Analisis Ragam
(Analysis of Variance, ANOVA)
Dr. Kusman Sadik, M.Si
Departemen Statistika IPB, 2017/2018
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 nkunits.
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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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i = pengaruh perlakuan (treatment) ke-i
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Yij = + i + 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
: correction factor
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JKT
JKP
JKG
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JKT
JKP
JKG
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H0 : Tidak ada perbedaan antar perlakuan
H1 : Minimal ada satu pasang perlakuan yang berbeda
atau
H0 : 1 = 2 = ... = k
H1 : Ada i j untuk i j
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 > F(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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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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