Tugas AD Kelompok 3 Graeco Latin

Rancangan GraecoLatin Square Mata Kuliah Analisis Data 1 Disusun oleh:

1. Anggun Yuanita Prieskawati 1308100021 1308100049 2. Wahyudi

3. Mega Silfiani 4. Ida Ayu Sevita Intansari 5. Rahmi Amelia 6. Arma Fa Fauziyatul Ma Mafrida 7. Dwi Ratnasari 8. Wahyuning Pintowati

1308100051 1308100079 1308100063 1308100093 1308100097 1308100109

Dosen : Dr. Irhamah, M.Si.

JURUSAN STATISTIKA FAKULTAS MATEMATIKA DAN ILMU PENGETAHUAN ALAM INSTITUT TEKNOLOGI SEPULUH NOPEMBER  SURABAYA 2011

Titles you can't find anywhere else

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

Titles you can't find anywhere else

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

Titles you can't find anywhere else

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

Titles you can't find anywhere else

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

Titles you can't find anywhere else

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

Titles you can't find anywhere else

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

Titles you can't find anywhere else

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

Rancangan Bujur Sangkar Graeco-Latin (RBSGL) Pada suatu percobaan atau penelitian, analisis hanya akan bersifat eksak  apabila apabila semua asumsi, umumnya mengenai bentuk bentuk distribusi distribusi,, dapat dipenuhi. dipenuhi. Tetapi terkadang pemenuhan asumsi tersebut sukar dilakukan sehingga dalam  banyak hal sering bergantung pada kecakapan dalam pemilihan metode analisis yang tepat, termasuk cara-cara perencanaan yang tepat untuk memperoleh data yang diperlukan. Untuk memaksimalkan kegunaan data dalam suatu analisis, dibutuhkan   peren perencan canaan aan ilmiah ilmiah,, yang yang lebih lebih dikena dikenall dengan dengan rancan rancangan gan percob percobaan aan.. Dalam Dalam rancangan percobaan memuat semua langkah lengkap yang perlu diambil sebelum melakukan percobaan supaya data yang diperlukan dapat diperoleh dan digunakan secara optimal. optimal. Hal ini nantinya nantinya akan membawa membawa kepada suatu analisis analisis objektif  objektif  serta dapat ditarik kesimpulan untuk persoalan yang sedang dibahas. Dalam Dalam sebuah sebuah percob percobaan aan bila bila unit-u unit-unit nit percob percobaan aan relatif relatif hetero heterogen gen,, maka dibutuhkan suatu rancangan percobaan yang dapat mengendalikan variasi yang yang terjad terjadii pada pada percob percobaan aan terseb tersebut. ut. Untuk Untuk menghi menghilan langka gkan n dua jenis jenis varias variasii digunakan Rancangan Bujur Sangkar Latin (RBSL) yaitu percobaan dengan cara melaksanakan pemblokan dua arah dan apabila diinginkan untuk menghilangkan tiga variasi, maka digunakan digunakan Rancangan Rancangan Bujur Sangkar Graeco Latin (RBSGL). Dalam makalah ini akan dijelaskan tentang RBSGL serta contoh aplikasi yang dise disert rtai ai deng dengan an peny penyel eles esai aian anny nyaa secar secaraa manu manual al dan dan deng dengan an meng menggu guna naka kan n

 software.

RANCANGAN BUJUR SANGKAR GRAECO-LATIN (RBSGL) a.

Pengertian

Rancan Rancangan gan bujur bujur Sangka Sangkarr Graeco Graeco-La -Latin tin (RBSGL (RBSGL)) bertuj bertujuan uan untuk  untuk  menghi menghilan langka gkan n tiga tiga jenis jenis varias variasi. i. RBSGL RBSGL diguna digunakan kan apabil apabilaa ditemu ditemuii suatu suatu

Titles you can't find anywhere else

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

Titles you can't find anywhere else

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

Titles you can't find anywhere else

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

Titles you can't find anywhere else

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

Titles you can't find anywhere else

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

Titles you can't find anywhere else

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

Alasan disebut disebut RBSGL, RBSGL, yaitu yaitu : 1.

