STATISTICAL METHODS AND TECHNIQUES FOR AGRONOMIC RESEARCH

AGRON-591(0+1): Master seminar
DEPARTMENT OF AGRONOMY,
Dr.Panjabrao Deshmukh Krishi Vidyapeeth,
AKOLA

STATISTICAL METHODS AND
TECHNIQUES FOR AGRONOMIC
RESEARCH
Duddumpudi Venkata Sri Akshay
PG19-AGR-2035
Submitted by:

Research
• Research is a scientific and systematic search for relevant
information on a specific topic. In short, the search for knowledge
through objectives and systematic method of finding solution to a
problem is research.
Purpose/objective of research
• To gain familiarity with a phenomenon or to achieve a new insight
into it.
• To attain the goal and To solve the problem.
• To maintain the system or to improve the system
• To portray accurately the characteristic of a particular individual
situation or a group.
• To test a hypothesis of a causal relationship between variables.
Akshay Duddumpudi Dr.PDKV, Akola

Agricultural Research - Types
• Basic research: Example – study of the genetic resistance of
rice to blast.
• Applied research or development research: Example –
recommendation of fertilizer doses, herbicides, insecticides
etc, insect resistance high yielding rice variety.
• Adaptive research: under varied conditions. Example –
Development of specific variety of rice for Aus or Aman or
Boro season, fertilizer recommendation for specific location or
land type or soil type.

Research Problem
• An agricultural problem may be defined as any difficulty in
converting efforts into economic agricultural production.
 Factors to be considered in determining the priority of researchable
problems
• Economic importance of the problem
• Technology/innovation available to overcome such a problem
• Cost and time needed to carry out the research
• Availability of the resources
• The ease of implementing the new technologies (probability of
adoption of the new technology)
• Probable distribution of benefits within the society.

Experimentation
Before a new variety, fertilizer, herbicide, fungicide,
insecticide or growth hormone is recommended to farmers, it
is necessary to test its potency under laboratory or field
conditions including farmers’ field. These trials are classified
into
• laboratory experiments,
• pot culture experiments,
• frame plot experiments,
• field experiments,
• green house experiments.

Important Agronomic Field Experiments
A. Tillage and soil management
B. Sowing time
C. Genotypes/varieties
D. Plant population
E. Weed Management
F. Water Management
G. Nutrient Management
H. Cropping and Farming systems mainly including Organic And Integrated
Farming Systems
I. Conservation Agriculture
J. Protected Cultivation
K. Climate Smart Agriculture
L. Precision farming
M. Drone Technology

IMPORTANT TERMINOLOGY
• Treatment: Objects of comparison in an experiment are
defined as treatments. Examples are Varieties tried in a trail
and different chemicals.
• Experimental unit: The object to which treatments are applied
or basic objects on which the experiment is conducted is
known as experimental unit. Example: piece of land, an
animal, etc
• Experimental error: The variations in response caused by
factors like heterogeneity of soil, climatic factors and genetic
differences, etc also may cause variations (known as
extraneous factors) are known as experimental error.

• Sample: A finite subset of statistical objects in a population is
called a sample and the number of objects in a sample is
called the sample size.
• Population: In a statistical investigation the interest usually
lies in the assessment of the general magnitude and the study
of variation with respect to one or more characteristics relating
to objects belonging to a group. This group of objects under
study is called population or universe.
• Random sampling: If the sampling units in a population are
drawn independently with equal chance, to be included in the
sample then the sampling will be called random sampling.

• Factor: Factor refers to a set of related treatments. We may
apply of different doses of nitrogen to a crop. Hence nitrogen
irrespective of doses is a factor.
• Levels of a factor: Different states or components making up a
factor are known as the levels of that factor. eg different doses
of nitrogen.
• Simple effect of a factor is the difference between its
responses for a fixed level of other factors.
• Main effect is defined as the average of the simple effects.
• Interaction is defined as the dependence of factors in their
responses. Interaction is measured as the mean of the
differences between simple effects

• Degrees of freedom:The number of degrees of freedom is the
number of observations that are free to vary after certain restriction
have been placed on the data. If there are n observations in the
sample,for each restriction imposed upon the original observation
the number of degrees of freedom is reduced by one.
• It is also defined as the difference between the total number of
items and the total number of constraints. If n is the total number of
items and , k the total number of constraints then the degrees of
freedom (d.f.) is given by d.f. = n-k
• Level of significance(LOS): The maximum probability at which we
would be willing to risk a type-I error is known as level of significance
or the size of Type-I error is level of significance. The level of
significance usually employed in testing of hypothesis are 5%, 1%.

