Information Technology Reference
In-Depth Information
summary of the crimes considered, together with the abbreviations used in the biplots
and tables discussed in this chapter:
Arsn
Annual number of reported
arson
cases.
AGBH
Annual number of reported
assault with the intention of inflicting grievous
bodily harm
cases.
AtMr
Annual number of reported
attempted murder
cases.
BNRs
Annual number of reported
burglary: nonresidential premises
cases.
BRs
Annual number of reported
burglary: residential premises
cases.
CrJk
Annual number of reported
carjacking
cases, a subcategory of
aggravated
robbery
cases.
CmAs
Annual number of reported
common assault
cases.
CmRb
Annual number of reported
common robbery
cases.
DrgR
Annual number of reported
drug related crime
cases.
InAs
Annual number of reported
indecent assault
cases.
Mrd
Annual number of reported
murder
cases.
PubV
Annual number of reported
public violence
cases.
Rape
Annual number of reported
rape
cases.
RAC
Annual number of reported
robbery with aggravating circumstances
cases.
Each contingency table has as columns the 14 serious crimes listed above and as its rows
the nine provinces:
ECpe
Eastern Cape
FrSt
Free State
Gaut
Gauteng
KZN
KwaZulu Natal
Limp
Limpopo
Mpml
Mpumalanga
NCpe
Northern Cape
NWst
North West
WCpe
Western Cape
As an example of a contingency table we consider the crime data for 2007/08. This
will be our data matrix
X
, to be subjected to a CA. Note that the symbols
X
,
R
,
C
and
E
have dual meanings in this chapter, to be distinguished in context:
(i)
X
, a general
p
×
q
contingency table in the form of a matrix;
R
,the
p
×
p
diagonal matrix containing the row sums of
X
;
C
,the
q
×
q
diagonal matrix
containing the column sums of
X
;and
E
, the independence matrix
R11
C
/
n
;
(ii) shorthand for the 9
14 crime data contingency table for 2007/08 and its asso-
ciated row-sum and column-sum diagonal matrices as well as its calculated
independence matrix.
×
Our data matrix (contingency table) is given in its transposed form in Table 7.5.
It follows from Tables 7.5 and 7.6 that the row sums - that is, the diagonal elements
of the matrix
R
- are 127 627, 75 580,
...
, 192 050. Symbolically, we write these sums as
x
1
.
,
x
2
.
,
...
,
x
9
.
respectively, where a dot indicates that summation is carried out over the
