Ez25936938

O.S. Balogun, B.A. Oyejola, T.J. Akingbade / International Journal of Engineering Research
and Applications (IJERA) ISSN: 2248-9622 www.ijera.com
Vol. 2, Issue5, September- October 2012, pp.936-938
Use Of Discriminant Analysis In Classification Of Drug Peddlers
And Non-Drug Peddlers In Kwara State.
*
O.S. Balogun, **B.A. Oyejola and ***T.J. Akingbade
*
Department of Statistics and Operations Research, Modibbo Adama University of Technology, P.M.B. 2076,
Yola, Adamawa State, Nigeria
**
Department of Statistics, University of Ilorin, Ilorin, Kwara State, Nigeria
***
Department of Mathematical Sciences, Kogi State University, Anyigba, Kogi State. Nigeria

Abstract
National Drug and Enforcement Agency has been The National Drug Law Enforcement Agency
using oral evidence in the past rather than a (NDLEA) in Nigeria is not an exemption. Some
statistical tool to classify drug offenders into Drug drugs are prohibited from the open market because of
Peddlers and Non-Drug Peddlers.The aim of this their side effect and abuse by public. The drug could
research is to construct a Discriminant Function be in tablet or liquid form such as Marijuana, Heroin,
that can be used to classify persons for drug and Cocaine etc. To restrict the use government
related offences into two groups namely: Drug placed ban on them and offenders are penalized.
Peddlers and Non-Drug Peddlers. The following A socially undesirable class, including prostitutes,
variables were used: Type of Exhibit, Age, Weight thieves and hoodlums had been known to use the
of Exhibit and Gender.A discriminant function forbidden drugs. The use also leads to violence
was obtained and used for classifying drug among the users and also stimulates sexual assaults
offenders into groups. The result shows that Type on the female folks. According to (Odedeji, 1992),
of Exhibit, Age, Weight of Exhibit and Gender those in peddling are ignorant of the problems caused
contribute to the discriminant function. The by the drugs. Persons or individuals arrested for the
misclassification rate obtained was 28.2%. related offences are taken to court and convicted
based on the oral evidences supplied and amount of
Keywords: Drug Peddlers, Non-Peddlers, substances caught with them. It is taken as given that
Discriminant Function, Classification. a peddler deserves a stiffer penalty than users. The
reason being that dealing with prohibited drugs could
Introduction be drastically reduced if those peddling face stiff
Discriminant analysis has had its earliest and most penalties. These individuals are very difficult into
widespread educational research applications in the peddlers and non-peddlers on the basis of possession
areas of vocational and careers development. Because and dealing and other variables.
education prepares people for a variety of positions in The current effort enables us use a scientific method
the occupational structures prevalent in their in classifying drug related offenders.
societies, an important class of education research
studies is concerned with testing of theories about the The Discriminant Model
causes of occupational placements and/or the The elements of the discriminant models are given as
estimation of production equations for allocating Z  a  W1 X 1  W2 X 2  ...  Wk X k
positions or anticipating such allocation. Where
Discriminant analysis is a descriptive procedure of Z = discriminant score
separation in which linear functions of the variables a = discriminant constant
are used to describe or elucidate the differences
between the two or more groups. That is, the aim of Wk = discriminant weight or coefficient
this analysis includes identifying the relative Xk = an independent variable or
contribution of say, p variables to separation of
groups and finding the optimal plane on which the predictors variable
points can be projected to best illustrate the Discriminant analysis uses ordinary least
configuration of the groups (Rencher, 2002). squares to estimate the values of the parameters „a‟
The classification of objects to groups is usually and Wk that minimize the within Group Sum of
thought of as partition of the objects into subsets in Squares. Discriminant Analysis involves deriving
which the members are more similar. Classifying linear combination of the independent variables that
individuals into groups such that there is a relative will discriminate between the prior defined groups in
homogeneity between the groups and heterogeneity such a way that the misclassification error rates are
between the groups is a problem which has been minimized (Dillion and Goldstein, 1984). The
considered for many years (Ganesalingam, 1989). function is given as

