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# 14. rancangan penelitian : contoh Split Plot Design (SPD)

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### 14. rancangan penelitian : contoh Split Plot Design (SPD)

1. 1. Contoh Soal : SPD – RAL Main Plot : Umur telur ( 1, 3, 5, 7 hari ) Sub Plot : Frek Pemutaran ( 4, 6, 8 kali/hari )
2. 2. Tabel 2. MP x SP x Ulg [ Transf. Arc. Sin √ % ] M a i n S u b Ulangan Total P l o t P l o t 1 2 3 F 1 56.79 67.21 63.43 187.43 U 1 F 2 63.43 67.21 67.21 197.85 F 3 71.57 71.57 67.21 210.35   S. Total 191.79 205.99 197.85 595.63 F 1 56.79 60.00 60.00 176.79 U 2 F 2 63.43 63.43 67.21 194.07 F 3 67.21 67.21 63.43 197.85   S. Total 187.43 190.64 190.64 568.71 F 1 50.77 53.73 53.73 158.23 U 3 F 2 60.00 56.79 60.00 176.79 F 3 67.21 63.43 67.21 197.85   S. Total 177.98 173.95 180.94 532.87 F 1 50.77 53.73 56.79 161.29 U 4 F 2 56.79 56.79 60.00 173.58 F 3 60.00 60.00 63.43 183.43   S. Total 167.56 170.52 180.22 518.30
3. 3. Tabel 3. MP x SP   U 1 U 2 U 3 U 4 Total SP F 1 187.43 176.79 158.23 161.29 683.74 F 2 197.85 194.07 176.79 173.58 742.29 F 3 210.35 197.85 197.85 183.43 789.48 Total MP 595.63 568.71 532.87 518.30 2215.5 1
4. 4. Perhitungan Jumlah Kuadrat 1. F K = 136436.80 2. JK Total = 1082.50 3. JK S Tot 1 = 481.40 4. JK M. Plot = 407.8164 5. JK Galat a = 73.58
5. 5. 6. JK S. Tot 2 = 923.6554 7. JK S. Plot = 467.6652 8. JK Interaksi = 48.17383 9. JK Galat b= 85.26
6. 6. Tabel 4. Analisis Variansi               S u m b e r Jumlah Deraja t Kuadra t F F tabel V a r i a s i Kuadra t Bebas Tenga h hit 0.05 0.01 M. Plot 407.82 3 135.94 14.780 4.070 7.590 Galat a 73.58 8 9.20 σ a = 3.033               S. Total 481.40 11   KK a = 4.928 % S. Plot 467.67 2 233.83 43.881 3.630 6.230 Interaksi 48.17 6 8.03 1.507 2.740 4.200 Galat b 85.26 16 5.33 σ b = 2.308               T O T A L 1082.5 0 35   KK b = 3.751 %
7. 7. »»» Memecah JK Main Plot                 Perlakua n U 1 U 2 U 3 U 4 Σ Ci.Ti r. Σ Ci2 J K Total Perl 595.63 568.71 532.87 518.30 (a) (b) (a2 /b) Linier -3 -1 1 3 - 267.83 3 x 3 x 20 398.516 2 Kuadrate r 1 -1 -1 1 12.35 3 x 3 x 4 4.23673 6 Kubik -1 3 -3 1 30.19 3 x 3 x 20 5.06353 4 Total           JK MP = 407.816 4
8. 8. »»» Memecah JK Sub Plot               Perlakuan F 1 F 2 F 3 Σ Ci.Ti r. Σ Ci2 J K Total Perl 683.74 742.29 789.48 (a) (b) (a2 /b) Linier -1 0 1 105.74 4 x 3 x 2 465.872 8 Kuadrater 1 -2 1 -11.36 4 x 3 x 6 1.79235 6 Total         JK SP = 467.665 2
9. 9. Tabel 5. Analisis Variansi               S u m b e r Jumlah Derajat Kuadrat F F tabel V a r i a s i Kuadrat Bebas Tengah hit 0.05 0.01 M. Plot 407.82 3 135.94 14.780 4.070 7.590 Linier 398.52 1 398.52 43.329 5.320 11.260 Kuadrater 4.24 1 4.24 0.461 5.320 11.260 Kubik 5.06 1 5.06 0.551 5.320 11.260 Galat a 73.58 8 9.1975 σ a = 3.033               S. Total 481.40 11   KK a = 4.928 % S. Plot 467.67 2 233.83 43.881 3.630 6.230 Linier 465.87 1 465.87 87.425 4.490 8.530 Kuadrater 1.79 1 1.79 0.336 4.490 8.530 Interaksi 48.17 6 8.03 1.507 2.740 4.200 Galat b 85.26 16 5.3288 σ b = 2.308               T O T A L 1082.50 35   KK b = 3.751 %
