Discriminant analysis is a statistical technique used to classify cases into mutually exclusive categories based on a set of predictor variables. It can be used to predict group membership for categorical dependent variables with two or more classes. The key steps involve determining the discriminant function coefficients using methods like direct entry or stepwise, assessing the significance of the discriminant functions, interpreting the coefficients, and validating the analysis with a holdout sample. Common applications include market segmentation, product usage analysis, perception research, and identifying responders in direct marketing.

1. Discriminate Analysis
The number of categories which is possessed by the criterion variable
describes the discriminant analysis technique.
The researchers are facilitated in the discriminant analysis to classify the
persons or objects into two or more categories. For example, consumers can be
classified as loyal and switchers. With the use of this technique the categories or
classes can be predicted which are mutually exclusive and in which individuals
are possible to be included. In many cases, the classification will be
dichotomous such as user and non-users, high and low, and so on.
Discriminant analysis is very similar to the multiple regression because in
both techniques dependent variables are predicted with the help of a linear
combination of continuous independent variables.
There is a basic difference in both techniques; in multiple regression
analysis is used to predict the continuous dependent variable. On the other hand
discriminant analysis is used to predict atleast two but generally three or more
levels of categorical dependent variables (e.g., high performers/moderate
performers/low performers, certification success/failure, employees who stay
for two years or less/employees who stay for five years/employees who stay for
ten or more years, etc.).
 Assumptions of Discriminate Analysis:
1) The observations are a random sample.
2) Each predictor variable is normally distributed.
3) There must be atleast two groups or categories, with each case belonging to
only one group so that the groups are mutually exclusive and collectively
exhaustive (all cases can be placed in a group).

2. 4) The groups or categories should be defined before collecting the data;
5) The attribute(s) used to separate the groups should discriminate quite clearly
between the groups so that group or category overlap is clearly non-existent or
minimal;
 Objectives of Discriminate Analysis:
The objectives of discriminant analysis are as follows:
1) Examination of whether significant differences exist among the groups, in
terms of the predictor variables.
2) Determination of which predictor variables contribute to most of the
intergroup differences.
3) Classification of cases to one of the groups based on the values of the
predictor variables.
4) Evaluate the accuracy of classification.
 Applications of Discriminate Analysis:
1)Market Segmentation: Discriminate analysis , a multivariate technique used
for market segmentation and predicting group membership is often used for this
type of problem because of its ability to classify individuals or experimental
units into two or more uniquely defined populations. For Example, if age has a
low discriminant weight then it is less important than the other variable.
2) Product Research: Distinguish between heavy, medium, and light users of a
product in terms of their consumption habits and lifestyles.
3) Perception/Image Research: Distinguish between customers who exhibit
favourable perceptions of a store or company and those who do not.

3. 4) Advertising Research: Identify how marketer segments differ in media
consumption habits.
5) Direct Marketing: Identify the characteristics of consumers who will
respond to a direct marketing campaign and those who will not.
 Steps in Discriminate Analysis:
1) Formulate the Problem: The first step in discriminant analysis is to
formulate the problem by identifying the objectives, the criterion variable, and
the independent variables. The criterion variable must consist of two or more
mutually exclusive and exhaustive categories. The predictor variables should be
selected based on a theoretical model or previous research, or, in the case of
exploratory research, the experience of the researcher should guide their
selection.
When the sample is large enough, it can be split in Half.One half serves as the
analysis sample and the other is used for validation. The role of the halves is
then inter-changed and the analysis is repeated. This is called double cross-
validation.
2) Determining the Discriminant Function Coefficients:
i) The direct method involves estimating the discriminant function so that all the
predictors are included simultaneously. In this case, each independent variable
is included, regardless of its discriminating power.
ii) An alternative approach is the stepwise method. In stepwise discriminant
analysis, the predictor variables are entered sequentially, based on their ability
to discriminate among groups is appropriate when the researcher wants to select
a subset of the predictors for inclusion in the discriminant function.

4. 3) Determine the Significance of Discriminant Function: It would not be
meaningful to interpret the analysis, if the discriminant functions estimated
were not stastically significant. The null hypothesis that, in the population the
means of all discriminant functions in all groups are equal can be stastically
tested.
4) Interpreting the Discriminant Function: The value of the coefficient for a
particular predictor depends on the other predictors included in the discriminant
function. The signs of the coefficients are arbitrary.
5) Assess Validity of Discriminant Analysis: Validation, the fifth step,
involves the developing the classification matrix. The discriminant weights
estimated by using the analysis sample are multiplied by the values of the
predictor variables in the holdout sample to generate discriminant scores for the
cases in the holdout sample. The cases are then assigned to groups based on
their discriminant scores and an appropriate decision rule. The percentage of
cases correctly classified is determined and compared to the rate that would be
expected by chance classification.