Experimental Design
An Experimental Design is a plan for the assignment
of the treatments to the plots in the experiment Designs differ primarily in the way the plots are grouped before the treatments are applied
How much restriction is imposed on the random assignment of treatments to the plots
A C B B D A D B D A C C A C B B D A D B D C A C
Why do I need a design?
To provide an estimate of experimental error
To increase precision (blocking) To provide information needed to perform tests of
significance and construct interval estimates To facilitate the application of treatments particularly cultural operations
Factors to be Considered
Physical and topographic features Soil variability Number and nature of treatments The crop Duration of the experiment Machinery to be used Size of the difference to be detected Significance level to be used Experimental resources Cost (money, time, personnel)
Cardinal Rule:
Choose the simplest experimental design that will give the required precision within the limits of the available resources
Completely Randomized Design (CRD)
Simplest and least restrictive Every plot is equally likely to be assigned to any
treatment
C
B
D
A
B
D
C
C
Advantages of a CRD
Flexibility Any number of treatments and any number of replications Dont have to have the same number of replications per treatment (but more efficient if you do)
Simple statistical analysis Even if you have unequal replication
Missing plots do not complicate the analysis
Maximum error degrees of freedom
Disadvantage of CRD
Low precision if the plots are not uniform
A
C B
B
D A
D
B D
A
C C
Uses for the CRD
If the experimental site is relatively uniform If a large fraction of the plots may not
respond or may be lost If the number of plots is limited
Design Construction
No restriction on the assignment of treatments to the plots
Each treatment is equally likely to be assigned to any plot Should use some sort of mechanical procedure to prevent
personal bias Assignment of random numbers may be by:
lot (draw a number ) computer assignment using a random number table
Random Assignment by Lot
We have an experiment to test three varieties: the
top line from Oregon, Washington, and Idaho to find which grows best in our area ----- t=3, r=4
A1
A
2
A
3 7
A
4 8
1 12 6 5
9 10 11 12
Random Assignment by Table
Select a starting point somewhere
in a table of random numbers Moving up or down, left or right, write down the first n (12) three digit numbers you come to Rank the numbers from smallest to largest Assign the first treatment to the first r (4) numbers in sequence, etc.
49416 97191 39100 53988 33423 81899 61547 17520 34502
44448 53798 17217 71087 67453 07449 18707 95401 75508
04269 12693 74073 84148 43269 37985 85498 55811 06059
Tabel Bilangan Teracak
14620 09724 95430 85125 12951 48477 81953 42783 17629 70473 19082 15232 73645 84146 09182 87729 73649 65584 56823 83641
56919
97310 07585
17803
78209 27040
95781
51263 26939
85069
52396 64531
61594
82681 70570
94252
72020 48392
77489
18895 06359
62434
84948 47040
20965
53072 05695
20247
74573 79799
25950 82937 60819 59041 74208
85189 16405 27364 37475 69516
69374 81497 59081 03615 79530
37904 20863 72635 84093 47649
06759 94072 49180 49731 53046
37950 09394 34800 36435 28187
77387 59842 28055 75946 31824
35495 39573 91570 85712 52265
78192 51630 99154 06293 80494
84518 78548 39603 85621 66428
39412 48480 95318
03642 50075 28749
87497 11804 49512
29735 24956 35408
14308 72182 21814
72094
63158
16385
49753
90185
84279
72635
56496
86259
30618
BILANGAN ACAK
937 149 908 361 953 749 180
URUTAN
1 2 3 4 5 6 7
PERINGKAT
21 2 19 10 23 17 4
PERLAKUAN
A1 A2 A3 A4 B1 B2 B3
951
018 427 918 772 243 494 704 549 957 157 571 226 195 278 506 239
8
9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24
22
1 11 20 18 8 12 16 14 24 3 15 6 5 9 13 7
B4
C1 C2 C3 C4 D1 D2 D3 D4 E1 E2 E3 E4 F1 F2 F3 F4
1
C 5 F 9 F 13
2
A 6 E 10 A 14
3
F 7 F 11 C 15
4
B 8 D 12 D 16
A1
17 B 21 A 22 18
D1
19 C 23 B
E
20 A 24 B
The CRD Analysis
We can: Estimate the treatment means Estimate the standard error of a treatment mean Test the significance of differences among the treatment means
RANCANGAN ACAK LENGKAP FULLY RANDOMIZED DESIGN UNGROUPED EXPERIMENT
1 7
13 19
2 8
14 20
3 9
15 21
4 10
16 22
5 11
17 23
6 12
18 24
Hipotesis : Ho = t1 = t2 = t3 = t4 = t5=t6 H1 = t1 t2 t3 t4 t5t6 Fh F.05 = Berbeda nyata Fh F.05 = Berbeda Tidak nyata
Jumlah Ulangan = (R-1) (T-1) 15
PERCOBAAN RANCANGAN ACAK LENGKAP (PRAKTIKUM 1)
PERLAKUAN A B C 43,1 42,3 41,1 ULANGAN 42,9 42,4 41,2 43,4 41,8 41,4 43,0 42,2 40,9 TOTAL RATA-RATA
D
E F TOTAL
39,9
37,2 37,0
40
38,2 36,8
39,7
38,6 37,4
39,2
37,7 36,5
Contoh penelitian RAL
Pengujian beberapa insektisida parasit dan telur serta hama
penggerek (Triporyza incertulas Walker) telah dilakukan di Lab. Hama dan Penyakit tanaman Faperta Unpad Jatinangor. Ada enam insektisida yang dipakai: Dursban 20 EC, Reldan 24 EC, Lebaycid 550 EC, Trebon 10 EC, Curacron dan Diazinon 60 EC. Konsentrasi yang digunakan adalah 2cc/l. Respon yang diamati adalah persentase parasit telur penggerek yang menetas. Jelaskan kesimpulan penelitian tersebut !!!
