1. 7 Field Plot Technique & Experimental Design

2. Factors that Affect the conduct of Field Experiment
Field Plot technique pertains to the study of kind of field plots best suited for a particular type of experiment. It is important that the most efficient type and arrangement of plots be used in each particular experiment in order to assure reliable results.
Factors that Affect the conduct of Field Experiment
Soil fertility status (Moisture, nutrient etc)
Environment
Genotype
Variable soil fertility Heterogeneity can be reduced
Replication/ Blocking
Plot size (0.1 to 0.01 acre)
Interplot competetion or border effect

3. Blocking Slope 10% 6% 2% Blocks are made
Fertility
Blocks are made
To make expt units more uniform
Thus making within block variation more
Number of blocks is equal to number of reps
High
Medium
Low
Slope
10% 6% 2%

5. Basic principles of a well designed experiment
It is a planned inquiry to discover new facts, or to confirm or deny the results of previous investigations.
Testing of predictions based on hypothesis, followed by the observations necessary to ascertain whether or not event occurred as predicted.
Basic principles of a well designed experiment
Control of outside variables
Randomization to reduce the chance of bias
Replication within the experiment to assess natural variability

6. Early Experimentation
In 1747, James Lind, while serving as surgeon on HM Bark Salisbury, carried out a controlled experiment to develop a cure for scurvy (Vitamin C deficiency).
Reviewed literature and suggested 6 suitable remedies
assuming that all treatments will cure scurvy
or at least one treatment will be better than the other
A quart of cider (fermented apple juice) per day
Twenty five gutts of elixir vitriol three times a day upon an empty stomach
Half a pint of seawater every day
A mixture of garlic, mustard and horseradish
Two spoonfuls of vinegar three times a day
Two oranges and one lemon every day.

7. Selected 12 men from the ship, all suffering from scurvy,
The men were paired, which provided replication.
randomized allocation of subjects to treatments was missing
Two weeks later
The men who had been given citrus fruits recovered dramatically within a week.
One of them returned to duty after 6 days and the other became nurse to the rest.
The others experienced some improvement, but nothing was comparable to the citrus fruits, which were proved to be substantially superior to the other treatments.

8. Steps in Experiments Hypothesis Treatments
Measures to reduce variation
Replication
Observations
Results
Significance of differences
Conclusion

9. Some basic definitions
Statistical Hypothesis:
There are generally two forms of a statistical hypothesis
null (typically represented as H0) : no differences exit among treatments or treatments are similar
Rejection of null hypothesis will prove that there are differences among treatments hence justifying research hypothesis
alternative (typically symbolised as H1 - this is the research hypothesis - the one we are really interested in showing support for!)
At least one of the treatment is significantly different

10. Replication: Randomization: Experimental error: Degree of freedom:
Experimental unit:
it is piece of experimental material to which a treatment is assigned
Replication:
Appearance of one treatment more than once in experiment is called replication
Randomization:
Each treatment has equal chance of being assigned to any experimental unit
Experimental error:
Variation among the experimental units which are treated alike
Degree of freedom:
the number of values in the final calculation of a statistic that are free to vary
The number of independent pieces of information that go into the estimate of a parameter is called the degrees of freedom (df)

11. Randomization Randomization by lot Random number table
For 4 treatments and 3 reps= 12 expt units
Make 12 pieces of paper, write down 1-12 on these pieces, fold the pieces, place them in box and shake thoroughly
Pick pieces one by one and allot treatment 1 to first 3 numbers drawn
Random number table
Select a starting point in random number table
Select first twelve three digit number in any direction from starting point
Rank them smallest to largest (ranks correspond to expt unit)
Assign treatment 1 to first 3 numbers (expt unit)
Sequence
Random Number
Rank (expt unit #)
Treatment 1
481 5 A 2
516 6 3
991 12 4
062 B
804 11
675 9 7
154 C 8
437
571 10
769 D
639
428

12. two estimates of a population variance are calculated
Analysis Of Variance.
This procedure employs the statistic (F) to test the statistical significance of the differences among the obtained MEANS
two estimates of a population variance are calculated
Variations among treatment means
Variation among experimental units within treatments (experimental error)
Calculation of statistic F

13. Types of Experiments Laboratory Controlled environment Green house
Field
Yield testing
Fertilizer response
Pesticide efficacy
Herbicide efficacy
Water requirement

