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Education aid to developing countries: A general or differentiated policy?
Studies in Educational Evaluation. Vol. 15, pp. 339-357, 1989 Printed in Great Britain. All rights reserved.
0191-491X/89 $0.00 + .50 (~ 1989 Pergamon Press plc
EDUCATIONAL STUDIES
EDUCATION AID TO DEVELOPING COUNTRIES: A GENERAL OR DIFFERENTIATED POLICY? Andreas Schleicher and T. Neville Postlethwaite International Encyclopedia of Education, Institute of Comparative Education, University of Hamburg, Sedanstrasse 19, 2000 Hamburg, F.R.G.
T h i s article e x a m i n e s t h e p o s s i b i l i t y of g r o u p i n g c o u n t r i e s t o g e t h e r on t h e b a s i s of v a r i o u s f i n a n c i a l a n d e d u c a t i o n a l i n d i c a t o r s .
It p r e s e n t s
an
e x a m p l e of a n a t t e m p t to c l u s t e r c o u n t r i e s in t e r m s of t h e s e i n d i c a t o r s a n d d i s c u s s e s t h e u s e of t h e r e s u l t a n t c l u s t e r s for aid a g e n c i e s .
It s u g g e s t s t h a t
w h e n c o u n t r i e s a r e c l u s t e r e d o n t h e b a s i s of i n d i c a t o r s it b e c o m e s e a s i e r to identify the major problems
associated with each cluster.
It a l s o s h o w s
c l e a r l y w h i c h c o u n t r i e s are like e a c h o t h e r a n d w h i c h are not. T h e r e is i n c r e a s i n g e m p h a s i s a t t h e e n d of t h e 1 9 8 0 ' s o n t h e of e d u c a t i o n a l i n d i c a t o r s .
In s o m e c a s e s t h e e m p h a s i s
collection
is o n s y s t e m level
i n d i c a t o r s , a n d in o t h e r c a s e s o n i n p u t , p r o c e s s a n d o u t c o m e i n d i c a t o r s to school systems.
O.E.C.D., a s well a s r e g i o n a l a g e n c y d e v e l o p m e n t b a n k s a n d
s o m e b i l a t e r a l aid a g e n c i e s a r e c a l l i n g for m o r e i n d i c a t o r d a t a c o l l e c t i o n to i n c r e a s e b o t h t h e r a n g e of i n d i c a t o r s a v a i l a b l e a n d t h e a c c u r a c y of the d a t a u s e d for t h e s e i n d i c a t o r s . O n c e t h e d a t a a r e c o l l e c t e d , a m a j o r i s s u e is h o w t h e y c a n b e s t be a n a l y z e d to b e of u s e for p o l i c y - m a k i n g .
T h i s article is e x p l o r a t o r y in n a t u r e
a n d p r o v i d e s a n e x a m p l e of h o w e x i s t i n g i n f o r m a t i o n o n i n d i c a t o r s c a n be u s e d in a s e c o n d a r y a n a l y s i s to derive m e a n i n g f u l ~ e l a t i o n s h i p s w h i c h c a n be of u s e to p o l i c y - m a k e r s a t t h e i n t e r n a t i o n a l level.
U n l e s s g r e a t e r u s e c a n be
m a d e of i n d i c a t o r d a t a , t h e c u r r e n t i n t e r e s t m a y w a n e . The
World
Bank
Education
Sector
339
Policy p a p e r in 1 9 8 0 (World B a n k ,
340
A. Sch/eicher and T. N. Post/ethwaite
1980, p. 8 6 - 8 7 ) d e l i n e a t e s five p r i n c i p l e s : to p r o v i d e b a s i c e d u c a t i o n for all c h i l d r e n a n d a d u l t s ; to i n c r e a s e p r o d u c t i v i t y a n d s o c i a l e q u i t y ; to a c h i e v e m a x i m u m i n t e r n a l efficiency of s y s t e m s for i n c r e a s i n g t h e q u a n t i t y a n d q u a l i t y of e d u c a t i o n ;
to
relate
education
and
work
effectively:
and
to
build
i n s t i t u t i o n a l c a p a c i t y to d e s i g n , a n a l y z e , m a n a g e a n d e v a l u a t e p r o g r a m s for e d u c a t i o n a n d training. T h i s is followed b y a s t a t e m e n t t h a t t h e n e e d s of c o u n t r i e s v a r y so m u c h b e c a u s e of t h e i r d i f f e r e n c e s in c u l t u r a l a n d h i s t o r i c a l b a c k g r o u n d s ,
economic
d e v e l o p m e n t , f i n a n c i a l c a p a c i t y a n d so on, t h a t t h e B a n k will n e e d to h a v e a h i g h d e g r e e of d i v e r s i t y in its p r o g r a m m i n g . countries
a r e r e a l l y so d i f f e r e n t a n d
O n e q u e s t i o n is w h e t h e r
a second
question
is w h e t h e r
the it is
p o s s i b l e to i d e n t i f y c l u s t e r s of c o u n t r i e s w i t h e a c h c l u s t e r h a v i n g d i f f e r e n t problems.
