1 1 Chapter Partially Balanced Incomplete Block Design PBIBD 8v 3k ie 3 plots is each block thenthetotal number of required blocks are xF8EBxF8F6xF8ECxF8F7xF8EDxF8F8 and ID: 521265
Download Pdf The PPT/PDF document "Analysis of Variance| Chapter 7 Partial..." is the property of its rightful owner. Permission is granted to download and print the materials on this web site for personal, non-commercial use only, and to display it on your personal computer provided you do not modify the materials and that you retain all copyright notices contained in the materials. By downloading content from our website, you accept the terms of this agreement.
| CKp 7 | PLO. ID | CKp 7 OocN DLJn PID TK Oncd LncopO OocN dLJn Kv vO dvnJ. TKy conncd dLJn ZOO K OocN L] Oo quO. A LcLon on uLnJ K n nd OocN L] L K oO nu of quLd pOLc L AnoK Lpon popy of K ID L K L L ffLcLncy Oncd. TKL n K OO K L K ocL of n B Kn L Oo K ocL of n A Analysis of Variance | CKp 7 | PLO. ID | EcK n Ln K K [cOy n Ln K ZKLcK K ocL 12... do no dpnd on K n A If ny Zo n nd K ocL Kn K nu of n ZKLcK oK ocL nd ocL of L j nd L Lndpndn of K pL of nd TK nu ...12...mjkvnnnpijkm cOOd K ocL pLOOy W conLd noZ K [pO d on cnJuO nd LnJuO ocLLon cK o undnd . RcnJuO AocLLon ScK ConLd n [pO of ocL cO. L K L[ n dnod 1 2 3 4 5 nd 6. Suppo K nUnd KL nJn ZLK pc o cK yoO K Zo oK yoO Ln K oZ K fL ocL. On noK yoO Ln K coOun L K cond ocL LnLnJ Zo yoO Ln K oK oZ K KLd ocL. Fo [pO ZLK pc o n 1 n 2 nd 3 occu Ln K oZ o Ky K fL ocL of n 1 n 4 occu Ln K ocL of n 1 nd K LnLnJ n 5 nd 6 K KLd ocL of n 1 Ky occu Ln K oK SLLOOy fo n 5 n 4 nd 6 occu Ln K oZ o Ky K fL ocL of n 5 n 2 occu Ln K cL of n 5 nd LnLnJ n 1 nd 3 Ln K oK cond oZ o Ky K KLd ocL of n 5. 1 2 4 5 6 Analysis of Variance | CKp 7 | PLO. ID | of OO K L[ n. Tn nu ocL ocL ocL fo n 1 K nu of fL ocL 2 nu of cond ocL 1 K nu of KLd ocL 2 TK vOu of 123ndnnn KoOd u fo oK n Oo. NoZ Z undnd K condLLon LLL of K dfLnLLon of pLOOy Oncd ocLLon cK Od o j ConLd n 1 nd 2. TKy K fL ocL ZKLcK n 1 L.. n 1 nd 2 K fL ocLn 6 L K KLd ocL ZKLcK n of n 1 nd Oo K KLd ocL ZKLcK n of n 2. TKu K nu of n ZKLcK oK L.. K 3 ocL of n K1 nd ocL of n K2th 1 ocL L SLLOOy conLd K n 2 nd 3 ZKLcK K fL ocL ZKLcK n 1 n 4 L K KLd ZKLcK n ocL of n 2 nd n 4 L Oo K KLd ZKLcK n ocL of n 3. TKu 123pijk cn Oo oLnd LLOOy. : TKL Kod cn ud o Jn 