Terdapat Terdapat 4 buah buah faktor faktor yaitu yaitu faktor faktor baris, baris, kolom, kolom, huruf-huru huruf-huruff Latin Latin dan hurufhurufhuruf Greek ;

2.

Keempa Keempatt fakt faktor or mempu mempunya nyaii taraf taraf yang yang sama sama;;

3.

Setiap perlakuan perlakuan hanya muncul muncul sekali sekali di setiap setiap baris, baris, kolom kolom dan huruf Greek 

Model Statistik untuk analisisi rancangan bujur sangkar Graeco-latin (RBSGL), yaitu : Yijkl = µ +θ i +τ   j + ω k  +ψ  l  + ε ijkl 

Model tersebut memiliki syarat-syarat, yaitu : i =

1, 2, 3, ..., p

j =

1, 2, 3, ..., p

k =

1, 2, 3, ..., p

l =

1, 2, 3, ..., p

 p = banyak taraf perlakuan

Keterangan : Yijkl

:

hasi hasill obser observa vasi siya yang ng dica dicata tatt dari dari bari bariss ke-i, ke-i, huru huruf  f  Greek  ke-k, kolom ke-l dan perlakuan ke-j

 µ 

:

rata-rata ke keseluruhan

θ   i

:

efek baris ke-i

τ     j

:

efek hu huruf la latin ke ke-j

ω   k 

:

efek huruf  Greek  Greek  ke-k 

ψ   l 

:

efek kolom ke-l

ε   ijkl 

:

sesatan random dengan ε   ~DNI (0, σ 2 ) ijkl  Model di atas diartikan bahwa besarnya hasil observasi yang dicatat

dari baris ke-i, perlakuan ke-j, huruf Greek ke-k, dan kolom ke-l dipengaruhi oleh rata-rata keseluruhan, efek baris ke-i, efek huruf Latin ke-j, efek huruf Greek ke-k, efek kolom ke-l dan besarnya sesatan random. Keempat faktor tidak boleh berinteraksi dikarenakan RBSGL adalah  percobaan faktor tunggal sehingga apabila ada interaksi dari keempat faktor akan

Titles you can't find anywhere else

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

Titles you can't find anywhere else

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

Titles you can't find anywhere else

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

Titles you can't find anywhere else

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

Titles you can't find anywhere else

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

Titles you can't find anywhere else

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

Tabel 1. Rancangan Bujur Sangkar Graeco-Latin

Kolom

Baris

1 A α  B γ    C δ   D

1 2 3 4

2

3 C γ    D α  A B δ  

B A δ   D γ    C α 

4 D δ   C B α  A γ   

b. Ana Analisi lisiss Sta Statist istik  *)

Langkah-langkah Langkah-langkah Analisis Statistik 

1.

Mene Menen ntuk tukan hip hipotes otesis is Model Efek Tetap H0 :

 µ 1

=  µ 2 =

... ...

=  µ a

(semua (semua perlak perlakuan uan member memberika ikan n hasil hasil yang yang

sama terhadap respon)  µ i ≠ µ   j

H1 : paling sed sedikit

(palin (paling g sediki sedikitt dua buah buah perlak perlakuka ukan n

memberikan hasil yang berbeda terhadap respon) atau H0 :

τ  1 = τ  2 =

... = τ  a

H1 : paling sedi edikit

=

0 (perlakuan tidak mempengaruhi respon)

τ i ≠ 0

(perlakuan mempengaruhi respon)

Model Efek Random H0 :

2 σ   = τ  

0 (terdapat variabilitas di antara perlakuan)

H1 :

2 σ   ≠ τ  

0 (terdapat variabilitas di antara perlakuan)

α 

2.

Menentukan

3.

Mene Menent ntuk ukan an daer daerah ah krit kritis is H0 ditolak, jika

*)

F0

> F(α   , (p -1), (p - 3)(p -1))

4.

Mene Menent ntuk ukan an stat statis isti tik k uji uji,, yait yaitu u F0 =

5.

