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Analisis Ragam / ANOVA
(Bagian II)
Dr. Kusman Sadik, M.Si
Departemen Statistika IPB, 2017/2018
The term “block design” originated from the design of
agricultural field trials, where “block” refers to a group
of adjacent plots.
A few typical examples for which the block design may
be appropriate are clinical trials to compare several
competing drugs, where the experimental subjects are
grouped in blocks according to age group.
Or subjects may be blocked according to
socioeconomic background.
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As its name implies, randomization is a basic part
of the block design.
This time, once the grouping of like experimental
subjects in blocks is accomplished, we randomly
select one subject from the first block to receive
treatment 1, one of the remaining subjects to
receive treatment 2, and so on.
The same procedure is repeated with a new
randomization for each of the remaining blocks.
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αi = pengaruh perlakuan (treatment) ke-iβj = pengaruh kelompok (block) ke-jCatatan : perbedaan perlakuan dan kelompok perlakuan
diacak di tiap kelompok, bukan sebaliknya.
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JKG = JKT – JKP - JKK
dbG = dbT – dbP - dbK
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KT(Galat)
an)KT(Perlaku
JKG/db
JKP/dbF
G
Phit
Tolak H0 jika Fhit > Fα(dbP , dbG)
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KT(Galat)
k)KT(Kelompo
JKG/db
JKB/dbF
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Bhit
Tolak H0 jika Fhit > Fα(dbK , dbG)
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Two-way ANOVA: Cutting Speed Data
(Johnson – p.564)
Source DF SS MS F P
Perlakuan 3 310 103,333 51,67 0,000
Blok 4 184 46,000 23,00 0,000
Error 12 24 2,000
Total 19 518
Perlakuan : tipe alat pemotong (tipe 1, 2, 3, dan 4)
Blok : jenis material yang dipotong (jenis 1, 2, 3, 4, dan 5)
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Individual 95% CIs For Mean Based on
Pooled StDev
Perlakuan Mean -------+---------+---------+---------+--
1 6 (---*---)
2 16 (---*---)
3 11 (---*---)
4 7 (---*---)
-------+---------+---------+---------+--
7,0 10,5 14,0 17,5
Berdasarkan Selang Kepercayaan di atas (CI), perlakuan (tipe alat
pemotong) mana yang paling baik? Jelaskan.
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Individual 95% CIs For Mean Based on
Pooled StDev
Blok Mean -----+---------+---------+---------+----
1 14 (----*----)
2 7 (----*----)
3 12 (----*----)
4 6 (----*----)
5 11 (----*----)
-----+---------+---------+---------+----
6,0 9,0 12,0 15,0
Berdasarkan Selang Kepercayaan di atas (CI),
a. Blok (jenis material) mana yang memiliki pengaruh berbeda? Jelaskan.
b. Jenis material mana yang paling mudah dipotong? Jelaskan.
Materi yang telah dibahas hanya mencakup RAL dan RAK, sebagai
materi dasar dalam metode Perancangan Percobaan (Experimental
Design).
Ada banyak materi lain yang mungkin diperlukan dalam penelitian,
diantaranya:
o Rancangan Faktorial (Factorial Design)
o Rancangan Split-Plot (Split-Plot Design)
o Rancangan Bujur Sangkar Latin (Latin-Squares Design)
Materi tersebut bisa dipelajari pada buku : Montgomery, D.C. 2013.
Design and Analysis of Experiments 8th. John Wiley & Sons, Inc.,
Canada.
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Pustaka
Johnson, R.A. and Bhattacharyya, G.K. 2010.
Statistics, Principles and Methods 6th. John Wiley
& Sons, Inc., New York.
Montgomery, D.C. 2013. Design and Analysis of
Experiments 8th. John Wiley & Sons, Inc., Canada.
Pustaka lain yang relevan.
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