2. Experimental Design
• Introduction:
• It is a plan used to collect the data
relevant to the problem under study in
such a way as to provide the basis for
valid and objective inference about the
stated problem.
3. • The plan consists of:
• 1) Selection of treatments whose effects
are to be studied
• 2) The specification of the experimental
layout
• 3) The assignment of treatments to the
experimental units
• 4) Collection of observation for analysis
4. • An experiment is planned to:
• a) Get maximum information for minimum
expenditure in the min. possible time
• b) Avoid systematic errors.
• c) Evaluate the outcomes critically and
logically
• d) Ignore spurious effect, if any
5. Following consideration used
to planning of exp.:
• 1) What is the exp.inteded to do?
• 2) What is the nature of treatments or
dependent variable and how are they to be
estimated?
• 3) How is the independent variable likely to
effect the treatments or dependent variables?
• 4) Are the factors to be held constant or varied?
If varied whether the variation is quantitative or
qualitative?
6. Analysis of experiment
• The sigificance of difference between the
means of 2 different samples can be
tested by
• Paired t-test or Z-test depending on the
sample size.
• If the sample size is less than 30 ----t-test
• ----------------------more than 30 ----Z-test
7. • Salesman 2 factor
• Time period 4
• Objective is to test the significance of
difference between the mean sales
reveneu t-test or ztest
• If the no.of sales man or factor is n more
than 2 then F-test can be used if more
then 2 then a comprehensive technique
Analysis of Variance ---ANOVA can be
8. ANALYSIS OF VARIANCE (
ANOVA)
• Decompositionng of total variability into its
components is called analysis of variance
9. Types of factors:
• A factor ,which has effect on response variable
of an exp.
• 1) Fixed factor:In an exp.,if a specific set of
treatments of a factor is selected with certainty
,then that factor is termed as fixed factor.In
such case the inference of the analysis of the
exp. is applied to only the set of treatments of
that factor. e.g if 4 salesman A,B,C and D ----
effect on sales
• then the inference is applied to only those 4.
10. 2) Random Factor:
• In an exp. , if a set of treatments of factors is
selected randomly from among the available
treatments ,then that factor is termed as
random factor. Under such situation, the
inference of analysis of the exp.can be
generalized to all of the treatment of factor.
• e.g if four salesmen A,D ,M and X are selected
randomly from available A,B,C-----Z for studying
their effect on the sales revenue
11. Effect of different explants
sources on shoot induction
• Explant No. of explant cultured Days to shoot initiation
No.of t.t Shoot initiation showing result
• Apical meristem 10 8-9 9
•
• Axillary meristem 10 10-12 7.2
•
• Nodal region 10 12-15 6.8
12. • Explant = Factor =1
• Level of factor or treatments=3
• Replicate = 5 are carried out to minimize
the error
• Response variable =2 Days , No. of t.t
• e.g. Replicate of 8-9=10,8,9,10,9
13. Types of Design:
• 2 types: 1) Systematic 2) Random
• Analysis of variance techniques are suitable to
randomized design only.The basic randomized
design are
• 1) Completely randomized design
• 2) Randomized complete block
• 3) Latin Square
• 4) Duncan”multiple range test
• 5) Factorial design
14. Basic Principles of
Experimental Design:
• 1) Randomization 2) Replication 3) Local control
• 1) Randomization: It is a random process assigning
treatments to the experimental units . Random -----every
sample has the equal possibility to selection.
• 2) Replication:It is the repetition of basic exp.or It is
a complete run of all the treatments to be tested in an
exp.It is used to ovoid the variation in an exp..An
individual repetition is called a replicate.It is used to:
• 1) To secure more accurate estimates of the
experimental error
• 2) To decrease the experimental error and increase the
precis
15. • 3) Local Control: It is a term referring
to the amount of balancing ,blocking and
grouping of the experimental unit. The
main purpose is to increase the efficiency
of an exp.design by decreasing the
experimental error.
16. 1) Completely Randomized
design
• CR is the simplest type of the basic design ,in which the
treatments are assigned to experimental units
completely at random.i.e the randomization is done
without any restriction.The design is completely flexible
i.e any no. of treatments and any no. of units per
treatment may be used.
• A CR is used in these situation: a) The experimental
units are homogenious b) The exp. are small on
Lab.scale.