3cO ocLLon cK Ln JnO fo n yoO y nJLnJ K Ln oZ nd coOun. Analysis of Variance | CKp 7 | PLO. ID | TK LnJuO ocLLon cK JLv L o 2cO ocLLon cK. L K of n ZKLcK dnod 12… TK n Ln KL cK nJd Ln oZ nd coOun ZK. 1TK yoO nJd foOOoZ: TK poLLon fLOOd up Ln K poLLon ov K pLncLpO dLJonO y K n nu 1 2.. copondLnJ o K yoO. FLOO K poLLon OoZ K pLncLpO dLJonO yLcOOy. TKL LJnn L KoZn 1 2 3 4 CoOun 1 2 3 2 1 2 2 3 2 4 3 2 2 qq - 1 21/2 NoZ d on KL nJn Z dfLn K fL nd cond ocL of K n foOOoZ. TK yoO nLnJ Ln K coOun 12...iiq K fL ocL of nd K cond ocL. TKu Zo n Ln K oZ o Ln K coOun K fL ocL of n . TZo n ZKLcK do no occu Ln K oZ o Ln K coOun K cond ocL of n NoZ Z LOOu KL nJn y K foOOoZLnJ [pO: L K 10 n. TKn . TK n n dnod 1 2… 10 nJd und K LnJuO Analysis of Variance | CKp 7 | PLO. ID | 1 2 3 4 5 CoOun 1 2 3 4 2 1 5 6 7 3 2 5 4 3 6 5 4 7 10 Fo [pO fo n 1 K n 2 3 nd 4 occu Ln K oZ o coOunn 5 6 nd 7 occu Ln K coOun o oZ. So K n 2 3 4 5 6 nd 7 K fL ocL of n. TKn of K n of n 1. Tn nu FL ocL Scond ocL 1 2 3 4 5 6 7 10 2 1 3 4 5 6 7 10 3 1 2 4 6 10 5 7 4 1 2 3 7 10 5 6 5 1 6 7 2 3 4 10 6 1 5 7 3 10 2 4 7 1 5 6 4 10 2 3 2 5 3 6 10 1 4 7 2 5 4 7 10 1 3 6 10 3 6 4 7 1 2 5 W ov fo KL O K K nu of fL nd cond ocL of cK of K 10 n 10 L ZLK 121263nd1.nnnnv Fo [pO K n 2 Ln K coOun of fL ocL occu L[ L vL]. Ln fL KLd fouK fLfK LJKK nd nLnK oZ. SLLOOy K n 2 Ln K coOun of cond ocL occu K L vL]. Ln K L[K vnK nd nK oZ. SLLO concOuLon cn vLfLd fo oK n. Analysis of Variance | CKp 7 | PLO. ID | TK L[ p vL]. 111122221122122111221221ondo ppppppp ZKLcK cn nJd Ln yLc Lc nd foOOoZ: 111111121112112221222122ppppppppªºªº…»…»…»…»¬¼¬¼W ZouOd OLN o cuLon K d no o d qu of u 2 Ln L onOy upcLp.32422120ªºªº…»…»¬¼¬¼In od o On KoZ o ZL K Lc Z conLd n 1 2 nd . No K K n L K cond ocL of n 1. ConLd onOy K oZ copondLnJ o n 1 2 nd nd oLn K On of nd foOOoZ: p Tn 1 nd 2 K fL ocL of cK oK. TK K coon n vL]. 3 4 nd 5 Zn K fL ocL of n 1 nd K fL ocL of n Tn 2 Tn 1 of n 1 n 2 TKo K n ZKLcK K 1of n 1 nd 2. Analysis of Variance | CKp 7 | PLO. ID | 1221nd: Tn 1 nd 2 K fL ocL of cK oK. TK Zo n vL]. 6 nd 7 ZKLcK coon Znn 1 nd K cond ocL of n 2. So 1221 p p Tn 2 Tn 1 of n 1 ocL of n 2 TKo Zo n ZKLcK K 1of n 1 nd K 2ocL of n 2. Analysis of Variance | CKp 7 | PLO. ID | p Tn 1 nd 2 K fL ocL of cK oK. TK L onOy on n vL]. n 10 ZKLcK L coon ocL of n 2. So Tn 2 Tn 1 ocL of n 1 ocL of n 2 TK n ZKLcK ocL of n 1 nd 2 10 Analysis of Variance | CKp 7 | PLO. ID | p Tn 1 nd K c fou n vL]. 