Mena Menari rik k kesi kesim mpula pulan n

Menghitung Jumlah Kuadrat

RK  perlakuan RKError 

Titles you can't find anywhere else

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

Titles you can't find anywhere else

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

Titles you can't find anywhere else

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

Titles you can't find anywhere else

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

Titles you can't find anywhere else

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

Titles you can't find anywhere else

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

 p

JK Baris

=

Yi ... 2

∑ i =1

 p

−

Y .... 2

; db = p-1

 N 

 p

JK Kolom

JK Greek

JK Perlakuan/Latin JKT

=

=

= =

Y ... ... l 2 Y .... 2 ∑  p − N  l =1  p

Y ..k .2

k =1

 p

 p

Y .  j..2

  j =1

 p

∑ ∑

−

−

; db = p-1

Y .... 2

; db = p-1

N  Y .... 2

; db = p-1

N 

JK Baris + JK Perlakuan + JK Greek + JK   Kolom +JK Error 

Sehingga, JK Error

=

JKT – JKBaris – JKKolom – JKPerlakuan –   JKGreek (db = (p-3)(p-1)) (p-3)(p-1)) Tabel 2. ANOVA

Sumber

db

JK

RK

Perlakuan

p-1

JKP

JKP/(p-1)

F 0=

Baris

p-1

JKB

JKB/(p-1)

F 0=

Kolom

p-1

JKK

JKK/(p-1)

Variasi

F RKP RKE RKB

RKE RKK  F0= RKE

F0= Huruf Greek

p-1

JK Greek

JK Greek/(p-1)

RKGreek  RKE

Error  TOTAL

(p-3)(p1) P2-1

JKE

JKE/((p-3)(p1))

JKT

*) Uji Perbandingan Ganda (uji ini dilakukan apabila pada pengujian model efek diperoleh kesimpulan H0 ditolak) 1. Meto Metode de LS LSD D ( Least   Least Significant Difference) Difference)

Prosedur ini digunakan untuk menguji hipotesis sebagai berikut:

Titles you can't find anywhere else

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

Titles you can't find anywhere else

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

Titles you can't find anywhere else

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

Titles you can't find anywhere else

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

Titles you can't find anywhere else

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

Titles you can't find anywhere else

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

dengan mengasumsikan bahwa yang digunakan adalah alternatif dua sisi, maka pasangan dari

dan

akan dikatakan berbeda secara signifikan jika:

.  Nilai statistik uji LSD •

Perulangan tidak sama LSD=

•

Perulangan sama LSD=

2. Meto Metode de Tu Tuke key y

Metode ini juga digunakan untuk menguji hipotesis seperti pada metode LSD: Ho:

;i j

H 1: Prosedur Tukey ini menggunakan  studentized range statistic dengan

dimana

dan

adalah rata-rata sampel yang tertinggi dan terendah.

Rata-rata dua sampel dikatakan berbeda secara signifikan jika nilai absolut dari selisih kedua sampel tersebut melebihi: untuk perulangan yang sama, dan

untuk perulangan yang berbeda.

CONTOH APLIKASI RBSGL Seorang peneliti mempelajari efek 5 formulasi (perlakuan) berbeda dari

Titles you can't find anywhere else

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

Titles you can't find anywhere else

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

Titles you can't find anywhere else

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

Titles you can't find anywhere else

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

Titles you can't find anywhere else

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

Titles you can't find anywhere else

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

Titles you can't find anywhere else

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

mentah dan disiapkan oleh beberapa operator. Dimana operator mempunyai skill dan pengalaman berbeda. Faktor tambahan lain dalam penelitian tersebut adalah uji perakitan (assemblies assemblies test ) yang dinotasikan dengan α, β, γ, δ dan

∈.

Berikut

ini adalah struktur data dari desain RBSGL. Tabel 3. Desain RBSGL

Baris

1

2 γ   

A α  B C γ    D δ   E∈

1 2 3 4 5

Kolom 3 C∈ D α  E A γ    B δ  

B C δ   D∈ E α  A

4

5

D E γ    A δ   B∈ C α 

E δ   A∈ B α  C D γ   

PENYELESAIAN SECARA MANUAL

Data Data pengam pengamata atan n atau atau obser observas vasii yang yang dipero diperoleh leh oleh oleh peneli peneliti ti adalah adalah sebagai berikut jika di desain sesuai RBSGL. Tabel 4. Desain RBSGL contoh aplikasi

Bahan Mentah 1

1

2

Operator  3 4

A α  =2

B γ   =20

C ∈ =19

D

2

4 B

C δ  =24

3

7 C γ   =18

=1

4

D δ  =2

5

6 E ∈ =22

Y  i ...