Perlakuan
1 56,0
54,4 41,2 49,5 59,1 35,7
295,9
2 48,2
44,3 38,5 52,1 57,6 38,4
279,1
Total 208,6
198,6 159,8 197,8 229,5 155,6
954,1
Rata 51,65
49,05 39,95 49,45 57,38 38,90
A
B C D E F Total
51,8 52,6
49,5 50,4 35,4 44,7 50,4 45,8 60,2 52,6 40,2 41,3
287,5 287,4
CARA PERHITUNGAN:
GT2 FK = ---------- = (954,1)2 : 24 =37929,45 Txr
JK Total = ( Yij2 FK = + .. + .. + ... FK = . JK. Perl. = A.2+ .+ F2 FK = 4 JK Total = 562 +.+ 41,372 FK = JK Galat = JK total JK Perlakuan = KT = JK/db galat
Tabel Sidik Ragam (ANOVA)
Sumber Ragam DB JK KT Fh F.05
Perlakuan
18195
3639
271,56
2,09
Galat
19
255
13,4
Total
24
18450
768,7
RANCANGAN ACAK LENGKAP
Untuk memperoleh manisan pepaya yang baik, sebelum
direndam dalam larutan sukrosa harus dilakukan blansing terlebih dahulu dengan tujuan untuk menginaktifkan
enzim-enzim. Masalahnya adalah berapa lama harus
dilakukan blansing tersebut. Seorang peneliti telah melakukan percobaan dengan 6 waktu blansing, yaitu: 3,
6, 9, 12, 15 dan 18 menit.
Rancangan Acak Lengkap
Perlakuan 1 2 Ulangan 3 4 Total Rata - rata
A B C D E F Total
43,1 42,3 41,1 39,9 37,2 37,0 240,6
42,9 42,4 41,2 40,0 38,2 36,8 241,5
43,4 41,8 41,4 39,7 38,6 37,4 242,3
43,0 42,2 40,9 39,2 37,7 36,5 239,5
172,4 168,7 164,6 158,8 151,7 147,7 963,9
43,10 42,17 41,15 39,70 37,92 36,92
Tabel Analisis Varians (ANOVA) RAL
Sumber Variasi Perlakuan Galat Total 5 18 23 db Jumlah Kuadrat 117,42 2.36 119,78 Kuadrat Tengah 23,48 0,13 Hit 180,61** F 0,05 2,77 0,01 4,25
Keterangan : * berarti berbeda nyata pada = 0,05
Perhitungan Jumlah Kuadrat (JK)
GT2 (963,9)2 FK = ---------- = ------------ = 38712,63 txr 6x4
JK Total = ( Yij2 FK = 43,12 + + 37,72 + 36,52 FK = 119,78 43,12 + 36,922 JK. Perl. = ( Y, J2 FK = -------------------------- - FK = 117,42 4 JK Galat = JK total JK Perlakuan = 119,78-117,42 = 2,36
UJI LANJUT: UJI BEDA RATA-RATA UJI LSD: - Fhit > Ftab - Harus ditetapkan pembanding (kontrol) Sd = (2(KT galat)/r = 2(0,13)/4=0,25 LSD = t/2, db galat x Sd = 2,10 x 0,25 = 0,53 UJI DUNCAN (LSR) LSR = SSR x Sx Sx = KT galat/r = 0,18 LSR = SSR x Sx
P 2 SSR 2,97 LSR 0,53
Rata2 Perlakuan F=36,92 a E=37,92 b D=39,70 c C=41,15 d B=42,17 e A=43,10 f
3 4 5 6 3,12 3,21 3,27 3,32 0,56 0,57 0,58 0,60
Beda dua rata-rata 1 2,78 4,23 5,25 6,18 1,78 3,23 4,25 5,18 1,45 2,47 3,40 1,02 1,95 0,93 LSD 0,53 0,53 0,56 0,57 0,59 0,60 LSR
KESIMPULAN PENELITIAN
Perlakuan A yaitu lamanya Blensing selama 3
menit merupakan perlakuan yang paling baik dan berbeda nyata dengan perlakuan lainnya Perlakuan F yaitu lamnaya blensing selama 18 menit merupakan perlakuan yang paling jelek dan berbeda nyata dengan perlakuan lainnya Semakin pendek waktu blensing semakin baik kualitas pepaya.