• Experimental Layout: The layout of an exp. is the
actual placement of the treatments on the experimental
units ,which may pertain to time,space or type of
material.An example of the experimental layout for CR
using 4 treatmentsA,B,C,D, each repeated 3 times:
17. • 1: CABD 2) CBCA 3) ADDB
• Advantages of CR:
• 1) The design is v.simple and is easily laid
out.
• 2) It has the simplest statistical analysis
• 3)It provides the maximum no.of degree
of freedom for error sum of square.
18. 2) Randomized complete block
design
• A RCB design may be defined as one in which
• 1) The experimental material is divided into groups or
blocks in such a manner that the experimental units
within a particular block are relatively homogeneous.
• 2)Each block contains a complete set of treatments i.e it
constitutes a replication of treatments.
• 3) The treatments are assigned at random to the
experimental units within each block,which means that
randomization is restricted within blocks.
• It is the most frequently used experimental design.
19. Advantages and
disadvantages:
• 1) The source of variation is controlled by
grouping the experimental material and hence
the estimate of the experimental error is
decreased.
• 2) The design is flexible i.e any no.not less than
2 of replication may be run and any no. of
treatments may be tested.
• 3) The exp. can be set up easily.
• 4) It is easy to adjust for the missing
observations
20. • Disadvantages:
• 1) It controls variability only in one
direction
• 2) It is not a suitable design when the no.
of treatments is v.large or when the
blocks are not homogeneous
21. 3) Latin Square design:
•
• The experimental error in RCB design is
reduced by controlling the source of extraneous
variation in one direction i.e by grouping the
experimental units in one way. When the
variation is found in two directions, it becomes
necessary to remove these two sources of
variation simultaneously.This end is achieved by
simultaneously blocking of experimental Units in
two mutually perpendicular directions called
Rows and Columns.
22. • So each column and rows is a complete block,
the grouping for a balanced arrangement is
performed that each treatment must appear
once in each row and each column. If there are
k treatments, the experimental area will be
divided into k rows and k columns resulting in k2
plot. or experimental units, as the exp. is laid in
square pattern. The treatments are then
assigned at random to plots or experimental
units.
23. • Such a double blocking of experimental
units and a corresponding doubly
restricted random assignment is called a
Latin Square design. LS design is an
arrangement of k treatments in a kxk square
,where the treatments are grouped in blocks in
two direction and treatments appear once and
only once in each direction. In LS design ,the
no. of rows ,the no. of columns and the no. of
treatments must all be equal
24. • Experimental layout:
• 1) It always constructed by rotation.
• e.g Five fertilizers A,B,C,D and E were
tested by arranging plants in LS design in
the field .Yield is shown as.
25. Advantages and
disadvantages:
• 1) LS design reduces the error variance
by controlling the two sources of variation.
• 2) It is more efficient than a RCB design.
• 3)It is less flexible than RCB design.it is
practical only for 5-10 treatments. More
than 10 it is seldom used.
26. Disadvantage:
• 1) Replication in LS design is costly
• 2) In agricultural experimentation, the
land requirement is rigid, the actual layout
may be laborious and the approach to the
central most plots is difficult.
27. • 4) Factorial Design:
• If the no. of factors is more than one, then there
is need for generalized design of experiment is
called as factorial design. e.g Exper. are often
planned to investigate the effect of different
rates of fertilizers,diff.dates of planting , diff.
categories of education, differ. Intensities of
stimulus etc.
28. • Independent variables
:fertilizers,planting,education,stimulus are called
factors.
• The values are such as rates,dates,categories
and intensities are known as levels or effects
• An exper. is called a factorial experiment if the
treatment consist of all possible combinations of
several levels of several factors.
29. 4) Duncan’s Multiple Range
Test:
• In statistics, Duncan's new multiple
range test (MRT) is a multiple
comparison procedure developed by David
B. Duncan in 1955. Duncan's MRT belongs
to the general class of multiple
comparison procedures that use the
studentized range statistic qr to compare
sets of means
30. • If there is significant difference between
the treatment means of the factor with
respect to that component in terms of the
response variable,then one can use
Duncan multiple range test to compare
the means of the treatments of that
component in that model.
31. • Duncan’s Multiple Range test is convenient,
because it combines the ease of hypothesis
testing with the power of testing each mean to
each mean.
• There are a number of methods to test WHICH
factors matter.
• It is used to compare the means of treatments
of that component in that model. This test was
developed by Duncan (1955)
32. • The steps of this test are:
• Step-1: Arrange the treatments averages
in the ascending order from left to right.
•
• Step-2: Find the standard error of each
treatment mean .
•