5 E δ  =24

2 ...

111

12321

D α  =3

4 E γ   =27

A ∈ =36 134

17956

D ∈ =38

0 E β  =2

A δ  =2

B α  =2

130

16900

E α  =31

6 A γ   =26

7 B ∈ =23

1 C

128

16384

C α  =2

2 D γ   =31 132

17424

A β  =3

B δ  =20

=2

Y i

=2

Titles you can't find anywhere else

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

Titles you can't find anywhere else

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

Titles you can't find anywhere else

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

Titles you can't find anywhere else

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

Titles you can't find anywhere else

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

Titles you can't find anywhere else

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

2. H0 = tidak ada perbedaan rata – rata tingkat pembakaran pada aircrew

 system berdasarkan bahan mentah H1= paling tidak terdapat satu perbedaan rata - rata tingkat pembakaran pada

aircrew system  berdasarkan bahan mentah. 3. H0 = tidak ada perbedaan rata – rata tingkat pembakaran pada aircrew

 system berdasarkan operator  H1= paling tidak terdapat rata – rata tingkat pembakaran pada aircrew system  berdasarkan operator  4. H0 = tidak ada perbedaan rata – rata tingkat pembakaran pada aircrew

 system berdasarkan uji perakitan H1= paling tidak terdapat rata – rata tingkat pembakaran pada aircrew system  berdasarkan uji perakitan

Perhitungan ANOVA GRAECO secara manual.  p

 p

 p

 p

∑∑∑∑Y ijkl 

SS_total =

2

i =1   j =1 k =1 l  =1

2

=

(24

=

16805

SS_baris =

1  p

+

20

−

2

+

19

16129

 p

∑Y 

2 ... i ...

−

i =1

111 (111 =

2

+ 134 134

2

2

=

+

68

 N  2

... + 31 ) −

635 635 2 25

676 676

Y ...2  N  + 130 130

5 =

−

Y ....2

2

+ 128 128

2

+ 132 132

2

) − 635 635 25

2

Titles you can't find anywhere else

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

Titles you can't find anywhere else

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

Titles you can't find anywhere else

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

Titles you can't find anywhere else

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

Titles you can't find anywhere else

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

Titles you can't find anywhere else

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

 p

1

SS_greek =

 p

=

∑Y 

2 .. k .

−

k =1

(135

2

119 + 119

2

Y ......2  N 

121 + 121

2

+ 122

2

+ 138

5

2

635 ) − 635

2

25

= 62

SS_latin =

1  p

 p

∑Y 

2 .  j ..

−

k =1

143 (143 =

2

101 + 101

2

Y ......2  N 

112 + 112

2

+ 149

2

+ 130

2

5

635 ) − 635

2

25

= 330

SS_Error = SStotal – SSbaris – SSkolom – SSgreek – SSlatin = 676 – 68 – 150 – 62 – 330 = 66 Sumber Perlakuan/Latin

1  p

Baris

1  p

Kolom

1  p

Greek 

1  p

Error Total

 p

∑Y 

2 .  j ..

k =1

SS Y ...2 −  N 

df  p-1

Y ...2

 p-1

 p

∑Y  − 2 ... i ...

 p

∑Y  − 2 ... ... l 

 N 

 p

∑Y 

2 .. k .