T h i s s h o u l d also h e l p d i f f e r e n t i a t e c o u n t r i e s w i t h s e v e r e p r o b l e m s
from those with minor problems. Is T h e r e a Middle P a t h ? It is h o p e f u l l y n o t too n a i v e to t h i n k it u s e f u l to "cluster" c o u n t r i e s w i t h different profiles. the Asian region
E a c h profile h i g h l i g h t s d i f f e r e n t p r o b l e m s . Considering for e x a m p l e , a n d a p p l y i n g .just t h e t w o f a c t o r s of (a)
e n r o l l m e n t in f i r s t g r a d e , a n d (b)
amount
of e x p e n d i t u r e
on e d u c a t i o n in
p e r c e n t a g e of s t a t e b u d g e t , t h e r e a r e c o u n t r i e s t h a t c o u l d b e c l u s t e r e d into four blocks.
Enrollment High E x p e n d i t u r e on E d u c a t i o n in p e r c e n t a g e of S t a t e Budget
In
this
example.
Enrollment/High Expenditure,
Hong
Expenditure,
Bangladesh
first g r a d e Low
High
Hong Kong
Bangladesh
Low
Philippines
Pakistan Afghanistan
Kong
Philippines
might
be
considered
High
might be High Enrolhnent/Low
m i g h t b e Low E n r o l h n e n t / i l i g h
Expenditure,
A f g h a n i s t a n a n d P a k i s t a n m i g h t be Low E x p e n d i t u r e / I , o w E n r o l h n c n t .
and
341
Education A i d to Developing Countries
A Conceptual Framework T h e c l a s s i f i c a t i o n e x a m p l e given a b o v e is b a s e d o n two i n d i c a t o r s only. O t h e r i n d i c a t o r s c o u l d b e a d d e d or deleted.
S i n c e it is c l e a r t h a t t h e c l u s t e r s
of c o u n t r i e s
indicators
f o r m e d will d e p e n d
i n d i c a t o r s is i m p o r t a n t .
on the
used,
the
choice
of
Moreover, p r o p e r l y c o l l e c t i n g t h e n e c e s s a r y d a t a to
m a k e t h e i n d i c a t o r s valid is e s s e n t i a l .
Areas from which other indicators m a y
be s e l e c t e d are listed below: Enrollment:
E n r o l l m e n t d a t a is i m p o r t a n t to c l a s s i f y c o u n t r i e s a s h a v i n g low
or h i g h e n r o l l m e n t s in p r i m a r y a n d s e c o n d a r y school.
It is also d e s i r a b l e to
h a v e t h i s b r o k e n d o w n b y sex. C o u n t r i e s h a v i n g h i g h e n r o l l m e n t s (i.e. h i g h percentages
of a n
age g r o u p in s c h o o l ) n e e d little or n o effort p u t into
increasing enrollments.
However, if girls are enrolled to a m u c h lower e x t e n t
t h a n b o y s , t h e n efforts are n e e d e d to enroll m o r e girls.
If t h e r e is g e n e r a l l y
low e n r o l l m e n t , t h e n efforts are n e e d e d to i n c r e a s e all e n r o l l m e n t s . F i n a n c e available:
I n f o r m a t i o n is n e e d e d o n t h e a m o u n t of f u n d i n g available
for e d u c a t i o n as well as o n the m o n e y p o t e n t i a l l y available.
The l a t t e r c o u l d be
e v a l u a t e d t h r o u g h s o m e i n d i c a t o r of e c o n o m i c g r o w t h . clearly in m o r e n e e d of aid t h a n rich c o u n t r i e s .
