cm), breadth (cm) ad weght (kg) were take from 5 lots/treatmets at radom. A radomzed comlete block desg (RCBD) wth 3 relcatos ad fve treatmets/varetes was used ths exermet. Fve (5) lats er lot ad fruts er lats (10 fruts er lot) were the orgal samlg la for ths exermet. A samlg la of selectg 4 lats at radom ad measurg fruts er selected lat (8 fruts er lot ad lots were 5m.e. 10m log ad.5m wde) was foud to be otmum ad ecoomcal for takg measuremets of frut attrbutes feld exermets o bottle gourd. Kewords: Measuremet, Otmum samle sze, Samlg techue ad Bottle gourd. Itroducto I a feld exermets, t s ecessar to determe the otmum samle sze as well as otmum umber of relcatos f researchers have to use samlg techues for collectg data from such exermets (Islam et al. 000). It s ot ossble to measure eld ad eld cotrbutg characterstcs o the whole of each exermetal ut. I a feld exermet, the researcher has to face the roblem determes otmum (effcet) samle sze for measurg lat characters (Federer, 1963). The researcher has to face the roblem of otmum (effcet) samle sze for measurg lat characters the feld exermet (Islam et al.001). The otmum samlg techue deeds o the varablt assocated wth varable ad the cost of reducg the varablt (Kemthore,195). Rge ad Nelso (1951) cotto, Patel ad Dalal (199) okra ad Hossa et al. (005) Brjal, Hossa et al. (008) Teasle gourd, Islam et 1,3&4 Scetfc Offcer, ASICT Dvso, BARI, Gazur-1701, Prcal Scetfc Offcer, ASICT Dvso, BARI, Gazur-1701, 5 M.Sc Statstcs, Rajshah Uverst, Bagladesh.

2 704 MOHAMMAD et al. al. (01) Sweet gourd ad Islam et al. (013) Btter gourd estmated the sze of samle eeded takg measuremets of lat characters. No such formato s avalable bottle gourd (Lageara scerara var.clavata). Ths exermet deals wth samle sze stud bottle gourd artcularl for takg measuremets of frut character lke Legth, Breadth ad Weght. The vestgato was carred out at Hortculture Research ceter (HRC), Bagladesh Agrcultural Research Isttute (BARI), Jodebur, Gazur The objectve of the stud s to fd out otmum samle sze for estmatg eld cotrbutg characters of the feld exermet o bottle gourd. Materal ad Method Samle sze deeds o the varablt assocated wth varable ad the cost of reducg that varablt. For such cases, t s ecessar to choose otmum samle sze ad umber of relcatos. Estmato of otmum samle sze ad umber of relcatos are obtaed b maxmzg the formato for a gve cost. There were fve treatmets/varetes used as treatmet ths exermet. The treatmets/varetes were LS , LS , LS 117-F-1, LS 117-A- ad BARI Lau-3. Exermetal lots were 5m (10m log ad.5m wde). Frut legth, breadth ad weght of bottle gourd (Lau) data were collected from the exermetal lot. Ths data were used to calculate otmum samlg la from eual observato er cell. The observato o frut legth (cm), breadth (cm) ad weght (kg) were take from 5 lots or treatmets selected at radom. The frut legth, breadth ad weght of frst two fruts from each selected lat utlzed ths aalss. There were 10 fruts (5 lats er lot x fruts er lat) er lot ad 50 fruts er relcato. Cosderg the tme factor, the data of three relcatos were collected for dervg otmum samlg la (Otmum the sese of tme volved takg fruts measuremets). A radomzed comlete block desg (RCBD) wth 3 relcato was used for ths exermet. The data were aalzed relcato wse b aalss of varace (ANOVA) techue (Table 1) to estmate varace comoets assocate wth lots ( ˆ ), lats ( ) ad fruts ( ). ˆ Aaltcal Model ˆ We have a exermet treatmets (lots) are take at radom, the lats are radoml selected from each treatmet. From each lat radom samlg ut s take. The observatos ma be deoted b Y where deote the treatmets (= 1,.. ), j the Plats (j = 1,,,) ad k the samlg ut (k = 1,,.., ).

3 DETERMINATION OF OPTIMUM SAMPLE SIZE FOR MEASURING 705 We also assume the followg model: Y m (1) a Where m thegeeral j mea α =the treatmets effect j the lats effect due to the (j)th exermetal ut. = the samlg effect due to the ()th observato For the stud we suose that the s are ormall ad deedetl dstrbuted wth varace, s are ormall ad deedetl dstrbuted wth varace ad j s are ormall ad deedetl dstrbuted. The s wll be deedet of the j s ad s f the samlg radom. The least suare estmates are obtaed as follows: mˆ a ˆ ( ) ˆ ( j j ˆ ( j. ) Also ) 1 j 1 k 1 j 1 k 1 j. k 1 Puttg these values euato (l) ad suarg ad summg o both sdes. The the total sum of suares ca be arttoed as: ( ) ( ) 1 j1 k roductter 1 j1 ( jk ) 1 j1 k 1 ( j ) j

4 706 MOHAMMAD et al. But roduct terms are usuall zero. Thus, Total (SS)= Treatmet (SS) + Plat (SS)+ Samlg (SS) Wth ther degrees of freedom (-1) = (-1) + (-1) + (-1) Table 1. The aalss of varace Sources of Varato (SV) Degrees of Freedom (D.F.) Sum of Suares (S.S) Mea Sum of Suares (MSS) Exected Mea Sum of Suares (EMSS) Plots/Treatmet (Levels A) Plats/Plot(Level B wth A) Fruts/Plat/Plot Samlg (-1) S..... (-1) j S..... (-1) S ( ) j. j k ( S r 1) 1 T S 1 S S Total -1 j k... Where, = umber of lot or treatmet, = umber of lats/lot ad, = umber of fruts/lat/lot. Also T= The mea sum of suare of Treatmet, P= The mea sum of suare of Plat, S= The mea sum of suare of Samlg resectvel. Accordg to estmato of otmum samlg la, Sedacor ad Cochra (1967), the varace comoet ma be estmated as. The comoets of varace ad estmated b, ˆ S, P adt.e P S ˆ ad ˆ T P Thus varace of mea s S ˆ ˆ () P ˆ