235 K fL ocL of n 1 nd K fL ocL of n . So Tn Tn 1 of n 1 n TKo fou n ZKLcK K 2ocL of n ocL Analysis of Variance | CKp 7 | PLO. ID | 1221nd: Tn 1 nd K K Zo n Zn K fL ocL of n 1 nd K cond ocL of n . So 1221 p p Tn Tn 1 of n 1 n TKo Zo n ZKLcK K 1ocL of n ocL Analysis of Variance | CKp 7 | PLO. ID | p Tn 1 nd K c L no n ZKLcK L ond ocL of n . So coOun of qu ud Kn fo 12423344245 K no cond ocL. TKL L dJn c ZK cond cnno dfLnd. Tn Tn 1 ocL of n 1 ocL of n TK no n ZKLcK ocL of n 1 nd ocL Analysis of Variance | CKp 7 | PLO. ID | i j FuK L L y o K OO K p Ln c. no Lndpndn. ConucLon of OocN of PITK OocN of PID cn oLnd Ln dLffn Zy KouJK n ocLLon cK. Evn dLffn OocN ucu cn oLnd uLnJ K ocLLon cK. W noZ LOOu KL y oLnLnJ dLffn OocN ucu uLnJ K LnJuO cK. ConLd K OL LOOuLon ZK 10 ZLK Z conLdd nd K fL cond nd KLd ocL of n AppocK 1: On Zy o oLn K n Ln OocN L o conLd K n Ln cK oZ. TKL conLu K of n o LJnd Ln OocN. WKn K OocN of PID oZ of K foOOoZLnJ O. Fo KL nJn K n LJnd Ln dLffn OocN nd foOOoZLnJ OocN TK p of ucK dLJn 510241nd0.bvrk 1 2 3 4 5 CoOun 1 2 3 4 2 1 5 6 7 3 2 5 4 3 6 5 4 7 10 OocN Tn OocN 1 1 2 3 4 OocN 2 1 5 6 7 OocN 3 2 5 OocN 4 3 6 10 OocN 5 4 7 10 Analysis of Variance | CKp 7 | PLO. ID | AppocK 2: AnoK ppocK o oLn K OocN of PID fo LnJuO ocLLon cK L foOOoZ: ConLd K pLZL coOun of K LnJuO cK. TKn dO K coon nd Ln oK. TK Lnd n ZLOO conLu K OocN. ConLd .J. K LnJuO ocLLon cK fo 5. TKn K fL OocN und KL ppocK L oLnd y dOLnJ K coon n Zn coOun 1 nd 2 ZKLcK uO Ln OocN conLnLnJ K n 2 3 4 5 6 nd 7. SLLOOy conLdLnJ K oK pL of coOun K cK pnd Ln K foOOoZOocN CoOun of n ocLLon cK Tn OocN 1 1 2 2 3 4 5 6 7 OocN 2 1 3 1 3 4 5 OocN 3 1 4 1 2 4 6 10 OocN 4 1 5 1 2 3 7 10 OocN 5 2 3 1 2 6 7 OocN 6 2 4 1 3 5 7 10 OocN 7 2 5 1 4 5 6 10 OocN 3 4 2 3 5 6 10 OocN 3 5 2 4 5 7 10 OocN 10 4 5 3 4 6 7 TK p of K PID 1010663nd4.bvrk SLnc oK K PID LLnJ fo K ocLLon cK o K vOu of 1212ndnnPP Ln K fo oK K dLJn. In KL c Z Kv 633242 .2120 ºªº »…» ¼¬¼AppocK 3: AnoK ppocK o dLv K OocN of PID L o conLd OO K fL ocL of JLvn n Ln OocN. Fo [pO Ln K c of K fL ocL of n 1 K n 2 3 4 5 6 nd 7. So K n conLu on OocN. SLLOOy oK OocN cn Oo found. TKL uO Ln K nJn of n Ln OocN conLdd y dOLnJ K coon n Z Analysis of