 p-1

2 Y ... ...

l =1

−

Y ......2

k =1

SS   perlakuan  p −1

 N 

i =1

MS

 p-1

 N 

 p −1

MS  E 

SS  kolom

MS  kolom

 p −1

MS  E 

SS  greek 

MS  greek 

 p −1

MS  E 

SS  Error 

-SSB – SSK  – SSG

(p-1) P2-1

( p − 2)( p −1)

 p

 p

∑∑∑∑Y ijkl  i =1   j =1 k =1 l =1

2

−

Y ....2  N 

MS  E 

MS  baris

(p-2)

 p

MS   perlakuan

SS  baris

SSE = SST - SStreatment +  p

F

Titles you can't find anywhere else

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

Titles you can't find anywhere else

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

Titles you can't find anywhere else

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

Titles you can't find anywhere else

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

Titles you can't find anywhere else

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

Titles you can't find anywhere else

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

Fhitung >F(0.05,4,8) = 3, 84 Kesimpulan

Karena Fhit Fhitung ung = 10 > 3,84 3,84 maka maka tola tolak k H0 artinya ada perbedaan tingkat 1. Karena  pembakaran pada aircrew system  berdasarkan formulasi Karena Fhit Fhitung ung = 2,06 2,06 < 3,84 3,84 maka maka gagal gagal tola tolak k H0 artinya tidak terdapat 2. Karena  perbedaan rata - rata tingkat pembakaran pada aircrew system  berdasarkan  bahan mentah.

3. Karena Fhitung Fhitung = 4,54 > 3,84 maka tolak H 0 artinya ada perbedaan tingkat  pembakaran pada aircrew system berdasarkan operator. Karena Fhitu Fhitung ng = 1,89 1,89 < 3,84 3,84 maka maka gagal gagal tolak tolak H 0 artinya tidak terdapat 4. Karena  perbedaan rata - rata tingkat pembakaran pada aircrew system  berdasarkan uji  perakitan.

UJI PERBANDINGAN BERGANDA TUKEY SECARA MANUAL 1. Ho:

; i j (rata ata-ra -rata ting ingkat pembakaran pada aircrew system

  berd berdas asark arkan an form formul ulas asii leve levell ke-i ke-i

rata rata-ra -rata ta ting tingka katt pemb pembak akar aran an pada pada

aircrew system  berdasarkan formulasi level ke-j) H1:

(rata-rata tingkat pembakaran pada aircrew system  berdasarkan

form formul ulas asii leve levell ke-i ke-i

rata-r rata-rat ataa ting tingka katt pemb pembak akar aran an pada pada aircrew system

 berdasarkan formulasi level ke-j) PERBANDINGAN GANDA FORMULASI

Kesimpulan

Titles you can't find anywhere else

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

Titles you can't find anywhere else

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

Titles you can't find anywhere else

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

Titles you can't find anywhere else

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

Titles you can't find anywhere else

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

Titles you can't find anywhere else

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

2&4

qHitung

7,47 Q0.05(5,20) 4,51

4.24

Tolak H0

2&5

Qtabel qHitung Qtabel

Q0.05(5,20)

4.24

Tolak H0

3&4 3&5 4&5

qHitung

5,76

Qtabel

Q0.05(5,20)

4.24

Tolak H0

qHitung Qtabel

2,8 Q0.05(5,20)

4.24

Gagal Tolak H0

qHitung

2,96 4.24

Gagal Tolak H0

Qtabel

Q0.05(5,20)

; i j (rata ata-ra -rata ting ingkat pembakaran pada aircrew system

2. Ho:

  berd berdas asark arkan an oper operato atorr ke-i ke-i

rata-r rata-rata ata ting tingka katt pemb pembak akar aran an pada pada aircrew

 system berdasarkan operator ke-j) H1:

(rata-rata tingkat pembakaran pada aircrew system  berdasarkan

opera perato torr ke-i ke-i

rata rata-r -rat ataa tin tingkat gkat pemb pembak akar aran an pada pada aircr aircrew ew syste system m

 berdasarkan operator ke-j)