P o o r c o u n t r i e s are
Size of c o u n t r y a n d p o p u l a t i o n d e n s i t y : problems
it will
have
in
T h e l a r g e r a c o u n t r y is, t h e m o r e both
the
a d m i n i s t r a t i o n of a n e d u c a t i o n a l s y s t e m a n d the d i s t r i b u t i o n of m a t e r i a l s .
communications,
which
will
affect
For
e x a m p l e , t h i s d i f f e r e n c e c a n be s e e n d r a m a t i c a l l y in t h e d i f f e r e n c e in size between Indonesia and Singapore. solutions. S t r u c t u r e of s c h o o l i n g : or 4 : 4 : 4.
T h e size p r o b l e m c a n r e q u i r e different
S o m e s y s t e m s h a v e a 6 : 3 : 3: s t r u c t u r e , o t h e r s 6 : 6
C o u n t r i e s w i t h similar s t r u c t u r e s m a y be s i m i l a r in o t h e r a r e a s
and m a y have corresponding needs.
S o m e c o u n t r i e s h a v e h i g h p r o p o r t i o n s of
c e r t a i n age g r o u p s in f o r m a l s c h o o l i n g a n d o t h e r s in n o n - f o r m a l e d u c a t i o n ; the h i g h e r t h e p r o p o r t i o n of a n age g r o u p in f o r m a l s c h o o l i n g , the less is the age g r o u p enrolled in n o n - f o r m a l e d u c a t i o n . e d u c a t i o n are h a r d to o b t a i n . and
other
have
many.
B u t a c t u a l figures on n o n - f o r m a l
S o m e c o u n t r i e s h a v e v e r y few p r i v a t e s c h o o l s
Given that
some recent
research
on costs
and
o u t c o m e s in w h i c h p r i v a t e s c h o o l s w o u l d a p p e a r to be m o r e c o s t effective t h a n p u b l i c s c h o o l s , c o u n t r i e s with a h i g h p r o p o r t i o n of w o r t h identifying.
p r i v a t e s c h o o l s are
Finally, the l o c u s of c o n t r o l in t e r m s of h o w m u c h m o n e y is
A. Schleicher a n d 7". N. Postlethwaite
342
s p e n t o n e d u c a t i o n , a n d w h e r e d e c i s i o n s are t a k e n o n w h a t will a c t u a l l y h a p p e n in s c h o o l s , is i m p o r t a n t .
T h u s t h e e x t e n t to w h i c h a c o u n t r y h a s a
h i g h l y c e n t r a l i z e d or d e c e n t r a l i z e d s y s t e m of e d u c a t i o n will be of i n t e r e s t to aid
agencies,
but
the
exact
measure
to
use
for
this
centralization-
d e c e n t r a l i z a t i o n d i m e n s i o n is n o t e a s y to identify. Ethnic homogeneity:
Is a c o u n t r y h i g h l y h o m o g e n e o u s (e.g. one l a n g u a g e only,
o n e religion only, 9 9 % of p e r s o n s b e i n g n a t i o n a l s k n o w i n g t h e c u l t u r e a n d t r a d i t i o n well) or is the c o u n t r y c o m p o s e d of m a n y different ethnic, l a n g u a g e or r e l i g i o u s g r o u p s ?
It is a s s u m e d
t h a t it is e a s i e r to c o n d u c t e d u c a t i o n
p r o g r a m s in a h o m o g e n e o u s r a t h e r t h a n a h e t e r o g e n e o u s society. Literacy and school achievement:
O n the o n e h a n d , a fully literate s o c i e t y
w i t h h i g h s c h o o l a c h i e v e m e n t (on a n i n t e r n a t i o n a l scale) n e e d s n o e x t e r n a l aid.
O n t h e o t h e r h a n d , e x t e r n a l aid w o u l d be n e e d e d in a s o c i e t y with a low
level of literacy.
However, t h e r e are p r o b l e m s in o b t a i n i n g s o u n d d a t a .
The
l i t e r a c y f i g u r e s of U n e s c o are u n r e l i a b l e b e c a u s e t h e y are b a s e d in p a r t on g r a d e levels r e a c h e d or o n g u e s s t i m a t e s .
It is q u e s t i o n a b l e to u s e r e a d i n g a n d
w r i t i n g a s a m e a s u r e of l i t e r a c y in c o u n t r i e s w i t h a n oral l e a r n i n g t r a d i t i o n . L i t e r a c y is o f t e n d e s i g n a t e d in t e r m s of c o m p e t e n c e in t h e official n a t i o n a l l a n g u a g e w h i c h m a y be different f r o m c o m p e t e n c e in a local l a n g u a g e , often m a s t e r e d b y m a n y m o r e p e r s o n s t h a n are literate in t h e i m p o s e d n a t i o n a l language.