Variance | CKp 7 | PLO. ID | TK PID ZLK Zo ocL cO popuO Ln pcLcO ppOLcLon nd cn cOLfLd Lno K foOOoZLnJ yp dpndLnJ on K ocLLon cK Reference: Classification and analysis of partially balanced incomplete block designs with two associate classes, R. Bose and Shimamoto, 1952, Journal of American Statistical Association, 47, pp. . LLn qu ZLK CycOLc nd TK LnJuO ocLLon cK K Ody n dLcud. W noZ LfOy pn oK yp of ocLLon cK. L K n ZKLcK cn pnd vpq . NoZ dLvLd K n Lno Joup ZLK cK Joup KvLnJ n ucK K ny Zo n Ln K Joup fL ocL nd Zo n Ln K dLffn Joup K cond ocL. TKL L cOOd K Joup dLvLLO yp cK. TK cK LpOy oun o nJ K vpq n Ln cnJO nd Kn K ocLLon cK cn [KLLd. TK coOun Ln K cnJO ZLOO fo K Joup. Und KL ocLLon cK 1nqp111qqprk nd K p of K cond NLnd unLquOy dLnd 2001 0112qpqqp§·§·¨¸¨¸©¹©¹rkv Analysis of Variance | CKp 7 | PLO. ID | r Kn KJoup dLvLLO dLJn L Ld o SucK LnJuO Joup dLvLLO dLJn cn OZy dLvd fo copondLnJ ID. To oLn KL Mu pOc cK n y Joup of n. In JnO Lf ID K K foOOoZLnJ p bvrk Kn d fo KL ID ZKLcK K p 1212 .bbvqvrrkqkrnpnq A Joup dLvLLO dLJn L Lf . NonLnJuO Joup dLvLLO dLJn cn dLvLdd Lno Zo cO – LJuO nd JuO. LJuOnd0rrkv . Fo KL dLJn bvpAOo cK OocN conLn K nu of n fo cK Joup o K u dLvLLO nd0.rrkv L dno K LLn qu yp PID ZLK conLn. In KL PID K nu of n [pLO . TK n y nJd Ln qu. Fo K c of Zo n K fL ocL Lf Ky occu Ln K oZ o K coOun nd cond ocL oKZL. Fo K JnO c Z N of 2 uuOOy oKoJonO LLn qu povLdd L [L. TKn Zo n K fL ocL Lf Ky occu Ln K oZ o K coOun o copondLnJ o K O of on of K LLn qu. OKZL Ky cond ocL. Und KL ocLLon cK 11112211111112niqnqqiiiqqiiqiiqiqiiiiqiiqiqiqiq Analysis of Variance | CKp 7 | PLO. ID | CycOLc Typ AocLLon ScK L K n nd Ky dnod y LnJ 12.... In cycOLc yp PID K fL ocL of n 121...odidididv OO dLffn nd 012...dvjn onJ K 1 dLffnc 12... ddjjnjj ducd cK of nu ...ddd occu L ZK cK of K nu 122...eee occu L ZK 121122......dddeee OO K dLffn nu 12… : To duc n LnJ od Z Kv o uc fo L uLO uOLpO of o K K . Fo [pO 17 ZKn ducd Fo KL cK 12111211211nnnnnnnnnn SLnJOy LLnNd OocN AocLLon ScK ZLK p 1nd .bvrkbv L K OocN nu of KL dLJn d n L.. . TK fL nd cond ocL Ln K LnJOy OLnNd OocN ocLLon cK ZLK Zo cO dLnd foOOoZ: DfLn Zo OocN nu of o K fL ocL Lf Ky Kv [cOy on n Ln Und KL ocLLon cK 121 2 2 2 2121 1 1 2 1 11 11 11nkrnbnrknrknrknnrkknknknnk Analysis of Variance | CKp 7 | PLO. ID | GnO TKoy of PID A PID ZLK