Latin Square DesignDepartment of Statistics丁方的设计的统计部门

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1、Latin Square DesignPrice Valuations for 8 Varieties of Tea, Prepared on 8 Days in 8 OrdersHarrison and Bose (1942), Sankhya, Vol6,#2,pp151-166Data Description Response: Mean Price Valuation among 6 judges 8 Tea Varieties (Crossing of Seed and Field Type): 4 jats (tea seed) BJ,KK,PG,CH 2 Field Types

2、- Pruned previous December, Unpruned 8 Dates of Manufacture (7/28 9/29) 8 Orderings of Preparation All varieties prepared on each date All varieties receive each order position of preparationOrder of Manufactured Samples, Valuations, MeansLatin Square Design - Model Model (8 Varieties, Dates, Orders

3、, N=82=64) : TermError Random Date todueEffect Order todueEffect Variety ofEffect Mean Overall , oneonly is thereNote .k.ijkjjjiiikkijkjikijkyyjyyiyykyjikyLatin Square Design - ANOVA & F-Test42)2)(1() 1(3) 1(2591. 22 Squares of SumError 7187823.208 Squares of Sum Date7181848. 08 Squares of SumOr

4、der 7182223. 88 Squares of SumVariety 63184486.31 :Squares of Sum Total281812.281.281.281.228181.ttttdfyyyyySSCSSRSSTTSSSSEdfyySSDatedfyySSOrderdfyySSVarietydfyyTSSEijkjiijkDjjOiiVkkijijkNote: We can partition Variety SS into main effects for jat and pruning, and their interaction (next slide)Decomp

5、osing Variety Sum of Squares3) 1 (33717. 04064. 04442. 72223. 81124064. 0321250.1342844.134 :Pruning3144442. 7167000.1223938.1321125.1326125.132 :Jat:nInteractio gJatxPrunin and Pruning Jat, into SSVariety thengPartitioni212.8.6.4.2.24.5.3.1.1412.8.7.46.5.34.3.22.1.1JPPmmJmmdfSSPSSJSSVarSSJPdfyPSSPy

6、yyyPyyyyPdfyJSSJyyJyyJyyJyyJAnalysis of VarianceEvidence of Jat and Pruning Main Effects, Interaction not significant at 0.05 significance levelPairwise Comparison of Jat MeansTukeys - q from Studentized Range Dist. k=4,n = (t-1)(t-2)=42 Note: Each Jat Mean is based on 2t=16 observations2194. 016053

7、8. 0784. 32),(05.tMSEkqWijn Bonferronis Method - t-values from table on class website with n = (t-1)(t-2)=42 and C=4(4-1)/2=62272. 0)8(2)0538. 0(2770. 222, 2/05.tMSEtBvCijVery close to significant difference Relative Efficiency Relative Efficiency of LS to CRD (how many times as many replicates woul

8、d be needed for CRD to have as precise of estimates of treatment means as LS does):796. 64842. 03719. 3)0538. 0(9)0538. 0(79689. 20264. 0) 1() 1(),(MSEtMSEtMSDateMSOrderMSEMSECRLSRELSCRWould need approximately 56 reps per variety to have as precise of estimates of variety means if experiment conducted as completely randomized design