Presentasi berjudul: "Bujur Sangkar Latin (RBL)"— Transcript presentasi:
1 Bujur Sangkar Latin (RBL) RancanganBujur Sangkar Latin (RBL)(Latin Square Design)Kuswanto-2012
2 Rancangan Bujur Sangkar Latin: RBL adalah pengembangan dari RAK.Dimana RBL diterapkan untuk lahan yangmempunyai 2 arah gradien penyebab heterogenitasSangat tepat untuk penelitian dengan gradien kemiringan dan kelembaban tanah
3 Imagine a field with a slope and fertility gradient: BCADEBCDAEABCDE
4 Imagine a field with a slope and fertility gradient: BCADEBCDAEABCDE
5 Imagine a field with a slope and fertility gradient: BCADEBCDAEABCDE
6 We refer to Latin Squares as 3x3 or 5x5 etc. A Latin square requires the same number of replications as we have treatments.Degrees of freedom are calculated as follows(6x6 example):Total = (6x6) – 1 = 35Rows = r -1 = 6 – 1 = 5Columns = c – 1 = 6 – 1 = 5Treatments = k – 1 = 6 – 1 = 5Error = 35 – 5 – 5 – 5 = 20or (r-1)(c-1) – (k – 1) = (5x5) – 5 = 20
7 Example:We are interested in the effect of 4 fertilizers (A,B,C,D) on corn yield. We have seed which was stored under four conditions and we have four fields in which we are conducting the experiment.stor1stor2stor3stor4Field1BDACField2Field3Field4
8 stor1stor2stor3stor4fld1BDACfld2fld3fld4Each treatment appears in each row and column once.Treatments are assigned randomly, but as each is assigned, constraints are placed on the next treatment to be assigned.
10 Then randomize the rows: 123452BCDEA5431Pay attention the row position!
11 Then randomize the rows: 123452BCDEA5431Pay attention the row position!
12 Then Randomize columns, then randomly assign treatments to letters: 53241ECBDA12345
13 Then Randomize columns, then randomly assign treatments to letters: 53241ECBDA12345
14 The LS design is most often used with a field to account for gradients in soil, fertility, or moisture.In a greenhouse, plants on different shelves (rak) and benches (bangku) may be blocked.Latin Squares are also useful when we know (or suspect variation) of a linear nature, but do not know the direction it will take (eg bark beetle study).The Latin Square design is only useful if both rows and columns vary appreciably. If they do not, a RCBD (RAK) or Completely randomized design (RAL) would be better (more degrees of freedom in the error term for F test)
15 Model Source of Variability Treatment (fixed) Row (random) How to analysis of a Latin Square:Three way model, treatment fixed effect, rows and columns are both random effects.No replication so same problem as RCB design (RAL) with experimental error. Must remove interaction from model – assume no interaction.Model Source of VariabilityTreatment (fixed)Row (random)Column (random)
16 Example: We want to compare effect of 4 different fertilizer on yield of potatoes. BDCA
17 Contoh : Hasil pipilan 4 varietas jagung LajurBaris1234Jlh baris1,64 (B)1,21(D)1,42(C)1,34(A)5,621,47(C)1,18(A)1,40(D)1,29(B)5,351,67(A)0,71(C)1,66(B)1,18(D)5,2251,56(D)1,65(A)0,66(C)5,17Jlh lajur6,354,3956,1454,47521,365Hitung jumlah perlakuan (P) dan rata-ratanya
18 Jumlah perlakuan dan rerata 5,8551,464B5,8851,471C4,2701,068D5,3551,339
20 Tabel Anova Kesimpulan : Perlakuan berbeda nyata SK DB JK KT F hit Ft5% Ft1%Baris30,030150,01005Lajur0,82730,2757Perlakuan0,42680,14226,59*4, ,78Galat60,12950,0215Total151,4139Kesimpulan : Perlakuan berbeda nyata
21 InterpretasiF hitung perlakuan berbeda nyata berarti 4 perlakuan tersebut secara statistik berbeda nyataPerbedaan antar perlakuan menyebabkan keragaman, dan keragaman yang disebabkan oleh perlakuan lebih besar daripada keragaman yang disebabkan oleh faktor sesatan percobaan (faktor lain)
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