Perancangan Percobaan

dan Analisis Ragam(Experimental Design and Analysis of Variance)

Dr. Kusman Sadik, M.Si

Departemen Statistika IPB, 2018/2019

Perancangan Percobaan (Rancob) : Experimental

Design.

Perlakuan : Treatment.

Ulangan : Replication.

Analisis Ragam : Analysis of Variance (Anova)

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In previous topic, we introduced methods for

comparing two population means.

When several means must be compared, more

general methods are required.

We now become acquainted with the powerful

technique called analysis of variance (ANOVA) that

allows us to analyze and interpret observations

from several populations/treatments.

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The term completely randomized design is

synonymous with independent random sampling

from several populations when each population is

identified as the population of responses under a

particular treatment.

Let treatment 1 be applied to n1 experimental

units, treatment 2 to n2 units,...,treatment k to nk

units.

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In a completely randomized design, n1

experimental units selected at random from the

available collection of n = n1+ n2 + … nk units are

to receive treatment 1;

n2 units randomly selected from the remaining

units are to receive treatment 2;

And proceeding in this manner, treatment k is to

be applied to the remaining nk units.

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αi = pengaruh perlakuan (treatment) ke-iYij = respon pada perlakuan ke-i dan ulangan ke-j

Yij = μ + αi + eij

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English Bahasa Indonesia

Total Sum of Squares / SST Jumlah Kuadrat Total / JKT

Treatment Sum of Squares / SST Jumlah Kuadrat Perlakuan / JKP

Error Sum of Squares / SSE Jumlah Kuadrat Galat / JKG

Mean Square / MS Kuadrat Tengah / KT

Mean Square of Treatment / MST Kuadrat Tengah Perlakuan / KTP

Mean Square of Error/ MST Kuadrat Tengah Galat / KTG

Degree of Freedom (df) Derajat Bebas (db)

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Sumber Jumlah Kuadrat

(JK)

Derajat Bebas

(db)

Kuadrat Tengah

(KT)

F-hit

Perlakuan JKP dbP = k - 1 KTP = JKP/dbP KTP/KTG

Galat JKG = JKT - JKP dbG = dbT - dbP KTG = JKG/dbG

Total JKT dbT = n - 1

k = banyaknya perlakuan

n = banyaknya data keseluruhan

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: correction factor

JKT

JKP

JKG

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JKT

JKP

JKG 16

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H0 : Tidak ada perbedaan antar perlakuan

H1 : Minimal ada satu pasang perlakuan yang berbeda

atau

H0 : μ1 = μ2 = ... = μk

H1 : Ada μi ≠ μj untuk i ≠ j

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KT(Galat)

an)KT(Perlaku

JKG/db

JKP/dbF

G

Phit

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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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One-way ANOVA: A; B; C; D

Source DF SS MS F P

Factor 3 68 22,67 4,34 0,018

Error 18 94 5,22

Total 21 162

Individual 95% CIs For Mean Based on Pooled StDev

Level N Mean StDev -+---------+---------+---------+--------

A 5 12,000 3,082 (--------*--------)

B 4 17,000 3,162 (---------*---------)

C 7 16,000 1,414 (------*------)

D 6 15,000 1,673 (-------*-------)

-+---------+---------+---------+--------

10,0 12,5 15,0 17,5

Jelaskan makna dari output Minitab tersebut.

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Selesaikan soal ini menggunakan Minitab, kemudian bandingkan

hasilnya dengan jawaban Anda pada No.1 di atas.

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Selesaikan soal ini menggunakan Minitab, kemudian bandingkan

hasilnya dengan jawaban Anda pada No.3 di atas.

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Selesaikan soal ini menggunakan Minitab, kemudian jelaskan

interpretasinya.

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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kusmansadik.wordpress.com

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