DISCRIMINABLE CLUSTER ANALYSIS

1. TITLE LOREM
IPSUM
Sit Dolor Amet
DISCRIMINABL
E CLUSTER
ANALYSIS
SUBMITTED TO:
PROF. SOMEN SAHU
DEPT. OF FES
-AGNIVA PRADHAN
M.F.Sc 2ND SEMESTER
DEPT. OF FNT
M/F/2021/03

2.  Discriminant analysis is a multivariate statistical technique used for classifying a
set of observation into pre defined groups.

3.  To understand group differences and to predict the likelihood that a particular
entity will belong to a particular class or group based on independent variables.

4. To identify the characteristics on the basis of which one can classify an indivisual as
–
Basket baller or volleyballer on the basis of anthropometric variables.
High or low performer on the basis of skill.
Junior or senior category on the basis of maturity parameter.
A riding-mower manufacturer would like to find a way of classifying families in a
city into those that a likely to purchase a riding mower and those who are not
likely to buy one.
A pilot random sample of 12 owner 12 non-owner in the city in under taken
that data is show next slide.

5. Observ
ation
Income (000 Rs) Plot Size
(000 sq. ft.)
Owner(1)
Non-
Owner(2)
1 60 18.4 1
2 85.5 16.8 1
3 64.8 21.6 1
4 61.5 20.8 1
5 87 23.3 1
6 110.1 19.2 1
7 108 17.6 1
8 82.8 22.4 1
9 69 20 1
10 93 20.8 1
11 51 22 1
12 81 20 1
13 75 19.6 2
14 52.8 20.8 2
15 64.8 17.2 2
Obser
vation
Income (000
Rs)
Plot Size
(000 sq.
ft.)
Owner(1)
Non-
Owner(2)
16 43.2 20.4 2
17 84 17.6 2
18 49.2 17.6 2
19 59.4 16 2
20 66 18.4 2
21 47.4 16.4 2
22 33 18.8 2
23 51 14 2
24 63 14.8 2

7.  The main purpose is to classify a subject into one of the two groups on the basis of
some independent traits.
 A second purpose is to study relationship between group membership and the
variables used to predict the group membership.

8.  When the independent variable is dichotomous or multichotomous.
 Independent variables are matric i.e. interval or ratio.

9.  Sample size: should be at least 5 times the number of independent
variables.
 Normal distribution: each of the independent variables is normally
distributed.
 Homogeneity of variance: all the variables have linear
homoscedastic relationship.
 Outliers: should not be present in the data.
 Non multicollinearity: there should not be any corelation among the
independent variables.

10.  Mutually exclusive: the groups must be mutually exclusive, with
every subject or case belonging to only one group.
 Classification: each of the allocations for dependent categories in the
initial classification are correctly classified.

11.  In, discriminant analysis the dependant variable is a categorical
variable, whereas independent variables are matric.
 After developing g the discriminant model for a given set of new
observation the discriminant function Z is computed.
Z = c+b1x1+b2x2+……+bnxn
C = constent
x1 ,x2, xn = independent variables
B1, b2, bn = coefficient
 The subject or object is assigned to first group if the value of Z is less
than 0 and to second group if more than 0.

12.  Step 1: the independent variable which have the discriminant power
are being chosen.
 Step 2: A discriminant function model is developed by using
coefficients of independent variables.
 Step 3: significance of discriminant function is tested by computing
Wilk’s Lambda
 Step 4: independent variable which possess importance in
discriminating the group are found.
 Step 5: classification of subjects to their respective groups are made.