5 DETERMINATION OF OPTIMUM SAMPLE SIZE FOR MEASURING 707 ˆ ˆ, ad table. for the character were obtaed from the aalss of varace The same varace of mea ca be altered for the mea b usg varous combatos of ad euato () S' ˆ ˆ ˆ (3) P ' ' Where ad are the altered values of ad resectvel. The comoet treatmets. ˆ was assumed as costat, as t rereseted varato due to Effcec of ew samlg la, E = S ˆ z (4) S' The formula of savg the work/tme load.e tme factor (TF) wthout sacrfcg recso as comared wth orgal la.e 10 fruts (5lat/lot x fruts/lat) er lot s defed as ' ' TF (%) = x 100 (5) ' ' Where, =5, =, =1,,------,5 ad =1,, ,5. Sce 10 fruts er lot s the orgal la or cotrol. Results ad dscusso The results of the stud were utlzed arrvg alterate samlg las (.e., alterg the value of from 1 to 5 lat er lot ad from 1 to 5 fruts er lat, makg total 5 samlg lats er lot) (Table-). The relatve effcec of each lat was worded out relato to orgal la (5 lats er lot ad fruts er lats). Usg euato-4 the relatve effcec of ew alterate samlg las s gve Table-3. The results (Table-3) dcated that the relatve effcec wth the umber of lats er lot ad umber of fruts er lat. The other alterate la wth 4 lat er lot ad fruts er lat (total 8 fruts er lot) had also 99.6 ercet effcec comarso to orgal la but had 0 ercet less amout feld work (Usg euato 5). The other la whch ca be emloed wth same effcec s to select 3 lats at radom er lot ad

6 708 MOHAMMAD et al. measure 3 fruts each selected lat (9 fruts er lot) had 94.1 but work load wll be about 10 ercet less tha the la wth 5 lats x fruts er lot. The results revealed that work load for feld oerato lke laggg of flowers, harvestg ad measuremet of dvdual frut could be reduced effectvel wthout sacrfcg effcec b selectg roer samlg la. Table. The estmated varace comoets for lots ( ), lats ( ) ad fruts ( ). ˆ ˆ ˆ Varace comoet Frut Legth Frut Breadth Frut Weght R-I R-II R-III R-I R-II R-III R-I R-II R-III Table 3. The relatve effcec for some of the alteratve samlg lats. Number of Frut Legth Frut Breadth Frut Weght Average Plats Fruts over R-I R-II R-III R-I R-II R-III R-I R-II R-III /lot /lat trats Cocluso Work/Tme Load (%) Amog dfferet samlg las a la wth 5 lats er lot ad 1 fruts (total 5 fruts er lot) had o a average ercet effcec.e., almost eual effcec whe comared wth orgal samlg la of 5 lats/lot ad

7 DETERMINATION OF OPTIMUM SAMPLE SIZE FOR MEASURING 709 fruts er lat (10 fruts er lot). B adotg ths ew la 50 ercet work load (tme) could be saved wthout sacrfcg recso. The we coclude that samlg of selectg 4 lats at radom er lot ad measurg fruts each selected lat (total 8 fruts er lot) aeared otmum ad effcet(closed to orgal samlg la.e. 10 fruts er lot ). Refereces Federer W. T Exermetal desg. Theor ad alcato, Oxford ad IBH Publshg Co. New Delh, Ida. Hossa,M.I.; Islam, M.S.; Hossa, M.A; Nasr, S. ad Yesm, S Determato of otmum samlg lat characters of brjal. Iteratoal Joural of Sustaable Agrcultural Techolog, 1(6): 5-9. Hossa,M.I.;Muhammad Shuab; Kabta; Muhammad Tare; M.S. Kabr ad M. A. Udd Otmum samlg for measurg dfferet lat characters of Teasle gourd. Eco-fredl Agrl. J. 1(3): Islam, M.S.; Mohammad.N.; Rahma.K.S, Rahma.M.M. ad Houe.A.K.M.A Otmum samlg for measurg dfferet lat characters of btter gourd. Ecofredl Agrl. J. 6(11): 34-37, 013. Islam, M.S.; Mohammad.N.; Rahma.K.S, Rahma.M.M. ad Houe.A.K.M.A. 01. A stud of otmum samlg for measurg dfferet lat characters of sweet gourd. J. Bagladesh Soc. Agrl. Sc. Tecol. 9(1&): Islam, M.S.; Se, K. ad Rahm, K Estmato of otmum samle sze ad umber of relcatos RCBD wth ueual observato er cell. Dhaka Uverst Joural of Scece, 48(1): Islam, M. S Statstcal develomet of feld lot techue for agroomc exermets. Uublshed Ph. D. thess, Dhaka Uverst, Dhaka, Bagladesh. Kemthore, O Desg ad aalss of exermet, Joh Wle ad Sos, Ic, New York, USA. Patel, J.N. ad Dalal, K.C. 199 Samlg techue for measurg od characters of okra. Gujarat Agrcultural Uverst Research Joural, 18(1): Rge.J.A. ad Nelso. WI L Some factors affectg the accurac of samlg cotto for fbre determatos. Agroom Joural 43: