model analisis ragam new2.ppt
TRANSCRIPT
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MODEL ANALISIS RAGAM
Pada Klasifikasi Eka ArahOne Way ANOVA
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Pada Populasi Tunggal
Berat Badan
μμ adalah nilai tengah populasi yang seharusnya, sehingga
Model Linier Populasi :
Yi = μ + εi
Di mana εi = galat
Karena hanya bekerja dengan 5 contoh yang berasal dari populasinya
Model linier Contoh :
Yi = ¯ + eiY
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Pada Contoh yang diambil dari Populasi Ganda
Mendapat Protein Rendah Mendapat Protein Tinggi
μ1
μ2
μτ1
τ2
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Model linier (Populasi)
Yij = μ + τi + εij
• Yij Nilai Pengamatan pada perlakuan
ke i dan contoh (ulangan) ke j• μ ¯ • τi ¯ - ¯
• εij Yij - ¯ = [(Yij - ¯ ) - (¯ - ¯ )
Y..
Y..Yi.
Yi. Y.. Y..Yi.
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Model linier (Contoh)
Yij = ¯ + (¯ - ¯ ) + [(Yij - ¯ ) - (¯ - ¯ ) ]
• Maka :
(Yij - ¯ ) = (¯ - ¯ ) + [(Yij - ¯ ) - (¯ - ¯ ) ]
Y.. Yi. Y.. Y.. Yi. Y..
Y.. Yi.Y.. Y.. Y..Yi.
Ragam Total (ST
2 )
Ragam Perlakuan
(SP2 )
Ragam Error (SG
2 )
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Ragam Total
• ST2 =
=
• JKT = Yij - FK
• FK =
Σ (Yij - Ϋ..) 2
( nt - 1)
Jumlah Kuadrat Total (JKT)
Derajat Bebas Total (Dbt)
Σ
(ΣYij)
nt
2
2
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Ragam Perlakuan
• SP2 =
=
• JKP = 1/n Yi. - FK
• FK =
Σ (Ϋi . - Ϋ..)2
( t - 1)
Jumlah Kuadrat Perlakuan (JKP)
Derajat Bebas Perlakuan (Dbp)
Σ
(ΣYij)
nt
2
2
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Ragam Error
• SE2 =
=
• JKE = JKT - JKP
Σ [(Yij -Ϋ..)2
t ( n - 1)
Jumlah Kuadrat Error (JKE)
Derajat Bebas Error (Dbg)
- Ϋi. - Ϋ..)]
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MENGHITUNG CEPATJUMLAH KUADRAT (JK)
• Bila ada Data sbb :T1 T2 T3 …………….. TtY11 Y21 Y31 …………….. Yt1
Y12 Y22 Y32 …………….. Yt2
Y13 Y23 Y33 ……………. Yt3
. . . ……………. .
. . . …………….. . Y1n Y2n Y3n ……………. Ytn
Y1. Y2. Y3. ……………. Yt. Y..
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MENGHITUNG CEPAT JUMLAH KUADRAT (JK)
JKT = Y11 + Y12 + . . . . . . Ytn - FK
Y1. + Y2. + . . . . . . Yt.
n
JKE = JKT - JKP
- FKJKP =
2 2 2
2 2 2
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UJI HIPOTESISPada Model :
Yij = μ + τi + εij Yij = μ + εij
Krn τi = 0, maka SP = S atau ------- = 1
Maka -------- = --------- = F hitung
Untuk H0 : τ1 = τ2 = τ3 = ……= τi = 0
H1 : Paling sedikit ada satu τi ≠ 0
Bila
Τi = 0
SP
SE
222
2SP
SE
2
2
KTP
KTE
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Kaidah Keputusan
• F Hitung
≤ F Tabel
> F Tabel
Terima H0
Terima H1
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(AN0VA=ANALISIS OF VARIANCE) One Way Class
SK DB JK KT F Hitung F Tabel1% , 5%
Perlakuan t -1 JKP KTP KTP/ KTE
Error t(n – 1) JKE KTE
Total nt - 1 JKT
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PENARIKAN KESIMPULAN
• F Hitung > F Tabel Ho ditolak• Kesimpulan : Perlakuan berpengaruh
nyata (P<0.05)• Kesimpulan : Perlakuan berpengaruh
sangat nyata (P<0.01)• Dari 6 perlakuan paling sedikit ada satu
perlakuan yang berbeda dengan perlakuan lain
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COEFISIEN VARIASI (CV)• KTE = S2 penduga σ2
• Galat Baku = Standard Error- Bagi Rata-rata Perlakuan ke i Syi = √ s2/n- Bagi Beda (selisih) antara rata-rata perlakuan ke i : Sy1.-y2.= Sd = √ 2s2
/n• Koefisien Keragaman = Koefisien Variasi :
CV = ------- x 100 % atau CV = ------- x 100 %
Y.. Y.. _ _S √ S2
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CONTOH 2. PERCOBAAN
• Dari 5 tablet sakit kepala yang diberikan ke pada 25 orang dicatat berapa lama tablet itu mengurangi rasa sakit. Ke 25 orang itu dibagi secara acak ke dalam 5 grup dan masing-masing grup diberi satu jenis tablet.
• Data yang diperoleh adalah sebagai berikut :
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Data Lamanya Hilang Rasa Sakit
A B C D E
54863
97869
35237
23414
76947
26 39 20 14 33 1325.2 7.8 4.0 2.8 6.6 5.28
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SELESAIKAN1. Sebutkan Rancangan Percobaan yang digunakan2. Sebutkan unit eksperiment, perlakuan, dan
ulangannya.3. Tuliskan model liniernya4. Tuliskan Hipotesis Statistiknya5. Hitunglah Jumlah Kuadrat Total, Perlakuan, dan Error.6. Sajikan Daftar ANOVA nya7. Buatlah kesimpulan
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DAFTAR SIDIK RAGAM = DASIRA (AN0VA=ANALISIS OF VARIANCE) RAL
SK DB JK KT F Hitung F Tabel5%
Perlakuan 4 79.440 19.860 6.90 2.87
Error 20 57.600 2.880
Total 24 137.040
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Pengamatan BerkelompokKelompok A B C D E Total
12345
54863
97869
35237
23414
76947
2625312030
Total 26 39 20 14 33 132Rata2 5.2 7.8 4.0 2.8 6.6 5.28
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DAFTAR SIDIK RAGAM = DASIRA (AN0VA=ANALISIS OF VARIANCE) RAK
SK DB JK KT F Hitung F Tabel5%
Kelompok 4 15.440
Perlakuan 4 79.440 19.860 7.64 3,01
Error 16 41.56 2.598
Total 24 137.040
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