N e v e r t h e l e s s , d e s p i t e all t h e s e c a v e a t s a b o u t t h e U n e s c o l i t e r a c y
figures, t h e y are the only figures available for m a n y c o u n t r i e s . The
International
Association
A c h i e v e m e n t (lEA) h a s m e a s u r e d
for
the
Evaluation
of E d u c a t i o n a l
a c h i e v e m e n t in s e v e r a l s u b j e c t a r e a s in
m a n y c o u n t r i e s , b u t t h e l a r g e s t n u m b e r of c o u n t r i e s p a r t i c i p a t i n g in a n y one s u b j e c t a r e a p r o j e c t w a s t w e n t y f o u r (in t h e S e c o n d I n t e r n a t i o n a l S c i e n c e Study).
Until the n u m b e r of c o u n t r i e s in t h e s e s t u d i e s i n c r e a s e s , it will n o t
be p o s s i b l e to u s e s c a l e d a c h i e v e m e n t b e s t s c o r e s in specific s u b j e c t s in cluster analyses.
B u t it w o u l d be h i g h l y desirable to do so.
E n r o l l m e n t is no p r o x y m e a s u r e for a c h i e v e m e n t .
T h e p e r c e n t a g e of a n
age g r o u p g r a d u a t i n g f r o m 12th g r a d e m a y be t h e s a m e in two c o u n t r i e s , b u t t h e i r a c h i e v e m e n t in m a t h e m a t i c s or s c i e n c e m a y be v e r y different.
T h a t is
w h y b o t h t h e e n r o l l m e n t a n d the a c h i e v e m e n t i n d i c a t o r s are n e e d e d . B y u s i n g all of the v a r i a b l e s in a c l u s t e r a n a l y s i s it s h o u l d be p o s s i b l e to identify different clusters
of c o u n t r i e s
a c c o r d i n g to o n e or m o r e of t e n
Education A i d to Developing Countries
variables.
Once the clusters
would be whether
343
have been identified, the next consideration
t h e c l u s t e r s a r e u s e f u l in t h e d e v e l o p m e n t of d i f f e r e n t i a l
p o l i c i e s for c o u n t r i e s l o c a t e d in d i f f e r e n t c l u s t e r s a n d of s i m i l a r p o l i c i e s for countries within the same cluster. An Example W h a t follows is a n a t t e m p t to e x a m i n e t h e p o s s i b i l i t y of f o r m i n g c l u s t e r s of c o u n t r i e s
using
example because
a v a r i e t y of e d u c a t i o n a l
indicators.
It is a n i m p e r f e c t
it h a s n o t b e e n p o s s i b l e to o b t a i n a n d u s e d a t a on all t h e
variables mentioned above. F o u r m a j o r g r o u p s of v a r i a b l e s w e r e identified: 1. F i n a n c i a l (5 v a r i a b l e s ) ; 2. E x p e n d i t u r e o n e d u c a t i o n (10 v a r i a b l e s ) ; 3. E n r o l l m e n t (17 v a r i a b l e s ) ; a n d , 4. l i t e r a c y r a t e s (8 v a r i a b l e s ) . T w e n t y - e i g h t A s i a n a n d Pacific c o u n t r i e s were considered. In o u r a t t e m p t to i d e n t i f y v a r i a b l e s a n d c o u n t r i e s in w h i c h d a t a w e r e a v a i l a b l e it s o o n b e c a m e o b v i o u s t h a t t h e r e w e r e s e v e r a l c o u n t r i e s for w h i c h some indicator data were missing.
G i v e n t h a t c l u s t e r a n a l y s i s d o e s n o t allow
for m i s s i n g d a t a , it w a s c l e a r t h a t e i t h e r c o u n t r i e s
or v a r i a b l e s h a d to b e
d r o p p e d or m i s s i n g v a l u e s e s t i m a t e d . T h e following s t e p s w e r e t a k e n : S t e p 1.
If t h e d a t a w e r e for l a t e r t h a n 1983, t h e y w e r e a c c e p t e d .
If,
h o w e v e r , t h e r e w e r e f i g u r e s for t h e t i m e b e t w e e n 1981 a n d 1983 a n d t h e difference b e t w e e n t h e l a s t two y e a r s a v a i l a b l e w a s l e s s t h a n 15%, t h e v a r i a b l e w a s r e t a i n e d .
