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: slope fertility B C C D A E D B E A A B C D E B C D E A C D E A B D E A B C E A B C D B C A D E C D E B A

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

A

B C D E

B

C D E A

C

D E A B

D

E A B C

E

A B C D B C A D E C D E B A

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

A B C D E

B C D E A C D E A B D E A B C E A B C D B C A D E C D E B A

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

fld1 fld2 fld3 fld4 C A stor1 B D A C stor2 D B B D stor3 A C D B stor4 C A 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 1 A B C D E 2 B C D E A 3 C D E A B 4 D E A B C 5 E A B C D

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

4 E C B A D 5 A D C B E

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

4 E C B A D 5 A D C B E

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

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

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 )

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 5 different fertilizer on yield of potatoes.

B D C A C A D B A D C B B A D C

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

21,365

Hitung jumlah perlakuan (P) dan rata-ratanya

Jumlah perlakuan dan rerata

Perlakuan A B C D Jumlah 5,855 5,885 4,270 5,355 Rerata 1,464 1,471 1,068 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 

SK DB Baris Lajur 3 3 Perlakuan 3 Galat Total 6 15

Tabel Anova

JK 0,03015 0,8273 0,4268 0,1295 1,4139 KT 0,01005 0,2757 0,1422 0,0215 F hit 6,59* Ft5% Ft1% 4,76 9,78 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)