mb0050 slides unit 12

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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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Unit-12 Analysis of Variance

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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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The total variation in the data set is called the total sum of

squares (TSS) and is computed as:

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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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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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7/24/2019 MB0050 Slides Unit 12



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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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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7/24/2019 MB0050 Slides Unit 12


Factorial Design

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7/24/2019 MB0050 Slides Unit 12


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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7/24/2019 MB0050 Slides Unit 12


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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