• Statistical hypothesis: a STANDARD. In statistics, a hypothesis is
concerned with a population of individuals and can always be
formulated as a statement about the probability distribution of the
variable at hand. Such a statement is known as statistical
hypothesis.
• Null Hypothesis: Null hypothesis is such a hypothesis, which is
usually a hypothesis of no difference is called null hypothesis and It
usually denoted by H0.
• Alternative Hypothesis: Any hypothesis, which is complementary to
the null hypothesis, is called an alternative hypothesis, usually
denoted by H1.
• Type I error (α): It is committed when we reject the hypothesis in
reality when it is true.

• Type II error (β): It is committed when we accept the hypothesis in
reality when it is not true (false)
• Range – It is the measure of dispersion. It is the difference between
least and the greatest values for observations.
• Mean – It is the average of the data.
• Deviation – The difference between two values, usually the
difference between an individual variate and the mean.
• Standard deviation (SD) – The value of SD is based on the deviation
from the arithmetic mean.
• Variance – It is the square of the standard deviation. It is being used
extensible in the statistical analysis of the results from experiments.

• Coefficient of variation (CV) – It is the standard deviation as a
percentage of the mean. This is necessary to know relative
variability. For comparison of samples low CV is preferred than
larger one.
• Test of significance – Test of significance is the procedure for
deciding whether the difference under study is significant or not.
Sample size is most important criterion (Large scale > 30 and small
scale < 30).
• Standard error (SE) – It is the measure of variability of the sample
mean from the population mean. SE is a measure of variability of an
individual variate from the sample mean. SE=SD/√n (When the
sample is small (<30) instead of n one should use n-1.)

• Standard error of difference (SEd) - It is the magnitude of difference
of two sample means.This will indicate whether there can be a
difference of observed magnitude between two sample means
drawn from the same population or not.
• Correction factor (CF) – A number subtracted from the sum of
squares of a group of items to obtain the sum of squares of the
deviations of each item from their mean.

• Critical difference: Critical difference may be defined as that
least significant difference equal to above which all the
differences are significant.
• Uniformity trial: The repetition of an experiment under exactly
the same controlled conditions as in the original trial.
• Fertility Contour Map : An approach to describe the
heterogeneity of land is to construct the fertility contour map.
This is constructed by taking the moving averages of yields of
unit plots and demarcating the regions of the same fertility by
considering those areas, which have yield of same magnitude.

DESIGN OF
EXPERIMENTS

Defnition
• Choice of treatments, method of assigning treatments to experimental units
and arrangement of experimental units in different patterns are known as
designing an experiment.
• Experimental design forms the backbone of agricultural sciences; it is an
integral component of every research endeavour in agricultural sciences.
Requirements
In planning any experiment, the experimenter needs to decide
a) What conditions to study or what are the treatments
b) What is the experimental material on which the experiment is to be
conducted,
c) What measurements to make or what are the responses and how to
measure these accurately and correctly. Response also denotes the
measurable outcome as a result of application of treatments on the
experimental units.

Three Basic Principles
• Randomization: The allocation of the treatments (objects of
comparison, which an experimenter has to try out in the field for
assessing their values) to different plots by a random process is
known as randomization.
• Replication: Repetition of treatments under investigation is known as
replication.
• Local control: The principle of making use of greater homogeneity in
groups of experimental units for reducing the experimental error is
known as local control.

Steps for running an experimental design
The main steps in conducting an experiment are given below:
 State the objectives of the study and the hypotheses to be tested.
 Determine the response variable(s) of interest that can be
measured.
 Determine the controllable factors of interest that might affect the
response variable(s) and the levels of each factor to be used in the
experiment.
 Determine the uncontrollable variables that might affect the
response variables.
 Determine the total number of experimental units and number of
replications of the treatments in the experiment, based on available
time and resources

 Select a suitable design for the experiment. The chosen design
should block the known nuisance variables and randomize the
experimental units to protect against unknown nuisance variables.
 Conduct a smaller pilot experiment and Review steps i-vi in case of
unsatisfactory situation.
 Perform the experiment strictly according to the experimental
design.
 Analyse the data from the experiment.
 Interpret the results and state the conclusions.
 Document the results and conclusions from the experiment.
 The most important thing to remember is that the treatments are
always labelled randomly.

