Pendugaan Data Hilang pada Rancangan Bujur Sangkar Latin dengan Analisis Kovarian

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LAMPIRAN

Lampiran 1.

Proses Pendugaan Galat pada RBSL dengan Satu Data Hilang

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�̂� =�

139

4 −34,3125� −1,17124688� 133

4 −33,1875�= 0,36429707

�̂�� =�� − �� =�� − ��…− ��− �̂� − �̂�− �� − ��…�

�̂11� = 27−34,3125−(−0,50039746)−2,15710879−0,10742675

−1,17124688(24−33,1875) = 1,68419260

�̂12� = 25−34,3125−(−0,50039746)−(−1,59289121)−0,95679082

−1,17124688(26−33,1875) = 0,24233477

�̂13� = 40−34,3125−(−0,50039746)−0,03554395−(−1,42851465)

−1,17124688(38−33,1875) = 1,94424256

�̂14� = 33−34,3125−(−0,50039746)−(−0,59976153)−0,36429707

−1,17124688(36−33,1875) =−3,87076993

�̂21� = 35−34,3125−0,53554395−2,15710879−0,95679082

−1,17124688(32−33,1875) =−1,57108789

�̂22� = 22−34,3125−0,53554395−(−1,59289121)−(−1,42851465)

−1,17124688(26−33,1875) =−1,40830116

�̂23� = 34−34,3125−0,53554395−0,035543953−0,36429707

−1,17124688(31−33,1875) = 1,31421758

�̂24_�= 44−34,3125−0,53554395−(−0,59976153)−0,10742675

−1,17124688(40−33,1875) = 1,66517147

�̂31� = 53−34,3125−(−0,84130139)−2,15710879−(−1,42851465)

−1,17124688(50−33,1875) =−0,89138088

�̂32� = 42−34,3125−(−0,84130139)−(−1,59289121)−0,36429707

−1,17124688(40−33,1875) = 1,77827618

�̂33_�= 33−34,3125−(−0,84130139)−0,03554395−0,10742675

−1,17124688(35−33,1875) =−2,73705428

�̂34� = 46−34,3125−(−0,84130139)−(−0,59976153)−0,95679082

−1,17124688(42−33,1875) = 1,85015898

�̂41� = 30−34,3125−0,80615489−2,15710879−0,36429707

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�̂42�= 41−34,3125−0,80615489−(−1,59289121)−0,10742675

−1,17124688(40−33,1875) =−0,61230979

�̂43� = 26−34,3125−0,80615489−0,03554395−0,95679082

−1,17124688(25−33,1875) =−0,52140586

�̂44_� = 18−34,3125−0,80615489−(−0,59976153)−(−1,42851465)

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Lampiran 2.

Langkah-langkah Analisis Kovarian pada RBSL dengan Satu Data

Menghitung Jumlah Kuadrat Total (JKT) dan Jumlah Hasil Kali Total (JHKT)

untuk variabel

X

dan

Y

�� = 18643−17622,5625 = 1020,4375 �� = 20203−18837,5625 = 1365,4375 �� = 19359−18219,9375 = 1139,0625

Menghitung Jumlah Kuadrat Baris (JKB) dan Jumlah Hasil Kali Baris (JHKB)

untuk variabel

_X

dan

_Y

�� =(124)

2_{+ (129)}2_{+ (167)}2_{+ (111)}2

4 −17622,5625 = 434,1875

�� =

(125)2_{+ (135)}2_{+ (174)}2_{+ (115)}2

4 −18837,5625 = 500,1875

�� =

(124)(125) + (129)(135) + (167)(174) + (111)(115) 4

−18219,9375 = 464,5625

Menghitung Jumlah Kuadrat Kolom (JKK) dan Jumlah Hasil Kali Kolom (JHKK)

untuk variabel

X

dan

Y

�� =

(132)2_{+ (132)}2_{+ (129)}2_{+ (138)}2

4 −17622,5625 = 10,6875

�� =

(145)2_{+ (130)}2_{+ (133)}2_{+ (141)}2

4 −18837,5625 = 36,1875

�� =

(132)(145) + (132)(130) + (129)(133) + (138)(141) 4

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Menghitung Jumlah Kuadrat Perlakuan (JKP) dan Jumlah Hasil Kali Perlakuan

