This document discusses different experimental designs used in analysis of variance (ANOVA). It describes the completely randomized design, randomized block design, Latin square design, and factorial design. For each design, it covers key aspects like blocking, randomization, replication, and advantages/disadvantages. The goal of experimental designs is to reduce experimental errors and improve precision when investigating relationships between independent and dependent variables.

1. EXPERIMENTAL
DESIGN-ANOVA
Group 8
PRESENTED BY

2. 1 Introduction
2 What is Design of Experiment
3 Completely Randomized Design
4 Randomized Block Design
5 Latin Square Design
6 Factorial Design
7 Conclusion
INDEX

3. EXPERIMENT
A procedure to investigate Cause and Effect
relationship
DEPENDABLE VARIABLE
Variable that gets measured, outcome affected by
independent variable
INDEPENDANT VARIABLE
Variable that gets manipulated, completely
independent.
WHAT IS AN EXPERIMENT

5. Point to be noted
When the dependent variable is not dependent on
independent variable : No relationship exists between
them
When they both are related: A causal relationship will
exist between the two.

6. .
EXPERIMENTER
CONTROL
• Distinguishing factor from true experiments and other
studies
• The level of independent variable administered is
controlled.
• Here we can take a control group and two respective
groups
• The effect of the independent variable gets isolated
and how it affects the dependent variable, its relation
can be calculated
• May involve blinding so as to avoid bias

7. LAYMAN EXAMPLE
Control
-Natural Growth
GROUP 2
Fertilizer 2
GROUP 1
Fertilizer 1

8. Independent Variable- Type of Fertilizer
Dependable Variable-Plant Growth
Group 1- Fertilizer A
Group 2 - Fertilizer B
Control- Natural growth
Here we will take certain number of plants and divide them into 3 groups as above. The
environmental conditions are kept same and the fertilizer amount used was the same. Then
BLINDING was done.
The inference observed would be that the growth of A,B and control would be different. Here the farmer can understand
how the independent variable which is the fertilizer used can affect the dependable variable which is the growth of the
plant.
let’s take a layman example

9. • A type of experiment or study where there is no experimental
control over the independent variable.
• The independent variable cannot be manipulated due to
certain constraints
• Here there is an introduction of potential confounding
variables, making it less vigorous than a true experiment
QUASI-
EXPERIMENTS

10. DESIGN OF EXPERIMENTS
• Plan of conducting an experiment- The research results are easy to interpret and
valid
• It includes the following activities that are
Writing its hypothesis, collecting and analyzing data
• It includes variables that we can control and variables that we cannot control.
• It must include the following while planning -
Be random and non biased, it should have a measure of error, have a clearly
defined objective and have sufficient accuracy.

11. IMPROVES PERFORMANCE
Improves performance of existing
process
MAKES AN IMPACT
SIMPLIFIES STATISTICS
ADDS CREDIBILITY
Adds reliability to the experiment and
overall research.
Reduces time to design and develop new
products
Achieve product and process robustness
Perform Evaluation of Materials.

12. • Recognition and problem statement
2. Choice of factors and selection of
response variables
3 Choice of design and conducting
the experiment
4 Statistical Analysis
5 Drawing Conclusions and
making assumptions
STEPS INVOLVED
IN DESIGN OF
EXPERIMENTS

13. Definitions involved
Treatment- The variants that are under study
Yield- A method of measuring response of treatment
Experimental units- Smallest division of experimental material
on which the treatment gets applied and on which the variable
gets measured
Blocks- Material is divided into groups and strata and data
should be between homogenous and heterogeneous
Experimental Error- A variation that occurs between the yields
of different plots even after receiving the same treatment ;
errors can be due to inherent variability, measurement error etc.
Precision- Reciprocal of variance of mean

14. Principles of
design of
experiments
RANDOMIZATION
For non biased results
REPLICATION
For increasing precision
LOCAL CONTROL
Reduce Experimental error and to reduce variability

15. Randomization
Essential for - a) Estimation of error
b) Minimize bias in the results
Randomization done - Each treatment gets an equal chance
The advantages of Randomization are-
a) Ensures independence of observation i.e. essential for
variance
b)Eliminates Bias

17. Replication
Re-running of the experiment in order to increase precision.
Allows the uncontrolled factors to balance out and acts as a bias reducing
tool
Uses of replication-
a)We obtain precise estimate of treatment effects
b)Provides an estimate of experimental error
c)For desired precision, the replication number can be obtained

18. Used to attain accuracy and reduce experimental error without
increasing number of replications and the effect of variability gets
reduced.
Done by formation of homogenous blocks that are
a) Homogenous within
b) Heterogeneous between
Local Effect

19. Advantages of Local effect
• Reduction of Experimental Errors
• Test procedure becomes more sensitive and powerful

20. Different Experimental Designs
The following designs are frequently
used:
1.Completely Randomized Design
2.Randomised Block Design
3.Latin Square Design
4.Factorial Design

21. Completely randomized sampling
design
Applied in the case when the experimental materials
are homogenous.
Based on two principles-
RANDOMIZATION
REPLICATION
Following are the situations in which we can apply this
design-
• CRD used in situations where experimental materials
are homogenous.
• CRD mostly used in chemical ,biological and banking
experience
• The observations on some units are missing or
destroyed.