ocL cO L dfLnd foOOoZ. L K n. L K OocN nd K L] of cK OocN L L.. K pOo Ln cK OocN. TKn K n OocN ccodLnJ o n ocL pLOOy Oncd ocLLon cK ucK K vy n occu o onc Ln OocN vy n occu [cOy Ln OocN nd Lf Zo n K ocL of cK oK Kn Ky occu oJK [cOy Ln 12... OocN. TK nu L Lndpndn of K pLcuO pL of ocL cKon. I L no ncy K KouOd OO dLffn nd o of K y ]o. If n cn nJd Ln ucK cK Kn Z Kv PID. No K K Zo n ZKLcK K ocL occu oJK Ln TK p 1212......bvrknnn d K p of K fL NLnd nd j d K p of K cond NLnd. I y nod K ...nnn nd OO j of K dLJn L oLnd fo K ocLLon cK und conLd... occu Ln K dfLnLLon of PID. If fo OO 12… Kn PID duc o ID. So ID L nLOOy PID ZLon ocL cO. TK p of PID cKon ucK K Ky Lfy K 11ibkvriinviiinrk 1Lf nLf.kijkijijkjkiivnpnpnpnijI foOOoZ fo K condLLon K K onOy 1/6 Lndpndn p of K cond | CKp 7 | PLO. ID | InpLon of CondLLon of PID TK LnpLon of condLLon TKL condLLon L Od o K oO nu of pOo Ln n [pLn. In ou LnJ K pOo Ln cK OocN nd K OocN. So K oO nu of pOo . FuK K n nd cK n L pOLcd L ucK K cK n occu o Ln on OocN. So K oO nu of pOo conLnLnJ OO K n L . SLnc oK K n coun K oO nu of OocN Knc bkvr SLnc ZLK pc o cK n K LnLnJ n cOLfLd fL cond… ocL nd cK n K ocL o K u of OO L K K oO nu of n [cp K n und conLdLon. 1nrk OocN Ln ZKLcK pLcuO n occu. In K OocN 1 pL of n cn found cK KvLnJ on of L . AonJ K pL K ocL of u occu L nd K 1.nrk ijkijkjkikijnpnpnpL K of ocL 12... of n . Fo cK n Ln j nu of ocL Ln . TKu K nu of pL of oLnd y NLnJ on n fo nd noK n fo on K on Knd L ijkpcLvOy.jjk | CKp 7 | PLO. ID | 1LfndLfjkjjkj nijpnijzL K n nd ocL. TK ocL of 12... KouOd conLn OO K nu of ocL of . WKn j LOf ZLOO on of K ocL of B 12... KouOd conLn OO K 1 nu of B D WLK TZo AocL ConLd PID und Zo ocL cK. TK p of KL cK 1112221212112212112212 ndbvrknnpppppp TK OLn odO LnvoOvLnJ OocN nd n ffc L 12...12...ijijijyibjv L K JnO n ffc ii j n ffc LfyLnJ 0ndijm L K L.L.d. ndo o ZLK ~0. TK PID L Lny pop nd quLpOLc dLJn. So Ln KL c K vOu of K p co 0o1 fo OO 12... nd fo OO 12... . TK cn Zo yp of nuOO KypoKL ZKLcK cn conLdd – on fo K quOLy of n ffc nd noK fo K quOLy of OocN ffc. W conLdLnJ K K LnOocN nOyL o Z conLd K nuOO KypoKL Od o K n ffc onOy. A don OL Ln K c of ID K OocN ffc cn conLdd und K LnOocN nOyL of PID nd K covy of LnOocN LnfoLon. 