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

G

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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