Determination of number of replications
 Although the answer largely depends upon the resources available,
there are some scientific reasons also that help in determining the
optimum replication number. They are
 The foremost important consideration in the determination of
replication number is that there should be adequate error degrees of
freedom. As far as possible, there should be about 12 degrees of
freedom for error.
 Availability of resources and precision required.
 Type of experimental material.
 Manageability of the experiment

Important designs for field experimentation
There are number of experimentation designs selection of which
depends on the number of treatments under study and type of study
to be undertaken. Most commonly used designs are
• Completely Randomized Design (CRD),
• Randomized Block Design (RBD),
• Latin Square Design (LSD),
• Factorial designs,
• Split Plot Design (SPD),
• Incomplete Block Design (IBD),
• Strip Plot Design (SPD) And
• Confounded.

Completely Randomized Design (CRD)
• CRD is the basic single factor design. In this design the treatments
are assigned completely at random so that each experimental unit
has the same chance of receiving any one treatment.
• But CRD is appropriate only when the experimental material is
homogeneous.
• In laboratory experiments and greenhouse studies, it is easy to
achieve homogeneity of experimental materials and therefore CRD
is most useful in such experiments.

Suitability Condition - CRD
• If field is completely homogenous then CRD is used.
• CRD is used under lab condition, mist chamber, green house
because in these we can make/ create homogenous condition.
• It is rarely used in field condition.
• This design can be used in equal or unequal number of
observations.
• In CRD the field is homogenous hence; we use replication and
randomization principles of design.
• Error degree of freedom(d.f.) is maximum in this design

•The null hypothesis will
be
Ho : μ1 = μ2=………….=μk
or There is no significant
difference between the
treatments

Advantages of a CRD
• Its layout is very easy. There is complete flexibility in this design i.e. any
number of treatments and replications for each treatment can be tried.
• Whole experimental material can be utilized in this design.
• This design yields maximum degrees of freedom for experimental error.
• The analysis of data is simplest as compared to any other design.Even if
some values are missing the analysis can be done.
Disadvantages of a CRD
• It is difficult to find homogeneous experimental units in all respects and
hence CRD is seldom suitable for field experiments as compared to other
experimental designs.
• It is less accurate than other designs.

Randomized Blocks Design (RBD)
• If the fertility gradient runs in one direction say from north to south or
east to west then the blocks are formed in the opposite direction.
Such an arrangement of grouping the heterogeneous units into
homogenous blocks is known as randomized blocks design.
• An ideal source of variation to use as the basis for blocking is one
that is large and highly predictable. Examples include,
 Soil heterogeneity, in a fertilizer or variety trial where yield data is
the primary character of interest.
 Direction of insect migration, in an insecticide trial where insect
infestation is the primary character of interest.
 Slope of the field, in a study of plant reaction to water stress.

Suitability condition
• RBD is commonly used in agriculture in field condition.
• It is used when fertility gradient runs in one direction.
• There should be homogeneity within blocks and heterogeneity
between block.
• In this design we use all three principles of design i.e.
Replication, Randomization and Local control.
• Each treatment must occur once & only once in each block.
• This design is suitable upto (10-12 )treatment.

Remarks:
• Large number of treatment is not used then it is not possible to
maintain the homogeneity within the block.
• Number of block = Number of replication.
• Number of plots in each block = Number of treatment.
Null hypothesis:
i) H01 : There is no significant difference between the treatment effects.
i.e. α1=α2=α3 =....................=αk
ii) H02: There is no significant difference between the block effects.
i.e. β1=β2=β3=....................=βr

Advantages of RBD
• The precision is more in RBD. The amount of information obtained in
RBD is more as compared to CRD.
• RBD is more flexible. Statistical analysis is simple and easy.
• Even if some values are missing, still the analysis can be done by
using missing plot technique.
Disadvantages of RBD
• When the number of treatments is increased, the block size will
increase. If the block size is large maintaining homogeneity is
difficult and hence when more number of treatments is present this
design may not be suitable.

Latin Square Design (LSD)
• When the experimental material is divided into rows and columns
and the treatments are allocated such that each treatment occurs
only once in each row and each column, the design is known as
LSD.
• Null hypothesis (H0) = There is no significant difference between
Rows, Columns and Treatment effects.
• i.e. i) H01: α1=α2=α3=....................=αi
• ii) H02: β1=β2=β3=....................=βj and
• iii) H03: γ1=γ2=γ3=....................=γk

Suitability condition - LSD
• Field trials in which the experimental area has two fertility gradients
running perpendicular to each other, or has a unidirectional fertility
gradient.
• Greenhouse trials in which the experimental pots are arranged in
straight line perpendicular to the glass or screen walls, such that the
difference among rows of pots and the distance from the glass wall
(or screen wall) are expected to be the two major sources of
variability among the experimental pots.
• Laboratory trials with replication over time such that the difference
among experimental units conducted at the same time and among
those conducted time constitute the two known sources of variability

Advantages of LSD
• LSD is more efficient than RBD or CRD. This is because of double
grouping that will result in small experimental error.
• When missing values are present, missing plot technique can be
used and analysed.
Disadvantages of LSD
• This design is not as flexible as RBD or CRD as the number of
treatments is limited to the number of rows and columns. LSD is
seldom used when the number of treatments is more than 12. LSD
is not suitable for treatments less than five.
• Because of the limitations on the number of treatments, LSD is not
widely used in agricultural experiments.