(JHKP) untuk variabel

_X

dan

_Y

�� =(139)

2_{+ (125)}2_{+ (134)}2_{+ (133)}2

4 −17622,5625 = 25,1875

�� =

(145)2_{+ (132)}2_{+ (133)}2_{+ (139)}2

4 −18837,5625 = 27,1875

�� =

(139)(145) + (125)(132) + (134)(133) + (133)(139) 4

−18219,9375 = 21,0625

Menghitung Jumlah Kuadrat Galat (JKG) dan Jumlah Hasil Kali Galat (JHKG)

untuk variabel

X

dan

Y

�� = 1020,4375−434,1875−10,6875−25,1875 = 550,375 �� = 1365,4375−500,1875−36,1875−27,1875 = 801,875 �� = 1139,0625−464,5625−8,8125−21,0625 = 644,625

Menghitung Jumlah Kuadrat Terkoreksi

�� terkoreksi = 801,875−

�� terkoreksi = 52,47508411−46,85998183 = 5,61510228 ��(�+�) terkoreksi = 838,0625−(653,4375)

2

561,0625 = 77,04110505

2

575,5625 = 59,13769139

�� terkoreksi = 59,13769139−46,85998183 = 12,27770956

Menghitung db terkoreksi untuk galat baris, kolom, dan perlakuan

db galat terkoreksi = (r – 1)(r – 2) -1= 5

db baris terkoreksi = r – 1 = 3

db kolom terkoreksi = r – 1 = 3

db perlakuan terkoreksi = r – 1 = 3

Menghitung Kuadrat Tengah (KT)

�� terkoreksi =46,85998183

5 = 9,37199637

�� terkoreksi =5,61510228

3 = 1,87170076

�� terkoreksi =30,18112322

3 = 10,06037441

�� terkoreksi =12,27770956

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�̂�� =�� − �� =�� − ��…− ��− �̂� − �̂�− �� − ��…�

�̂11� = 27−34,25−(−0,49056041)−1,34009482−0,20754315

−1,14717238(24−33,1875) = 2,23256870

�̂12� = 25−34,25−(−0,49056041)−(−0,53490518)−(−0,27735351)

−1,14717238(26−33,1875) = 0,29812060

�̂13� = 40−34,25−(−0,49056041)−(−0,29952589)−(−1,35849137)

−1,14717238(38−33,1875) = 2,37781058

�̂14� = 33−34,25−(−0,49056041)−(−0,50566375)−1,42830173

−1,14717238(36−33,1875) =−4,90849989

�̂21� = 31,5−34,25−(−0,29952589)− −1,34009482−(−0,27735351)

−1,14717238(32−33,1875) =−2,15094822

�̂22_� = 22−34,25−(−0,29952589)−(−0,53490518)−(−1,35849137)

−1,14717238(26−33,1875) =−1,81177606

�̂23� = 34−34,25−(−0,29952589)−(−0,29952589)−1,42830173

−1,14717238(31−33,1875) = 1,43018964

�̂24�= 44−34,25−(−0,29952589)−(−0,50566375)−0,20754315

−1,14717238(40−33,1875) = 2,53253464

�̂31_� = 53−34,25−0,42733648− −1,34009482−(−1,35849137)

−1,14717238(50−33,1875) =−0,94577561

�̂32� = 46−34,25−0,42733648−(−0,53490518)−1,42830173

−1,14717238(40−33,1875) = 2,61415512

�̂33�= 33−34,25−0,42733648−(−0,29952589)−0,20754315

−1,14717238(35−33,1875) =−3,66460368

�̂34� = 46−34,25−0,42733648−(−0,50566375)−(−0,27735351)