PERBAN PERBANDIN DINGAN GAN GANDA GANDA OPERAT OPERATOR OR 1&2

qHitung Qtabel

1&3

1&4

5,6 Q0.05(5;20)

qHitung Qtabel qHitung

Kesimp Kesimpula ulan n 4.2 4

Tolak H0

4.2 4

Gagal To Tolak H0 H0

2,18 Q0.05(5;20) 3,58 4.2

Titles you can't find anywhere else

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

Titles you can't find anywhere else

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

Titles you can't find anywhere else

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

Titles you can't find anywhere else

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

Titles you can't find anywhere else

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

Titles you can't find anywhere else

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

Titles you can't find anywhere else

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

4 3&4

qHitung

1,4

Qtabel 3&5

Q0.05(5;20)

qHitung

Gagal To Tolak H0 H0

4.2 4

Gagal To Tolak H0 H0

4.2 4

Gagal To Tolak H0 H0

2,02

Qtabel qHitung

4&5

4.2 4

Q0.05(5;20) 0,62

Qtabel

Q0.05(5;20)

Langkah-langkah mengerjakan soal rancangan graeco. Misalnya terdapat contoh seperti pada Tabel 1. Tabel 5. Contoh Soal Rancangan Graeco

Bahan 1

2

Operator  3

A α  =2

B γ   =20

C ∈ =19

D

=2

E δ  =24

4

4

2

B β  =1

C δ  =2

D α  =3

E γ   =27

A ∈ =36

7

4

0

3

C γ   =18

D ∈ =3

=2

A δ  =2

B α  =2

8

6

D δ  =2

E α  =3

7 B ∈ =23

1

A γ   =2

6

1

6

Mentah 1

4

E

4

5

C

=2 2

Titles you can't find anywhere else

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

Titles you can't find anywhere else

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

Titles you can't find anywhere else

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

Titles you can't find anywhere else

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

Titles you can't find anywhere else

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

Titles you can't find anywhere else

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

mentah 1 1 1 1 1 2 2 2 2 2 3 3 3 3 3 4 4 4 4 4 5 5 5 5

1 2 3 4 5 2 3 4 5 1 3 4 5 1 2 4 5 1 2 3 5 1 2 3

perakitan 1 3 5 2 4 2 4 1 3 5 3 5 2 4 1 4 1 3 5 2 5 2 4 1

1 2 3 4 5 1 2 3 4 5 1 2 3 4 5 1 2 3 4 5 1 2 3 4

24 24 20 20 19 19 24 24 24 24 17 17 24 24 30 30 27 27 36 36 18 18 38 38 26 26 27 27 21 21 26 26 31 31 26 26 23 23 22 22 22 22 30 30 20 20 29 29

Titles you can't find anywhere else

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

Titles you can't find anywhere else

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

Titles you can't find anywhere else

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

Titles you can't find anywhere else

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

Titles you can't find anywhere else

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

Titles you can't find anywhere else

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

1. Ketik data data seperti pada pada Tabel 6 ke dalam minitab minitab yang dapat dapat dilihat dilihat seperti  pada Gambar 1.

Gambar 1. Data Rancangan Graeco

2. Klik Stat, sorot sorot ANOVA dan dan klik general general linier model model yang dapat dilihat dilihat seperti pada Gambar 2.

Titles you can't find anywhere else

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

Titles you can't find anywhere else

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

Titles you can't find anywhere else

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

Titles you can't find anywhere else

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

Titles you can't find anywhere else

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

Titles you can't find anywhere else

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

3. Setelah Setelah melakukan melakukan perintah pada pada langkah 2, akan akan muncul windows windows General Linier Model yang dapat dilihat seperti pada Gambar 3. a

 b

c

Gambar 3. Windows General Linier Model

a. Masukkan Masukkan variabel variabel respon respon ke ke dalam box box Response Responsess   b. Masukkan Masukkan kodingan kodingan dari baris baris (bahan mentah), mentah), huruf greek (formulas (formulasi), i), kolom(uji perakitan) dan perlakuan (operator) ke dalam box Model c. Kosong Kosongkan kan box Random Random Factor Factor jika jika pada pada model model tidak tidak terdapat terdapat variab variabel el

