# LATIN SQUARE Erlina Ambarwati.

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LATIN SQUARE Erlina Ambarwati

LATIN SQUARE Used if there are two source of variation among experimental unit Two directional blocking: column and row Treatment=row=column Impractical (disadvantage) Erlina Ambarwati 4/10/2017

Perbedaan: Antar tandan & antar sisir
A B C D Sumber keragaman: Antar Tandan Antar Sisir E Erlina Ambarwati 4/10/2017

Perbedaan kesuburan dan pencahayaan
Beda Pencahayaan S1 S2 S3 S4 B E D A K S U R N Erlina Ambarwati 4/10/2017

Tata letak dasar LS C B D A D C B A B A C D D A C B A B C D 4/10/2017
Erlina Ambarwati

Pengacakan Latin Square /Kolom
D B A B D C A D B C A B D C A Kolom diacak: 3, 2, 4, 1

Pengacakan LS (baris) C D C B B A B C B C B B C B B A=1 B=2
Perlakuan diacak: 1, 3, 2, 4 C=3 D=4 4/10/2017 Erlina Ambarwati

Latin Sqaure Row I A B C D Row II C D A B Row III D C B A
Row IV B A D C Column Erlina Ambarwati 4/10/2017

Linear Model for LS i = 1, 2, 3, ….., t j = 1,2, 3, ……, t
k = 1, 2, 3, ….., t Erlina Ambarwati 4/10/2017

Berbagai Nilai duga dengan model
Erlina Ambarwati 4/10/2017

Erlina Ambarwati 4/10/2017

Xijk -  = ζi + αj + βk + εikj, ζi , αj, βk & εijk independen
  (Xijk - )2 =   (ζi + αj + βk + εijk)2   (Xij - )2 =   ζ i ∑∑ αi2 +   βj   εijk2 JK total JK perlakuan JK Baris JK Kolom JK sesatan   (Xijk - )2=   Xijk2 + t22 – 2t22 =   Xijk2 – t2 2 =   Xijk2 – t2 (  Xij)2/(t)2 =   Xijk2 – (  Xij)2/t2

JK perlakuan JK plk =t  i2 4/10/2017 Erlina Ambarwati

JK BARIS JK baris =t  αj2 4/10/2017 Erlina Ambarwati

JK KOLOM JK baris =t  βk2 4/10/2017 Erlina Ambarwati

Erlina Ambarwati 4/10/2017

Analysis of Variance Table for a LATIN SQUARE
Source df SS MS F Treatment t-1 SST MST=SST/(t-1) MST/MSE Rows SSR MSR=SSR/(t-1) MSR/MSE Columns SSC MSC=SSC/(t-1) MSC/MSE Error (t-1)(t-2) SSE MSE=SSE/(t-1)(t-2) Total t2-1 SSTot Statistical Decision: when Ho is true, MSTr/MSE ~ F;(t-1);,(t-1)(t-2) if VRF reject 4/10/2017 Erlina Ambarwati

Example 1: A=15 B=8 C=9 D=12 C=10 D=7 A=16 B=7 C=7 D=10 D=11 A=10 B=9
4/10/2017 Erlina Ambarwati

Conclusion: There are significant diferrent between treatment effect
ANOVA SR df SS MS F F table Row 3 8 2,6667 1ns 4,76 Column 24 3ns Treatment 96 32 12** Error 6 16 Total 15 144 Conclusion: There are significant diferrent between treatment effect Erlina Ambarwati 4/10/2017

Missing Data pada LS R= jumlah pengaruh baris C= jumlah pengaruh kolom
T= jumlah pengaruh treatment G= grand total (jumlah total) t = jumlah treatment atau jumlah kolom atau jumlah baris Erlina Ambarwati 4/10/2017

Konsekuensi adanya missing data untuk uji lanjut dg LSD
a. Jika tidak ada missing data b. Mengandung satu missing data c. Mengandung dua missing data t1 dan t2 : angka ulangan efektif Erlina Ambarwati 4/10/2017

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