Factorial Experiments
• When two or more number of factors are investigated
simultaneously in a single experiment such experiments are
called as factorial experiments.
• In general if there are n factors each with p levels then it is
known as pn factorial experiment.
• Based on the experiment , it includes the design of
CRD,RBD,LSD,etc., and denoted as f-CRD (or) f-RBD (or) f-
LSD.

Types of Factorial Experiments
• A factorial experiment is named based on the number of factors and
the levels of each factor. For example,
• Ex1 : If there are four factors each at two levels, the experiment is
known as 2x2x2x2 or 24 factorial experiment.
• Ex2 : In general if there are n factors each with p levels then it is
known as pn factorial experiment.
• For differing number of levels, the arrangement is described by their
products. For example, the experiment with three factors, first at 2
levels, the second at 3 levels and the third at 4 levels, is designated
as 2x3x4 factorial experiment.

Advantages of Factorial experiments
• In such type of experiments we study the individual effects of each factor
and their interactions.
• In factorial experiments a wide range of factor combinations are used.
• Factorial approach will result in considerable saving of the experimental
resources, experimental material and time.
Disadvantages of Factorial experiments
• If block size increases it may be difficult to maintain homogeneity of
experimental material, experimental error INCREASES.
• All treatment combinations are to be included for the experiment irrespective
of its importance and hence this results in wastage of experimental material
and time.
• When many treatment combinations are included the execution of the
experiment and statistical analysis become difficult.

Split-plot Design
• In field experiments certain factors may require larger plots
than for others. For example, experiments on irrigation, tillage,
etc requires larger areas.
• On the other hand experiments on fertilizers, etc may not
require larger areas.
• To accommodate factors which require different sizes of
experimental plots in the same experiment, split plot design
has been evolved.

Suitability conditions
• A Split plot design is used when one factor requires larger area
(main plot) than other factor requiring smaller area (sub plot).
• This design is suited for a two factor Experiments.
• When one factor requires higher precision than the other factor
which requires higher precision will be allotted to sub plots

Strip- Plot Design
• The strip plot design is specifically suited for a two factor
experiment in which the desired precision for measuring the
interaction effect between the two factors is higher then that
for measuring the main effect of either one of the two factors.
• This is accomplished with the use of three plot sizes:
1. Vertical strip plot for Ist factor vertical factor.
2. Horizontal strip plot for IInd factor – horizontal factor
3. Intersection plot for the interaction between the two factors.

Suitability Conditions
• Both factors are require large area.
• The emphasis will be given to interaction effect.
• There is no preference for selecting of any two treatments.
• The degrees of precision associated with the main effects of both
factors are sacrificed in order to improve the precision of the
interaction effect.
• The vertical strip- plot and the horizontal strip plot are always
perpendicular to each- other.

Long Term Experiments
• long term experiment is an experimental procedure that runs through a long
period of time, in order to test a hypothesis or observe a phenomenon that
takes place at an extremely slow rate.
• Here we discuss the experiments that are conducted over different locations
or different seasons
Some examples of long-term experiments are:
• Long-term fertility trials, which are designed to evaluate changes in soil
properties and nutrients as a consequence of the application of some soil
amendments over time.
• Maximum yield trials, which are designed to measure crop yields and
change over time, in both physical and biological environments under
intensive cropping and best management.
• Weed control trials, which are designed to measure the change in weed
population over time following different types of weed control measures.

References
• Experimental Designs by Ravi R Saxena and Roshan
Bhardwaj
• Statistical Procedures For Agricultural Research By
Kwanchai A. Gomez And Arturo A. Gomez
• Statistical Analysis of Agricultural Experiments (Part - I :
Single Factor Experiments) by V K Gupta, Rajender Parsad,
Lal Mohan Bhar, Baidya Nath Mandal ; ICAR-IASRI.
• ICAR e-course notes : STAM-101
• ANGRAU course notes : STCA-101

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