Chapter Eighteen
Discriminant Analysis

18-2
Chapter Outline
1) Overview
2) Basic Concept
3) Relation to Regression and ANOVA
4) Discriminant Analysis Model
5) Statistics Associated with Discriminant Analysis
6) Conducting Discriminant Analysis
i.
Formulation
ii.
Estimation
iii. Determination of Significance
iv. Interpretation
v.
Validation

18-3
Chapter Outline
7)
Multiple Discriminant Analysis
i.
Formulation
ii.
Estimation
iii.
Determination of Significance
iv.
Interpretation
v.
Validation
8)
Stepwise Discriminant Analysis
9)
Internet and Computer Applications
10)
Focus on Burke
11)
Summary
12)
Key Terms and Concepts

18-4
ANOVA, Regression, and Discriminant
Analysis
ANOVA
REGRESSION
DISCRIMINANT ANALYSIS
Similarities
Number of
One
One
One
dependent
variables
Number of
independent
Multiple
Multiple
Multiple
variables
Differences
Nature of the
dependent
Metric
Metric
Categorical
variables
Nature of the
independent
Categorical
Metric
Metric
variables
Table
18.1

18-5
Discriminant Analysis
Discriminant analysis
is a technique for analyzing data
when the criterion or dependent variable is categorical and
the predictor or independent variables are interval in
nature.
The objectives of discriminant analysis are as follows:
Development of
discriminant functions
, or linear
combinations of the predictor or independent variables,
which will best discriminate between the categories of the
criterion or dependent variable (groups).
Examination of whether significant differences exist among
the groups, in terms of the predictor variables.
Determination of which predictor variables contribute to
most of the intergroup differences.
Classification of cases to one of the groups based on the
values of the predictor variables.
Evaluation of the accuracy of classification.

18-6
When the criterion variable has two categories, the
technique is known as
two-group discriminant
analysis.
When three or more categories are involved, the
technique is referred to as
multiple discriminant
analysis
.
The main distinction is that, in the two-group case, it is
possible to derive only one discriminant function.
In
multiple discriminant analysis, more than one function
may be computed.
In general, with
G
groups and
k
predictors, it is possible to estimate up to the smaller of
G
- 1, or
k
, discriminant functions.
The first function has the highest ratio of between-
groups to within-groups sum of squares.
The second
function, uncorrelated with the first, has the second
highest ratio, and so on.
However, not all the functions
may be statistically significant.
Discriminant Analysis

18-7
Discriminant Analysis Model
The
discriminant analysis model
involves linear
combinations of
the following form:
D
=
b
0
+
b
1
X
1
+
b
2
X
2
+
b
3
X
3
+ . . . +
b
k
X
k
where
D
=
discriminant score
b
's
=
discriminant coefficient or weight
X
's
=
predictor or independent variable
The coefficients, or weights (
b
), are estimated so that the
groups differ as much as possible on the values of the
discriminant function.

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- Fall '19