14. Basic Experimental designs
It is a rule or formal plan for the assignment of treatments to be used to the experimental units (plots).
Experimental design differ
Grouping of plots prior treatment application
Restrictions on randomization of treatments
Why Experiments are designed
To facilitate the application of treatment, operations and recording of data
To provide information required to perform tests of significance and to convert interval estimates
To increase precision by planned grouping of plots and elimination of group differences from experimental error
To provide an estimate of experimental error

15. Choice of field experimental design
Following points may be considered
Physical and topographic features of experimental site
Amount and pattern of soil variability
Number and nature of treatments
Crop to be used
Duration of the experiment
Nature of the machinery to be used
Size of the differences to be detected
Significance level to be used
Cost required to complete the experiment
Choose the simplest experimental design which will give the required precision within the limits of the available resources

16. Experimental Designs Completely randomized design
Randomized complete block design
Latin square design
Factorial Design
Split Plot Design
Augmented Design

17. CRD Advantages, disadvantages and uses
Flexibility:
Any number of treatments and any number of replications
Replication per treatment need not to be the same
Simple statistical analysis
The analysis is not complicated despite unequal replication of treatment
Missing plots
The analysis is not complicated by missing data
Maximum error degree of freedom
No other expt. Design provide higher df (e) with similar no. plots and treatments
Disadvantage
Low precision if Expt. Units are not uniform
i.e. why it is used mainly in lab, green house and controlled environment expts.
It can be used/ Application
Experimental unit is more uniform
Number of expt. Units may damaged
Number of units is limited (it provides maximum error df)

18. Randomized Complete Block Design (RCBD)
Widely used in Agricultural experiments
As easy as CRD
More precise than CRD provided expt. Units are made uniform through blocking
Less flexible than CRD
equal number of reps for each treat
One source of variation isolated from Experimental error

19. RCBD ADVANTAGES DISADVANTAGES USES Remove one source of variation
Any no. of treatments and any no. of blocks (but each treatment must be replicated in each block)
Statistical analysis is simple
Broaden the scope of trial by blocking for different conditions
DISADVANTAGES
Missing data cause difficulty in analysis
Assignment of treatment in wrong block
Less efficient if more than one source of unwanted variation
Less efficient in than CRD if expt units are uniform
USES
It can be used to eliminate source of unwanted variation
Provides unbiased estimates of the means of blocking

20. Latin Square Design 1 2 3 4 A B C D More restrictive than RCBD
Expt units/ plots are square of number of Treatments
Row grouping
Column grouping
Ensure each treatment appears only once in each row and column 1 2 3 4 A B C D

21. Randomization 1 2 3 4 A B C D 4 Treatments A, B, C, D
First row in alphabetical order
In subsequent row - shift letter one position –
Randomize Order of the rows (e.g. 2, 1, 3, 4)
Randomize Order of the column (e.g. 4, 2 ,3, 1) 1 2 3 4 B C D A 4 2 3 1 A C D B

22. Comparison of Means ANOVA Range Tests
Duncan’s Multiple Range Test (DMR)
Least Significant Differences (LSD)
Tukey’s Test
LSD provides a valid test criteria in 2 situations
Making comparisons planned in advance of data observed- (treatment with control)
Comparing adjacent ranked means (to choose a winner)
LSD should not be used
For all possible pair-wise comparisons
Making more comparisons > no. df Treatment

23. Factorial Design
The experiment whose design consists of two or more factors, whose experimental units take on all possible combinations of these levels across all such factors.

24. Split Plot Design
An experiment in which an extra factor (second) is introduced into a study by dividing the large experimental units (whole unit) for the first factor into smaller experimental units (sub-units) on which the different levels of the second factor will be applied.
Each whole unit is a complete replicate of all the levels of the second factor (RBD). The whole unit design may be CRD, RCBD or LS design.
ADVANTAGES
If an experiment is designed to study one factor, a second factor may be included at very little cost.
Since sub-unit variance is generally less than whole unit variance, the sub-unit treatment factor and the interaction are generally tested with greater sensitivity.

25. Split Plot Design DISADVANTAGES
Analysis is complicated by the presence of two experimental error variances, which leads to several different SE for comparisons.
High variance and few replications of whole plot units frequently leads to poor sensitivity on the whole unit factor.
POSSIBLE APPLICATIONS
Experiments in which one factor requires larger experimental units than the other factor.
Experiments where greater sensitivity may be desired for one factor than for the second factor.
Introduction of a new factor into an experiment which is already in progress.