Titles you can't find anywhere else

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

Titles you can't find anywhere else

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

Titles you can't find anywhere else

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

Titles you can't find anywhere else

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

Titles you can't find anywhere else

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

Titles you can't find anywhere else

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

Gambar 4. Windows Comparisons

Minitab akan default comparison pada pilihan pairwise comparisons. Gunakan comparison with a control jika terdapat variabel pengontrol percobaan. a. Masuk Masukka kan n kodi koding ngan an dari dari bari bariss (bah (bahan an ment mentah ah), ), huru huruff greek greek (for (formu mula lasi si), ), kolo kolom( m(uj ujii pera peraki kita tan) n) dan dan perl perlak akua uan n (ope (opera rato tor) r) ke dala dalam m term term untu untuk  k  membandingkan pasangan level-level dalam faktor.  b. Centan Centang g metode metode dalam perband perbanding ingan an ganda ganda yang diingink diinginkan an pada pada checkl checklist ist meth method od..

Dala Dalam m

pem pembah bahasan asan

 perbandingan ganda.

ini, ini,

dig digunak unakan an

meto metode de

Tukey key

dala dalam m

Titles you can't find anywhere else

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

Titles you can't find anywhere else

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

Titles you can't find anywhere else

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

Titles you can't find anywhere else

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

Titles you can't find anywhere else

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

Titles you can't find anywhere else

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

Titles you can't find anywhere else

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

menampilkan tabel ANOVA, koefisien dari persamaan covariate dan tabel  pengamatan yang tidak biasa (unusual observations) yang dapat dilihat seperti  pada Gambar 5.

Titles you can't find anywhere else

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

Titles you can't find anywhere else

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

Titles you can't find anywhere else

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

Titles you can't find anywhere else

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

Titles you can't find anywhere else

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

Titles you can't find anywhere else

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

formulasi uji perakitan operator Error Total

S = 2.87228

4 4 4 8 24

330.000 62.000 150.000 66.000 676.000

330.000 62.000 150.000 66.000

R-Sq = 90.24%

82.500 15.500 37.500 8.250

10.00 1.88 4.55

0.003 0.208 0.033

R-Sq(adj) = 70.71%

Sebesar 90.24% model dapat menjelaskan respon re spon Unusual Observations for respon Obs 24

respon 29.0000

Fit 25.6000

SE Fit 2.3685

Residual 3.4000

St Resid 2.09 R

R denotes an observation with a large standardized residual. Grouping Information Using Tukey Method and 95.0% Confidence bahan mentah 2 5 3

N 5 5 5

Mean 26.8 26.4 26.0

Grouping A A A

Titles you can't find anywhere else

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

Titles you can't find anywhere else

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

Titles you can't find anywhere else

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

Titles you can't find anywhere else

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

Titles you can't find anywhere else

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

Titles you can't find anywhere else

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

formulasi = 4 formulasi 5

subtracted from:

Lower -10.08

Center -3.800

Upper 2.481

-----+---------+---------+---------+(-----*-----) -----+---------+---------+---------+-10 0 10 20

Tukey Simultaneous Tests Response Variable respon All Pairwise Comparisons among Levels of formulasi formulasi = 1 subtracted from:

formulasi 2 3 4 5

Difference of Means -8.400 -6.200 1.200 -2.600

formulasi = 2

SE of Difference 1.817 1.817 1.817 1.817

T-Value -4.624 -3.413 0.661 -1.431

Adjusted P-Value 0.0108 0.0529 0.9597 0.6270

 p-value < 0.05 sehingga dapat

subtracted from:

Difference

SE of

Adjusted

dika dikata taka kan n

perba erband ndin inga gan n

Titles you can't find anywhere else

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

Titles you can't find anywhere else

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

Titles you can't find anywhere else

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

Titles you can't find anywhere else

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

Titles you can't find anywhere else

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

Titles you can't find anywhere else

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

1

5

21.4

B

Means that do not share a letter are significantly different.