22. Factors for
calculating CRD
All CRDs with one primary factor are designed by 3
numbers:
• k, indicates number of factors
• L, indicates number of levels
• n, indicates number of replications
Total sample size which indicates number of runs
(N=k*L*n)

23. Example of CRD

24. Example
k=1 factor
• L = 4 levels of that single factor (called “1”, “2”,
“3” and “4”)
• n = 3 replications per level
• N =L*n = 12 runs
Features-a) The whole field is divided into
plots.
b)Treatment wise randomization is done
c)Divided into 2 compartments
d)Local Control is not adapted

25. Advantages of CRD
• Simple & Easy
• Maximum number of degree of freedom is
used
• Flexibility
• Unbiased
• Statistical Efficacy
• Independence
• Wide Applicability

26. Disadvantages of Completely Randomized Designing
• Less accurate
• Reduces Precision
• Increases Experimental errors
• Inefficient use of resources
• Limited ability to detect interaction

27. RANDOMIZED
BLOCK DESIGN

28. INTRODUCTION ABOUT
RANDOMIZED BLOCK DESIGN
…..
A randomized block design is a type of
experiment where the experimental units
are divided into blocks based on some
characteristics that may affect the outcome.
The blocks are formed to reduce the effect
of extraneous variables and minimize the
variability within blocks

29. INTRODUCTION ABOUT
RANDOMIZED BLOCK
DESIGN…..
The design requires that every
treatment be applied an equal number
of times in every block and is suitable
only when the block is large enough to
accommodate all treatments once. It is
also possible to use a randomized
design with repetitions. The treatments
should be allocated randomly within
each block

30. BLOCKS Randomization Replication
Analysis of
Variance
(ANOVA)
STEPS IN RANDOMIZED BLOCK
DESIGN
Blocks are groups of
experimental units that are
expected to be similar in some
aspect that might affect the
response variable
Experimental units are
randomly assigned to
treatment groups within
each block
Each treatment is
applied to multiple
experimental units
within each block.
The data collected in
a randomized block
design are typically
analyzed using
analysis of variance.
mainly The design
can be analyzed by
two-way ANOVA

31. Example :
Suppose a researcher wants to test the effectiveness of three different
types of fertilizers on crop yield.
The researcher divides the field into blocks based on soil type and
randomly assigns each fertilizer treatment to different plots within each
block.
This design helps to reduce the variability of the dependent variable
within blocks and increase the precision of the treatment effects

32. ADVANTAGES :
• The efficiency level is high.
• It reduces experimental errors.
• It increases precision.
DISADVANTAGES :
• It is not suitable for a larger number
of treatments.
• The analysis is easy but becomes
complicated when a missing plot
technique is required.

33. LATIN
SQUARE
DESIGNS

34. DEFINITION
This design is appropriate when the response may be
affected by two different sources of variation each of which can
assume k different levels or positions.
It is suitable only when the number of rows, the number of columns
and the number of treatments are equal

35. A B C D
B C D A
C D A B
D A B C
C B A D
B C D A
A D C B
D A B C
each objects appears once and only once
in each row and column
it can be of 5*5, 6*6,...

36. In LSD we have three factors
• Rows
• Columns
• Treatments ( letters A,B,C,.....)
THE NUMBER OF TREATMENTS=NO. OF ROWS=NO.OF COLUMNS= n
The treatments are assigned to row-column combinations using
a Latin square arrangements

37. ANALYST/
INSTRUMENT
1 2 3 4
a A B C D
b B C D A
c C D A B
d D A B C
A - Day 1
B -Day 2
C -Day 3
D -Day 4

38. Advantages
1.Controls more variation
2.Results in a smaller mean square for error.
3.Simple analysis of data
4.Analysis is simple even with missing plots
Disadvantages
1. large and unmanageable very readily.
2. if the number of treatments is too small, errors are possible
3.Number of treatments is limited to the number of replicates which
seldom exceeds 10.