Bujur Sangkar Latin (RBL) Rancangan Bujur Sangkar Latin (RBL) (Latin Square Design) Kuswanto-2012

Rancangan Bujur Sangkar Latin: RBL adalah pengembangan dari RAK. Dimana RBL diterapkan untuk lahan yang mempunyai 2 arah gradien penyebab heterogenitas Sangat tepat untuk penelitian dengan gradien kemiringan dan kelembaban tanah

Imagine a field with a slope and fertility gradient: B C A D E B C D A E A B C D E

Imagine a field with a slope and fertility gradient: B C A D E B C D A E A B C D E

Imagine a field with a slope and fertility gradient: B C A D E B C D A E A B C D E

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 = 35 Rows = r -1 = 6 – 1 = 5 Columns = c – 1 = 6 – 1 = 5 Treatments = k – 1 = 6 – 1 = 5 Error = 35 – 5 – 5 – 5 = 20 or (r-1)(c-1) – (k – 1) = (5x5) – 5 = 20

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. stor1 stor2 stor3 stor4 Field1 B D A C Field2 Field3 Field4

stor1 stor2 stor3 stor4 fld1 B D A C fld2 fld3 fld4 Each 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.

How to randomizing?? 1 2 3 4 5 A B C D E 1 2 3 4 5

Then randomize the rows: 1 2 3 4 5 2 B C D E A 5 4 3 1 Pay attention the row position!

Then randomize the rows: 1 2 3 4 5 2 B C D E A 5 4 3 1 Pay attention the row position!

Then Randomize columns, then randomly assign treatments to letters: 5 3 2 4 1 E C B D A 1 2 3 4 5

Then Randomize columns, then randomly assign treatments to letters: 5 3 2 4 1 E C B D A 1 2 3 4 5

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)

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 Variability Treatment (fixed) Row (random) Column (random)

Example: We want to compare effect of 4 different fertilizer on yield of potatoes. B D C A

Contoh : Hasil pipilan 4 varietas jagung Lajur Baris 1 2 3 4 Jlh baris 1,64 (B) 1,21(D) 1,42(C) 1,34(A) 5,62 1,47(C) 1,18(A) 1,40(D) 1,29(B) 5,35 1,67(A) 0,71(C) 1,66(B) 1,18(D) 5,225 1,56(D) 1,65(A) 0,66(C) 5,17 Jlh lajur 6,35 4,395 6,145 4,475 21,365 Hitung jumlah perlakuan (P) dan rata-ratanya

Jumlah perlakuan dan rerata 5,855 1,464 B 5,885 1,471 C 4,270 1,068 D 5,355 1,339

Hitung JK FK = (21,365)²/16 = 28,529 JKt = {(1,640)² + …+ 0,660)² -FK = 1,4139 JKb = (5,62)² + …+ (5,170)² -FK = 0,03015 JKl = (6,350)² +…+ (4,475)² -FK = 0,8273 JKp = (5,855)² + …+ (5,355)² -FK = 0,4268 JKe = JKt-JKb-JKl-JKp = 0,1295 Masukkan ke tabel ANOVA 

Tabel Anova Kesimpulan : Perlakuan  berbeda nyata SK DB JK KT F hit Ft5% Ft1% Baris 3 0,03015 0,01005 Lajur 0,8273 0,2757 Perlakuan 0,4268 0,1422 6,59* 4,76 9,78 Galat 6 0,1295 0,0215 Total 15 1,4139 Kesimpulan : Perlakuan  berbeda nyata

Interpretasi F hitung perlakuan berbeda nyata berarti 4 perlakuan tersebut secara statistik berbeda nyata Perbedaan antar perlakuan menyebabkan keragaman, dan keragaman yang disebabkan oleh perlakuan lebih besar daripada keragaman yang disebabkan oleh faktor sesatan percobaan (faktor lain)