If t h e f i g u r e s for 1980
a n d 1981 differed b y l e s s t h a n 10%, t h e n t h e v a r i a b l e w a s S t e p 2.
retained. O n t h e b a s i s of S t e p 1, a n y c o u n t r y w i t h m o r e t h a n t h r e e v a r i a b l e s missing was dropped.
S t e p 3.
A n y v a r i a b l e w i t h d a t a m i s s i n g for f o u r or m o r e c o u n t r i e s w a s
S t e p 4.
dropped. G i v e n t h a t t h e r e still r e m a i n e d c o u n t r i e s a n d v a r i a b l e s w i t h m i s s i n g d a t a p o i n t s (those u n d e r l i n e d in T a b l e 1), a p r o c e d u r e w a s u s e d to e s t i m a t e t h e v a l u e s . T h i s c o n s i s t e d of r u n n i n g a c l u s t e r a n a l y s i s of c o u n t r i e s w i t h o u t t h o s e v a r i a b l e s w i t h m i s s i n g data points.
For one variable, cluster mean values were inserted.
344
A. Schleicher and T. IV. Post/ethwaite
T h e n a n o t h e r c l u s t e r a n a l y s i s w a s r u n a n d v a l u e s inserted.
This
iterative p r o c e d u r e w a s u s e d until all m i s s i n g v a l u e s h a d b e e n inserted.
This is n o t a n ideal p r o c e d u r e a n d it m u s t be s t r e s s e d
t h a t it w o u l d h a v e b e e n h i g h l y desirable to have h a d a c c u r a t e a n d c o m p l e t e data.
However, after m i s s i n g v a l u e s h a d b e e n e s t i m a t e d
a n d inserted, the s t a n d a r d deviation for a variable w i t h i n a c l u s t e r w a s n o t m o r e t h a n 10%.
This implies t h a t t h e e s t i m a t i o n
p r o c e d u r e u s e d p r o v i d e d r e a s o n a b l e e s t i m a t e s for the m i s s i n g d a t a points. T h e r e s u l t of the a p p l i c a t i o n of t h e s e f o u r s t e p s w a s t h a t t h e d a t a set c o n t a i n e d e i g h t e e n c o u n t r i e s a n d fifteen v a r i a b l e s :
F o u r i n d i c a t o r s of wealth,
t h r e e i n d i c a t o r s of e x p e n d i t u r e o n e d u c a t i o n , six i n d i c a t o r s of e n r o l l m e n t , a n d literacy rates.
The d a t a set is p r e s e n t e d in Table 1.
E x p l a n a t i o n of i n d i c a t o r s : Note 1 :
F i g u r e s in bold a n d u n d e r l i n e d were s u b s t i t u t e d b y the withinc l u s t e r m e a n s as explained in Step 4 above.
Note 2:
The t e r m s e c o n d level e d u c a t i o n (Unesco definition) refers to s e c o n d a r y s c h o o l s t h a t provide g e n e r a l or specialized i n s t r u c t i o n b a s e d u p o n at least four y e a r s of p r e v i o u s i n s t r u c t i o n at the first level, a n d w h i c h do n o t aim at p r e p a r i n g the p u p i l s for a given t r a d e or o c c u p a t i o n .
Note 3:
Public e x p e n d i t u r e on e d u c a t i o n does n o t i n c l u d e foreign aid received for e d u c a t i o n .
Note 4:
C u r r e n t e x p e n d i t u r e on e d u c a t i o n i n c l u d e s e x p e n d i t u r e on a d m i n i s t r a t i o n , e m o l u m e n t s for t e a c h e r s a n d s u p p o r t i n g t e a c h i n g staff, s c h o o l b o o k s a n d o t h e r t e a c h i n g m a t e r i a l s a n d m a i n t e n a n c e of s c h o o l b u i l d i n g s .
SRI-LANKA
THAILAND
FK~G-KC~G
KOREAIS.
SINGAPOFE
TONGA
13
14
15
16
17
18
3.3
3.2
3.8
2.5
3.1
2,3
1.2
0.6
MALEDIVES
PHILIPPINES
11
5.2
6.3
2,3
1.6
1.6
2.1
3.0
2.3
1,5
1.2
MALAYSIA
12
10
FIJI
9
PAKISTAN
6
BURMA
NEPAL
5
CHINA
INDIA
4
6
INDONESIA
7
BAN~ESH
3
AFGHANISTAN
2
No.
