LECTURE 16
Analysis of Variance (ANOVA)
This lecture covers material on conducting an Analysis of Variance
(ANOVA).
Microsoft Excel is used for some applications.
Read:
Chapter 10, Sections 10.4 to 10.5
In earlier chapters, we studied statistical inference for a single population
mean and the comparison of two population means.
But what if a
manager wants to compare two or more populations to check whether
their means are the same or not?
Or if there are several samples of data,
the manager may want to know whether they belong to the same
population or different populations.
The purpose of this lesson is to introduce the concepts that are
incorporated within the analysis of variance technique.
Analysis of
variance, often referred to as
ANOVA
, is a statistical procedure by which
the user can perform a test of significance to test whether a set of
population means are significantly different from one another.
It is an
extremely useful technique for comparing the means of more than two
groups.
There are many different and complex forms that ANOVA can take
depending on the business questions to be answered and the research
design utilized.
This lesson will explain the procedure that can also be
used for the simplest design  the completely randomized design.
1
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View Full DocumentHypotheses to be tested by ANOVA
If we have more than two populations  say
k
populations; then their
means are
μ
1
,
μ
2
,
μ
3
,....
μ
k
.
We want to test if all the means are equal.
The hypotheses in this case would be of the form:
The null hypothesis H
0
is:
μ
1
=
μ
2
=
μ
3
= .
.... =
μ
k
.
The alternative hypothesis H
a
is: Not all the population means are equal.
Therefore even if two population means are not equal, we want to reject
H
0
.
Assumptions:
1.
The populations are normally distributed.
2.
The variances (i.e.,
σ
2
) are equal in all populations.
3.
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 Summer '08
 SINGER
 Statistics, Statistical hypothesis testing, 175

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