Tukey 95.0% Simultaneous Confidence Intervals Response Variable respon All Pairwise Comparisons among Levels of operator operator = 1 subtracted from: operator 2 3 4 5

Lower 0.919 -3.481 -1.681 -0.881

operator = 2 operator 3 4

Center 7.200 2.800 4.600 5.400

Upper 13.481 9.081 10.881 11.681

-----+---------+---------+---------+(--------*--------) (--------*--------) (--------*--------) (--------*--------) -----+---------+---------+---------+-7.0 0.0 7.0 14.0

subtracted from:

Lower -10.68 -8.88

Center -4.400 -2.600

Upper 1.881 3.681

-----+---------+---------+---------+(--------*--------) (--------*--------)

Titles you can't find anywhere else

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

Titles you can't find anywhere else

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

Titles you can't find anywhere else

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

Titles you can't find anywhere else

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

Titles you can't find anywhere else

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

Titles you can't find anywhere else

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

3 4 5

-4.400 -2.600 -1.800

operator = 3

subtracted from:

operator 4 5

Difference of Means 1.800 2.600

operator = 4

operator 5

1.817 1.817 1.817

SE of Difference 1.817 1.817

-2.422 -1.431 -0.991

0.2028 0.6270 0.8525

T-Value 0.9909 1.4313

Adjusted P-Value 0.8525 0.6270

T-Value 0.4404

Adjusted P-Value 0.9907

subtracted from:

Difference of Means 0.8000

SE of Difference 1.817

Keterangan: Sig (P-Valu (P-Value) e) yang yang telah telah dihigh dihigh light light text text warna warna hijau hijau adalah adalah perban perbandin dingan gan   berganda antar operator yang menunjukkan adanya perbedaan yang signifikan

Titles you can't find anywhere else

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

Titles you can't find anywhere else

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

Titles you can't find anywhere else

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

Titles you can't find anywhere else

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

Titles you can't find anywhere else

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

Titles you can't find anywhere else

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

Titles you can't find anywhere else

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

Langkah-langkah Langkah-langkah dengan menggunakan SPSS

1. Ketik data pada pada Tabel Tabel 6 ke dalam dalam spss, spss, seperti seperti pada pada Gambar Gambar 4.

Titles you can't find anywhere else

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

Titles you can't find anywhere else

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

Titles you can't find anywhere else

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

Titles you can't find anywhere else

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

Titles you can't find anywhere else

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

Titles you can't find anywhere else

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

3. Setelah melakuk melakukan an langkah langkah 2 maka akan akan muncul muncul windows windows Univariate Univariate seperti seperti  pada Gambar 8. a

 b

Titles you can't find anywhere else

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

Titles you can't find anywhere else

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

Titles you can't find anywhere else

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

Titles you can't find anywhere else

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

Titles you can't find anywhere else

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

Titles you can't find anywhere else

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

5. Klik Button Button Contrast Contrastss untuk mengece mengecek k tipe kontras, kontras, anda anda dapat dapat mengabaikan mengabaikan kontras sehingga klik Continue seperti pada Gambar 10.

Titles you can't find anywhere else

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

Titles you can't find anywhere else

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

Titles you can't find anywhere else

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

Titles you can't find anywhere else

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

Titles you can't find anywhere else

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

Titles you can't find anywhere else

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

 b. Centang Centang jenis uji perban perbandinga dingan n ganda yang yang dinggink dingginkan an pada Equal Equal Variance Variance Asumed, jika data sudah homogeny. Dalam pembahasan ini akan digunakan metode Tukey dalam perbandingan berganda sehingga Checklist Tukey yang akan dipilih. c. Klik Klik But Butto ton n Cont Contin inue ue 8. Klik Klik Button Button Save Save jika jika ingin ingin menampil menampilkan kan nilai nilai predik prediksi si (Predict (Predicted ed Value), Value),

Titles you can't find anywhere else

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

Titles you can't find anywhere else

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

Titles you can't find anywhere else

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

Titles you can't find anywhere else

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

Titles you can't find anywhere else

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

Titles you can't find anywhere else

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

Tabel 8. Output SPSS

Titles you can't find anywhere else

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

Titles you can't find anywhere else

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

Titles you can't find anywhere else

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

Titles you can't find anywhere else

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

Titles you can't find anywhere else

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

Titles you can't find anywhere else

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

Titles you can't find anywhere else

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

Titles you can't find anywhere else

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

Titles you can't find anywhere else

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

Titles you can't find anywhere else

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

Titles you can't find anywhere else

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

Titles you can't find anywhere else

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.

Titles you can't find anywhere else

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.