26. Augmented Design
In agricultural experiments often the existing practices or check varieties called control treatments are compared with new varieties or germplasms collected through exotic or domestic collections, called test treatments.
In some cases experimental material for test treatments is limited and it is not possible to replicate them in the design.
However, adequate material is available for replicating control treatments in the design. Augmented Designs are useful for these experimental situations.
In an augmented randomized complete block design, the test treatments are replicated once in the design and control treatments appear exactly once in each block.
It provides an estimate of experimental error for comparing test entries with check or control Varieties
It provides a way of adjusting the yield of new selections for differences from block to block

27. Calculations Source of variation: Total variation is partitioned into
Rows
Columns
Treatments
Error
Degree of Freedom
Total = (Treatment)2 – 1
Row, Column, Treatment = Treatment – 1
Error = (Treatment – 1) (Treatment – 2)
Sum of Squares
Mean Squares
F-Calc

28. 1 2 3 4 5
A 33.8
B 33.7
D 30.4
C 32.7
E 24.4
D 37
E 28.8
B 33.5
A 34.6
C 33.4
C 35.8
D 35.6
A 36.9
E 26.7
B 35.1
E 33.2
A 37.1
C 37.4
B 38.1
D 34.1
B 34.8
C 39.1
D 32.7
E 37.4
A 36.4 A B C D E
Treat Sum
178.8
175.2
178.4
174.5
145.8
Treat Mean
35.76
35.04
35.68
34.9
29.16

29. 1 2 3 4 5
SUM
Mean
33.8
33.7
30.4
32.7
24.4
155
31.0 37
28.8
33.5
34.6
33.4
167.3
35.8
35.6
36.9
26.7
35.1
170.1
34.0
33.2
37.1
37.4
38.1
34.1
179.9
36.0
34.8
39.1
36.4
180.4
36.1
174.6
174.3
170.9
169.5
163.4
852.7
170.5
34.92
34.86
34.18
33.9
32.68
170.54
Correction Factor =
(GT)2/Total Observ.
Total Sum of squares =
(33.8) (36.4)2 - Cf
296.66
Row SS =
1/5 *(155) (180.4)2 -cf
87.40
Column SS=
1/5 *(174.6) (163.4)2 -cf
16.56
Treat SS =
1/5 *(178.8) (145.8)2 -cf
155.89
Error SS =
Total SS - Row SS- Col SS - TreatSS
36.80

30. Degree of freedom
the number of values in the final calculation of a statistic that are free to vary
The number of independent pieces of information that go into the estimate of a parameter is called the degrees of freedom (df)
In general, the degrees of freedom of an estimate is equal to the number of independent scores that go into the estimate minus the number of parameters estimated as intermediate steps in the estimation of the parameter itself.
Imagine you are picking people to play in a team. You have eleven positions to fill and eleven people to put into those positions. How many decisions do you have? In fact you have ten, because when you come to the eleventh person, there is only one person and one position, so you have no choice. You thus have ten 'degrees of freedom' as it is called.
Likewise, when you have a sample, the degrees of freedom to allocate people in the sample to tests is one less than the sample size. So if there are N people in a sample, the degrees of freedom is N-1.

31. Completely Randomized Design (CRD)
One-way ANOVA

32. Experimental Unit: Treatment:
Piece of experimental material which is assigned with treatment
It may be
human
Animal
Test tubes
Pots
Field plots
Treatment:
It is a procedure whose effect is to be noted on expt. Unit
Medicine
Nutrients
Herbicides
Pesticides

33. RCBD – One Missing Value
Blocks
Treatment
Rep 1
rep 2
Rep 3
Rep 4
Total 1
32.1
35.6
41.9
35.4
145 2
30.1
31.5
37.1
30.8
129.5 3
25.4
27.1
33.8
31.1
117.4 4
24.1 33
31.4
88.5 5
26.1 31
31.9
122.8 6
23.2
24.8
26.7
101.4
161
183
173.3
187.3
704.9

34. Missing Data One Missing value X = tT + rR – G (t-1)(r-1)
X = Missing value
t = Number of treatment
r = Number of Repeats
T = Total of treatment with a missing value
R = Total of replication with a missing value
G = grand total with a missing value
X = (6*88.5) + (4*173.3) – 704.9
(6-1) (4-1)
X = – 704.9
5*3
X = 34.62