012:... H O on pL of L dLffn. | CKp 7 | PLO. ID | TK nuOO KypoKL Od o K OocN ffc L of no ucK pcLcO Ovnc nd cn d LLOOy. TKL Z LOOud OL Ln c of ID. In od o oLn K Oqu L of nd Z LnLL] of K u of qu du o LduO ijij ZLK pc o nd TKL uO Ln K K noO quLon ZKLcK cn unLfLd uLnJ K L[ noLon. TK of ducd noO quLon Ln L[ noLon f OLLnLnJ K OocN CRNKNQVNKB R KkITKn K dLJonO On of 112... K offdLJonO On of oLnd Lfnnd KfLocLLfnnd KcondocL 12...jjijijcnn jjjj z SuofOocNoOLnZKLcKnoccu1.jijijjijjjQVjrknnN[ Z p o LpOLfy K [pLon of L j K u of OO n ZKLcK K fL ocL of n nd j K u of OO n ZKLcK K cond ocL of n. TKn jjjj | CKp 7 | PLO. ID | 12.. co 11221121221121 1 1.jjjjjjjjjjjjkQrkSSrkSSrkSOOOO OOO IpoLnJ K Ld condLLon 221112121112... jjjkQrkSabSjvOOO12212211nd.arka TK quLon ud o oLn K dMud n u oL j dno K dMud u of ov K of Ko n ZKLcK K fL ocL of n. W no K ZKn Z dd K j fo OO Kn occu L Ln K u vy fL ocL of j occu L Ln K u nd vy cond ocL of L Ln K u ZLK 11121 K 2121111111212222111111211222122 Su of ZKLcK K fL ocL of n 11jjjjjjjkQkQQjrkSnpSpSrkppSpbSaOOOOOOOO222112 122222111111.brkppOOOnd kQkQ12121122221 kQabSkQabS | CKp 7 | PLO. ID | NoZ oOvLnJ K Zo quLon K L of 22121 121222121....kbQbQ ababW K j L oOuLon of K ducd noO quLon. TK nOyL of vLnc cn cLd ou y oLnLnJ K undMud OocN u of qu BlockunadjkbkK dMud u of qu du o n TreatadjjjSSQ. TK u of qu du o o rrortTotalBlockunadjTreatadjSSSSSSSS TotalijSSy012:... L Kn d on K LLc /1/1TreatadjErrorunadjSSvSSbkbv111Trvbkvb H L Mcd. | CKp 7 | PLO. ID | TK LnOocN nOyL of vLnc fo LnJ K LJnLfLcnc of n ffc L JLvn Ln K foOOoZLnJ O: Souc Su of quDJ of n InOocN Treatadj Blockunadj kbkyucLonErrortTreatdfv Blockdfb bkbv TdMTT ErrorMSE T Total dfbk No K Ln K LnOocN nOyL of PID nOyL K p ZK Z oLnd j nd OLLnd j 221121jjjjkQrkS OOO noK poLLOLy L o OLLn Lndof . If Z OLLn j Lnd of j Z ppocKd Kn K oOuLon K O ZoN LnvoOvd Ln K uLnJ of 112Qnn. If Kn OLLnLnJ j ZLOO LnvoOv O ZoN Ln oLnLnJ j ZK j dno K dMud u of L ov K of Ko n ZKLcK K cond ocL of n. WKn Z do o oLn K foOOoZLnJ L of K n ffc L o 21112 11212111kbQbQabab | CKp 7 | PLO. ID | 1111112211212 2121112222211.arkbrkppOOO j nd cn cLd ou LLOOy. TK vLnc of K Ony con of L of n Ln c of 22 121 1 12222212jjjjbkQkQbkQkQababL 2212 12222212 122222122Lfnnd KfLocLLfnnd KcondocL.kbbababababW ov K K vLnc of dpnd on K nu of nd Ln K n K ZKK Ky K fL o cond ocL. So dLJn L no vLnc Oncd. u vLnc of ny Ony con quO und JLvn od of ocLLon vL]. fL o cond. TK L ZKy K