10. 10. »»» Uji Beda Nyata Terkecil (BNT) ««« »»» Untuk Main Plot BNT 0.05= 2.3060 x 1.4296 = 3.2968 BNT 0.01= 3.3550 x 1.4296 = 4.7965 U 1 U 2 U 3 U 4 Rataan 66.1811 63.1900 59.207 8 57.588 9 U 4 8.5922 5.6011 1.6189 - U 3 6.9733 3.9822 - U 2 2.9911 - U 1 -
11. 11. »»» Untuk Sub Plot BNT 0.05= 2.1200 x 0.9424 = 1.9979 BNT 0.01= 2.9210 x 0.9424 = 2.7528         F 1 F 2 F 3 Rataan 56.978 3 61.857 5 65.790 0 F 3 8.8117 3.9325 - F 2 4.8792 - F 1 -
12. 12. »»» Untuk Antar Sub Plot dalam tiap Main Plot BNT 0.05= 2.1200 x 1.8848 = 3.9958 BNT 0.01= 2.9210 x 1.8848 = 5.5056           Main F 1 F 2 F 3 Plot Rataan 62.4767 65.9500 70.1167 F 3 7.6400 4.1667 - U 1 F 2 3.4733 -   F 1 -     F 1 F 2 F 3 Rataan 58.9300 64.6900 65.9500 F 3 7.0200 1.2600 -
13. 13. BNT 0.05= 2.1200 x 1.8848 = 3.9958 BNT 0.01= 2.9210 x 1.8848 = 5.5056           Main F 1 F 2 F 3 Plot Rataan 52.743 3 58.930 0 65.950 0 F 3 13.206 7 7.0200 - U 3 F 2 6.1867 -   F 1 -     F 1 F 2 F 3 Rataan 53.763 3 57.860 0 61.143 3 F 3 7.3800 3.2833 - U 4 F 2 4.0967 -
14. 14. »»» Untuk Antar Main Plot dalam setiap Sub Plot BNT 0.05= 2.206 2 x 1.8413 = 4.0622 BNT 0.01= 3.122 0 x 1.8413 = 5.7486       Sub U 1 U 2 U 3 U 4 Plot Rataa n 62.4767 58.9300 52.7433 53.7633 U 4 8.7133 5.1667 1.0200 - F 1 U 3 9.7333 6.1867 - U 2 3.5467 -   U 1 -
15. 15. BNT 0.05= 2.206 2 x 1,8413 = 4,0622 BNT 0.01= 3.122 0 x 1,8413 = 5,7486       Sub U 1 U 2 U 3 U 4 Plot Rataa n 65.9500 64.6900 58.9300 57.8600 U 4 8.0900 6.8300 1.0700 - F 2 U 3 7.0200 5.7600 - U 2 1.2600 -   U 1 -
16. 16. BNT 0.05= 2.2062 x 1,8413 = 4,0622 BNT 0.01= 3.1220 x 1,8413 = 5,7486       Sub U 1 U 2 U 3 U 4 Plot Rataa n 70.1167 65.9500 65.9500 61.1433 U 4 8.9733 4.8067 4.8067 - F 3 U 3 4.1667 0.0000 - U 2 4.1667 -   U 1 -
17. 17. N = 36 Σ Y = 2215.51 Σ X = 144.00 Σ Y2 = 137429.29 01 Σ X2 = 756.0000 Y bar = 61.54 X bar = 4.00 Σ XY = 8594.2100 Σ x2 = Σ X2 - Σ ( X )2 / N = 180 Σ y2 = Σ Y2 - Σ ( Y )2 / N = 1082.496 76 Σ xy = Σ XY - (Σ X)(ΣY) / N = -267.83 Regresi Pada Main Plot
18. 18. Koefisien regresi ( b ) = Σxy / Σx2 = - 1.48794444 Intersep ( a ) = Y bar - ( b ) ( X bar ) = 67.49372222 Persamaan Garis Regresi Linier : Y = 67.4937222 - 1.48794444 X Koefisien Determinasi ( r2 ) = ( JK Regresi / JK Total ) x 100 % = 36.815 Persen Koefisien Korelasi ( r ) = √ ( JK Regresi / JK Total ) = 0.6067
19. 19. Regresi 55 60 65 70 1 3 5 7 Umur Telur (hari) DayaTetas Linier
20. 20. Regresi Pada Sub Plot N = 36 Σ Y = 2215.51 Σ X = 216 Σ Y2 = 137429.29 01 Σ X2 = 1392 Y bar = 61.54 X bar = 6 Σ XY = 13504.54 Σ x2 = Σ X2 - Σ ( X )2 / N = 96 Σ y2 = Σ Y2 - Σ ( Y )2 / N = 1082.4967 6 Σ xy = Σ XY - (Σ X)(ΣY) / N = 211.48
21. 21. Koefisien regresi ( b ) = Σxy / Σx2 = 2.20291667 Intersep ( a ) = Y bar - ( b ) ( X bar ) = 48.3244444 Persamaan Garis Regresi Linier : Y = 48.3244444 + 2.20291667 X Koefisien Determinasi ( r2 ) = ( JK Regresi / JK Total ) x 100 % = 43.037 Persen Koefisien Korelasi ( r ) = √ ( JK Regresi / JK Total ) = 0.6560
22. 22. Regresi 55 60 65 70 4 6 8 Frekuensi Pemutaran DayaTetas Linier