35. RCBD – More than One Missing Value
REPS
Treatment 1 2 3 4 5
Total
22.3
21.8
21.2 20
85.3
18.3
18.5
21.5
17.3
75.6
17.2
17.9
16.7 69
14.9
12.6
13.1
14.4
12.4
67.4
72.7
51.6
49.5
57.1
66.4
297.3

36. Missing Data More than one Missing value
Approximation
85.3/4 = 21.25
69.0/4 = 17.2

37. Treatment
REPS 1 2 3 4 5
Total
22.3
21.8
21.25
21.2 20
106.55
18.3
18.5
21.5
17.3
75.6
17.2
17.9
16.7
86.2
14.9
12.6
13.1
14.4
12.4
67.4
72.7
51.6
70.75
74.3
66.4
335.75

38. Missing Data More than one Missing value
Calculation for first Value
X = tT + rR – G
(t-1)(r-1)
X = Missing value
t = Number of treatment
r = Number of Repeats
T = Total of treatment with a missing value
R = Total of replication with a missing value
G = grand total with a missing value
X = (4*75.6) + (5*51.6) – 335.8
(4-1) (5 -1)
X = – 335.8
3 * 4
X = 18.7

39. Treatment
REPS 1 2 3 4 5
Total
22.3
21.8
21.2 20
85.3
18.3
18.7
18.5
21.5
17.3
94.3
17.2
17.9
16.7
86.2
14.9
12.6
13.1
14.4
12.4
67.4
72.7
70.3
49.5
74.3
66.4
333.2

40. Missing Data More than one Missing value
Calculation for Second Value
X = tT + rR – G
(t-1)(r-1)
X = Missing value
t = Number of treatment
r = Number of Repeats
T = Total of treatment with a missing value
R = Total of replication with a missing value
G = grand total with a missing value
X = (4*85.3) + (5*49.5) – 333.2
(4-1) (5 -1)
X = – 333.2
3 * 4
X = 21.3

41. Treatment
REPS 1 2 3 4 5
Total
22.3
21.8
21.3
21.2 20
106.6
18.3
18.7
18.5
21.5
17.3
94.3
17.2
17.9
16.7
87.8
14.9
12.6
13.1
14.4
12.4
67.4
72.7
70.3
70.8
75.9
66.4
356.1

42. Missing Data More than one Missing value
Calculation for Third Value
X = tT + rR – G
(t-1)(r-1)
X = Missing value
t = Number of treatment
r = Number of Repeats
T = Total of treatment with a missing value
R = Total of replication with a missing value
G = grand total with a missing value
X = (4*69) + (5*57.1) – 337.3
(4-1) (5 -1)
X = – 333.2
3 * 4
X = 18.8

43. Treatment
REPS 1 2 3 4 5
Total
22.3
21.8
21.3
21.2 20
106.6
18.3
18.7
18.5
21.5
17.3
94.3
17.2
17.9
18.8
16.7
87.8
14.9
12.6
13.1
14.4
12.4
67.4
72.7
70.3
70.8
75.9
66.4
356.1

44. Height of plants with variable nutrients
Treatments (Nutrient type)
Pot # 1 2 3 4 5
42.2
28.4
18.8
41.5
33.0
34.9
28.0
19.5
36.3
26.0
29.7
22.8
13.1
31.7
30.6
18.5
10.1
31.0
19.4
28.2
Total
Sum
106.8
117.1
61.5
168.7
89.6
543.7
Rep ( r) 20
Ave. (y)
35.6
23.42
15.38
33.74
29.87
27.18

45. Calculations for ANOVA
Degrees of freedom
Total df = Total number of experimental units – 1 = 20-1 =19
Treatment df = total number of treatments – 1= 5-1 = 4
Error df = Total df-treatment df = 19-4 = 15
Correction factor = (grand total)2/ total expt units (observations)
Sum of squares
CF = (543.7)2/20 =
Total SS = (42.2) 2 + (34.9) (30.6) CF =
Treat SS = (106.8) 2 + (117.1) (89.6) CF =
Error SS = Total SS – Treat SS = – =
Mean Squares
Treat MS = Treat SS/ Treat df = /4 =
Error MS = Error SS/ Error df = /15 =
F-Calc
Treat MS/ Error MS = /24.12 = 11.17
F (tab) at 15 error df = 3.06 (at 5% level) & 4.89 (at 1% level)