936 | P a g e

D( X )  bX
1
Under the hypothesis H 0 :   and common
where b  S ( X1  X 2 )
1 2
variance covariance matrix the test statistic F is
X  ( X1  X 2 ) distributed as a F  distribution with P and
Where, D( X ) is a 1 n vector of n1  n2  p  1 df i.e.
discriminant scores, b  is a 1 p vector of F  F : ( p, n1  n2  p  1)
discriminant weights, and X is a p  n matrix Using the above relationship H 0 is rejected at the
containing the values of the n individuals on the p
1
significance level  , if F  F ( p, n1  n2  p  1)
independent variables. S the inverse of the pooled .
sample variance – covariance matrix of the Classification Rule
independent variable. The Mahalanobis generalized
2 Assign an individual with realized score X
distance D Statistic is used to determine whether
the between group differences in mean score profiles on the p independent variables to G1 if D( X )  C
are statistically significant. Large values of D
2
otherwise, to G2 if D( X )  C
would lead us to believe that the groups are Where
sufficiently spread in terms of mean separation
(Dillion and Goldstein, 1984). It is given as: C  ( X  X )S 1 ( X  X ) We assume that in
D 2  ( X 1  X 2 )S 1 ( X 1  X 2 ) each group observed scores on the p independent
variables as multivariate normal with mean
The test can be constructed by forming:
n1n2 (n1  n2  p  1) D 2 i , i  1, 2
and variance – covariance matrix S ,
1

Z and if we can further assume that the prior
n1  n2 (n1  n2  2) p probabilities of group membership and costs of
misclassification of an individual that actually
belongs to group 1(2) into 2(1) are equal.
Conclusion: The vector of the 2 group means are
Data Analysis and Result not the same.
The analysis is done to compute the
discriminant weights, to examine the associated (b) Test for equality of group means
significance and assumption tests based on linear individual variable
combination of the predictor variables and also to
classify each case into one of the two groups it Table 2: t  test for equality of mean
closely resembles. The variables used in this
analysis are Dependent variable: group 1, group 2 Hypothesis: H 0 : t1  t2 vs H 1 : Not H 0
and Independent variables: Type of Exhibit ( X 1 ) ,
Age ( X 2 ) , Weight of Exhibit ( X 3 ) and Gender X1  X 2
Test Statistic: t 
(X4) . 1 1
SP 
(a) Test for equality of means N1 N 2
Table 1: Wilks‟ Lamda
Test of Wilks‟ Lamda Sig.
function(s) N1S12  N 2 S2 2
Where Sp 
1 0.919 0.000 N1  N 2  2
Hypothesis: H 0 : 1   2 vs H1 : Not H 1 t df Sig .
BSS Variable
Test Statistic:   Age 0.2739 260 0.785
BSS  WSS Weight 4.4161 260  0.001
  0.05
(i) Age
Decision: since p  value (0.001)  0.05,
Reject H 0 . Decision: Since p  value ( 0.785)  0.05.
Reject H 0 .

937 | P a g e

Conclusion: There is a difference in the mean ages 2 15.4 84.6 100
for group 1 and group 2.
From the table 71.8% of the group cases were
(ii) Weight of Exhibit correctly classified while 28.2% were wrongly
Decision: Since p  value ( 0.001)  0.05. classified.
Reject H 0 .
Conclusion
Conclusion: There is a difference in the mean In general, we were able to construct a
Weight of Exhibits for group 1 and group 2. Discriminant score: (1) for detecting the variables
(c) Table 3: Canonical Discriminant (Type of Exhibit, Age, Weight and Gender) that
Function Coefficient allow the researcher to discriminate between Drug
Function Peddlers and Non –Drug Peddlers, and (2) for
Variable classifying cases into different groups which is
1 better than oral evidence. Also, we have shown that
the group differs with regards to the mean of
Exhibit 1.373 variables, and the variables to predict group
Age 0.022 membership.
Weight 0.104
Gender 0.151 References:
Constant 1. Dillion, .W.R. and Goldstein, .S. (1984),
1.653 “Multivariate Analysis Method and
Hence, Applications. John Wiley Sons, Inc.
D( X )  1.653  1.373 X 1  0.022 X 2  0.104 X 3  0.154 X 4
Canada.
2. Fisher, R.A. (1936), “The Use of
Multivariate Measurements in Taxonomic
(d)Table 4: Classification of Results Problems”, Annals of Eugenics, 7, 179-
Predicted 188.
Group 3. Ganesalingam, .S. (1989), “Classification
and Mixture Approaches to Clustering via
Membership Total Maximum Likelihood”.Applied Statistics,
1 2 38, NO. 3, Page 445-466.
Original 4. Odedeji, A.O. (1992), Drugs in the Third
count World in Drugs and Society to Year 2000,
67 52 119 Ed by Vamos And Corrivean, Page 116-
1 119.
22 121 143 5. Rencher, A.C. (2002), Method of
2 Multivariate Analysis, Second Edition.
% 56.3 43.7 100 John Wiley and
1 Sons, Inc.

938 | P a g e

Ez25936938

Recommended

Recommended

More Related Content

Viewers also liked

Viewers also liked (20)

Similar to Ez25936938

Similar to Ez25936938 (20)

Ez25936938