−1,14717238(42−33,1875) = 1,99622417

�̂41� = 30−34,25−0,36274983− −1,34009482−1,42830173

−1,14717238(26−33,1875) = 0,86415512

�̂42�= 41−34,25−0,36274983−(−0,53490518)−0,20754315

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�̂43�= 24,5−34,25−0,36274983−(−0,29952589)−(−0,27735351)

−1,14717238(25−33,1875) =−0,14339655

�̂44� = 18−34,25−0,36274983−(−0,50566375)−(−1,35849137)

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Lampiran 4.

Langkah-langkah Analisis Kovarian pada RBSL dengan Dua Data

Menghitung Jumlah Kuadrat Total (JKT) dan Jumlah Hasil Kali Total (JHKT)

untuk variabel

X

dan

Y

�� = 18643−17622,5625 = 1020,4375 �� = 20246,5−18769 = 1477,5

�� = 19369,5−18186,75 = 1182,75

Menghitung Jumlah Kuadrat Baris (JKB) dan Jumlah Hasil Kali Baris (JHKB)

untuk variabel

_X

dan

_Y

�� =(124)

2_{+ (129)}2_{+ (167)}2_{+ (111)}2

4 −17622,5625 = 434,1875

�� =

(125)2_{+ (131,5)}2_{+ (178)}2_{+ (113,5)}2

4 −18769 = 601,88

�� =

(124)(125) + (129)(131,5) + (167)(178) + (111)(113,5) 4

−18186,75 = 510,25

Menghitung Jumlah Kuadrat Kolom (JKK) dan Jumlah Hasil Kali Kolom (JHKK)

untuk variabel

X

dan

Y

�� =

(132)2_{+ (132)}2_{+ (129)}2_{+ (138)}2

4 −17622,5625 = 10,6875

�� =

(141,5)2_{+ (134)}2_{+ (131,5)}2_{+ (141)}2

4 −18769 = 18,88

�� =

(132)(141,5) + (132)(134) + (129)(131,5) + (138)(141) 4

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Menghitung Jumlah Kuadrat Perlakuan (JKP) dan Jumlah Hasil Kali Perlakuan

(JHKP) untuk variabel

_X

dan

_Y

�� =(139)

2_{+ (125)}2_{+ (134)}2_{+ (133)}2

4 −17622,5625 = 25,1875

�� =

(145)2_{+ (127)}2_{+ (133)}2_{+ (143)}2

4 −18769 = 54,0

�� =

(139)(145) + (125)(127) + (134)(133) + (133)(143) 4

−18186,75 = 31,0

Menghitung Jumlah Kuadrat Galat (JKG) dan Jumlah Hasil Kali Galat (JHKG)

untuk variabel

X

dan

Y

�� = 1020,4375−434,1875−10,6875−25,1875 = 550,375 �� = 1477,5−601,88−18,88−54,0 = 802,75

�� = 1182,75−510,25−10,125−31,0 = 631,375

Menghitung Jumlah Kuadrat Terkoreksi

�� terkoreksi = 802,75−

�� terkoreksi = 80,88707802−78,45403702 = 2,428041 ��(�+�) terkoreksi = 821,63− (641,5)

2

561,0625= 88,16046675

2

575,5625 = 94,46850907

�� terkoreksi = 94,46850907−78,45403702 = 16,01447205

Menghitung db terkoreksi untuk galat baris, kolom, dan perlakuan

db galat terkoreksi = (r – 1)(r – 2) -2= 4

db baris terkoreksi = r – 1 = 3

db kolom terkoreksi = r – 1 = 3

db perlakuan terkoreksi = r – 1 = 3

Menghitung Kuadrat Tengah (KT)

�� terkoreksi =78,45403702

4 = 19,61350926

3 = 0,809347

3 = 3,23380991

�� terkoreksi =16,01447205

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