46. Construction of ANOVA table
Analysis of plant height grown on different nutrient media
** Highly significant (at 1% level)
Source of Variation Df SS MS F
Total 19
Nutrient type 4
269.41
11.17**
Error 15
361.58
24.12

47. Coefficient of variation (cv):
CV = (SQRT Error MS/ grand mean)*100 = (SQRT 24.12/ 27.18) * 100 = 18.1%
Standard Errors (SE) = SQRT (Error MS/r)
SE1 = SQRT (24.12/3) = 2.83
SE2 = SQRT (24.12/5) = 2.20
SE3 = SQRT (24.12/4) = 2.45
SE4 = SQRT (24.12/5) = 2.20
SE5 = SQRT (24.12/3) = 2.83
Interval estimate (at 5% level)
For Treat 4 = Mean Tr4 + t * SE4
= *2.20 =
Standard Error for comparison of Treat 1 and 2
Treat 1 and 2 = SQRT {Error MS (r1+r2)}/ (r1*r2)
= SQRt {24.12(3+5)}/ 3*5
= 3.58

48. RCBD – Solved Example Soil Block Treatment Rep 1 rep 2 Rep 3 Rep 4
Total
Mean 1
32.1
35.6
41.9
35.4
145
36.25 2
30.1
31.5
37.1
30.8
129.5
32.37 3
25.4
27.1
33.8
31.1
117.4
29.35 4
24.1 33
31.4
124.1
31.02 5
26.1 31
31.9
122.8
30.70 6
23.2
24.8
26.7
101.4
25.35
161
183
208.9
187.3
740.5
26.8
30.5
34.8
31.2
30.85

49. RCBD – Solved Example
Correction Factor (CF) = (grand total)2/(no. of treatment* no. of reps or block)
= (740.5)2/ (6*4)
= /24 =
Total sum of square (TSS) = (32.1)2 + (30.1) 2 + (25.4) (26.7) 2 –CF = =
Replication Sum of square (RSS) = (Total Rep1) 2/no.of treats+(Total Rep2) 2/no.of treats (Total Rep3) 2/no.of treats+(Total Rep4) 2/no.of treats-CF
= (161) 2/6 + (183) 2/ 6 + (208.9) 2/6 + (187.3) 2/6
= – =
Treatment Sum of Square (TrSS) = (Total Treat1) 2/no.of reps+(Total Treat2) 2/no.of reps (Total treat3) 2/no.of reps+(Total Treat 4) 2/no.of reps (Total Treat5) 2/no.of reps+(Total Treat6) 2/no.of reps –CF
= (145) 2/4 + (129.5) 2/4 + (117.4) 2/4 + (124.1) 2/ (122.8)2/4 + (101.4)2/4 –CF
= – =
Error Sum of Squares (ESS) = Total SS- Rep SS - Treatment SS
= – –
= 64.13
Mean Square Rep (RMS) =RSS/ rep df
= /3 = 58.08
Mean Square Treat (TrMS) =TrSS/ traet df
= /5 = 47.53
Mean Square Error (EMS) =ESS/ (traet df)*(rep df)
= 64.13/15 = 4.28
F-Calc (reps) = RMS/ EMS = 58.08/4.28 = 13.59
F-Calc (treats) = TrMS/ EMS = 47.53/4.28 = 11.12

50. RCBD – Solved Example CV% = ((SQRT (EMS))/ Grand Mean)*100
= (2.069/30.85)*100
= 0.067*100
= 6.7%
SE (Tr) = SQRT (EMS/r)
= sqrt (4.28/4)
= sqrt (1.07)
= 1.034
SE (Difference between 2 Treatments) = SQRT (2*EMS/r)
= sqrt (2*4.28/4)
= sqrt (2.14)
=1.46

51. Solved Example Treatments= 6, Reps= 4
SOV df MS
F.calc.
Treat 5
2976.4
24.8**
Error 18
120.0
Variety
Yield 1
50.3 2
69.0 3
24.0 4
94.0 5
75.0 6
95.3
Variety
Yield 6
95.3 4
94.0 5
75.0 2
69.0 1
50.3 3
24.0
Variety
Yield 6
95.3 4
94.0 5
75.0 2
69.0 1
50.3 3
24.0
Variety
Yield 6
95.3 4
94.0 5
75.0 2
69.0 1
50.3 3
24.0
LSD = tά 2EMS/r = (2*120)/4= (5%)
LSD = tά 2EMS/r = (2*120)/4= (1%)