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Program : MBA
Semester : III
Subject Code : MB0050
Subject Name : Research Methodology
Unit Number : 12
Unit Title : Analysis of Variance
Lecture Number : 12
Lecture Title : Analysis of Variance
Book Id : B1700
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Analysis of Variance
Objectives :
Explain the meaning and assumptions of conducting analysis of
variance.
Describe completely randomized design.
Describe the randomized block design in two-way analysis of
variance.
Explain factorial design.
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Lecture Outline
Introduction
Completely Randomized Design in a One-way ANOVA
Randomized Block Design in Two-way ANOVA
Factorial Design
Summary
Check Your Learning
Activity
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Introduction
The Analysis of Variance (ANOVA) technique helps to draw
inferences whether the samples have been drawn from
populations having the same mean.
The basic principle underlying the technique is that the total
variation in the dependent variable is broken into two partsone
which can be attributed to some specific causes and the other thatmay be attributed to chance.
In ANOVA, the dependent variable in question is metric (interval
or ratio scale), whereas the independent variables are categorical
(nominal scale).
In ANOVA, it is assumed that each of the samples is drawn from a
normal population and each of these populations has an equal
variance.
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Completely Randomized Design in aOne-way ANOVA
Completely randomized design involves the testing of the equality
of means of two or more groups.
In this design, there is one dependent variable and one
independent variable. The dependent variable is metric
(interval/ratio scale) whereas the independent variable is
categorical (nominal scale).
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Completely Randomized Design in aOne-way ANOVA
The total variation in the data set is called the total sum of
squares (TSS) and is computed as:
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Completely Randomized Design in aOne-way ANOVA
The variation within the sample, which is attributed to chance, is
referred to as the error sum of squares (SSE). This could be
computed by subtracting the treatment sum of squares from the
total sum of squares. This is shown as:
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Completely Randomized Design in aOne-way ANOVA
For a given level of significance, the computed F statistic is compared
with the table value of F with (k-1) degrees of freedom in the
numerator and k(n-1) degrees of the freedom for the denominator. If
the computed F value is greater than the tabulated F value, the null
hypothesis is rejected.
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Randomized Block Design in Two-way ANOVA
The total sum of square is partitioned into three componentsone
due to treatment, second due to block and the third one due to
chance (called the error sum of squares).
We have another component called block sum of squares (SSB)
which is computed as:
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Randomized Block Design in Two-way ANOVA
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Factorial Design
In factorial design, the dependent variable is the interval or the
ratio scale and there are two or more independent variables which
are nominal scale.
If there are two independent variables each having three cells,
there would be a total of nine interactions.
The main advantage of factorial design over randomized block
design is that it is possible to measure the main effects as well as
the interaction effects of two or more independent variables at
various levels.
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Factorial Design
C
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Summary
RA Fisher developed the theory of analysis of variance. This technique could
be used to test the equality of more than two population means in one go.
The basic principle underlying the technique is that the total variations in
the dependent variable can be broken into two componentsone which can
be attributed to specific causes and the other one may be attributed to
chance.
The analysis of variance techniques in this unit are illustrated through the
completely randomized design, randomized block design and factorial
design.
In a completely randomized design, there is one dependent and one
independent variable. The dependent variable is metric whereas the
independent variable is categorical.
In factorial design, the dependent variable is metric and there are two or
more independent variables which are non-metric.
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Check Your Learning
1. What is the analysis of variance?
Ans: If there are more than two populations, the test for the equality of means
could be carried out by the analysis of variance (ANOVA) technique.
2. Differentiate using suitable examples between the one-way and two-way
analysis of variance.
Ans: If there is one independent variable (one factor) divided into various
categories, we have one-way analysis of variance. In the two-way analysis of
variance, two factors each divided into the various categories are involved.
3. What are the characteristics of randomized block design?
Ans: A randomized block design has one dependent and two independent
variables each with two or more categories.
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Activity
Visit a few stores (say, 9) randomly in your town selling three
different styles of chairs. The stores can be categorized as small,
medium and large sizes. What design would you choose to study
the effect of styles of chairs and store size on sales? Detail the
procedure.
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