Country
3ountry
set
of
18,0
11,0
24.2
26.0
19,1
12,0
8.0
8.0
21.0
24.0
10.0
15.0
5.0
2,9
14,0
10.1
19,0
15.0
11.8
7.8
6.6
6.2
4.2
2.9
2,6
9.1
3.8
-0.3
4.8
3.0
2.5
1.0
1.6
13.7
-1.8
10.5
7.5
3.5
5.3
1.7
1.8
3.8
-0.2
3,0
6.6
1.2
3.6
2.5
3.8
0.5 4.9
0.5 3.3
-2,1
0,4
2.3
7,1
4.2
5.6
t .0
2.3
-3.0
2.4
1,2
1,6
1.6
2.1
1,4
2.6
470
7260
2110
6330
860
360
660
1860 430
2.3
5.5 3.2
1850
9.1 1.5
380
3.1
3,4
160
4.3
180
260
2.0
310
54O
2.2
1.2
130
2.8
160
2.6 2.2
105
115
96
105
97
103
1 07
99 108
110
118
102
42
93
90
118
60
14
0.84 0.94 0,68 1.05
94 71 78
0.59
53
69
0.38
78
0,30
0.36
37
0.64
0,26
24
61
0.37
15
30
0.26
30
0.08
0.44
34
(; 38
0.25
39
68
0.34
50
0.29
7 18
GDFUH ENR1FM ENR2FM EFF21
3.4
9.4
4,6
4.3
1.7
1.4
2.1
AGRICGRP INDUSGRP ~
indicators
E)~=EDCF EXFEDTB ~
I: F i n a l
Table
19,63
27.08
39.93
27.33
20.43
15,91
30.72
~
24.06
28,13
25.25
44.83
31,13
37,60
55.45
26.44
46.97
36.73
PTQ1
21,35
20.45
35.08
25.10
25,76
23 90
32.11
22.00
22 16
2.64
17,86
28 45
15.52
26 68
18.40
15.85
26.23
21.16
PTQ2
147.11
1049.54
772.2l
712.00
172.41
233.39
268.03
217.00
330.62
185.47
158.80
170,78
88.99
149.90
152.93
188.59
201.91
724.08
PSQ1
99.83
96.33
99.07
99.80
94.03
97.43
90.60
95.30 95.77
89.50
97.22
91.33
87.17
76.67
86.87
74.67
70,03
21.77
13.07
36,50
77.83
24.53
8.90
LF
92.06
90.30
85.77
88.00
92.80
92.93
86.97
43,80
41.40
64.43
88.13
44.33
41,74
LM
~,
,,~
r0 -<
~
~"
~z
346
A. Schleicher and T. N. Postlethwaite
The m e a n i n g of each indicator label in Table 1 is given below: Educational Expenditure EXPEDCP EXPEDTB
C u r r e n t e x p e n d i t u r e on e d u c a t i o n as a p e r c e n t a g e of GNP. E x p e n d i t u r e on e d u c a t i o n as a percent age of total state budget.
Financial GDPGRPH AGRICGRP INDUSGRP POPGRP GDPUH
A n n u a l growth of domestic p r o d u c t i o n per i n h a b i t a n t in percent. A n n u a l growth of agricultural p r o d u c t i o n in percent. (Def. see UN Statistical Yearbook 1986). A n n u a l growth of industrial p r o d u c t i o n in percent. (Def. see UN Statistical Yearbook 1986). A nnual population growth rate. (Average of first four year s for which dat a were available). A nnual GDP per capita in US $. (Scaled on scale 4 - 100 for all count ri es in d a t a set).
Enrollment ENR 1 F MP ENR2FMP EFF21 PTQ 1 PTQ2 PSQ 1
Gross e nr ol l m e nt ratios male and female first level of education. Gross e nr ol l m e nt ratios male and female second level of e d u c a t i o n Total n u m b e r of pupils enrolled in second-level i n s t i t u t i o n s divide by total n u m b e r of pupils enrolled in first level institutions. P u p i l / T e a c h e r ratio first level. P u p i l / T e a c h e r ratio second-level. (Computed from total figures). Pupils per school first level. (Computed from total figures).
Literacy LM
LF
Literacy of males from fifteen to thirty four years. (Computed from weighted p e r c e n t a g e s of illiterate people of the age g r o u p s 15-19, 20-24, 25-34 years). Literacy of females aged from fifteen to thirty four years. (Computed from weighted p e r c e n t a g e s of illiterate people of the age g r o u p s 15-19, 20-24, 25-34 years).
Education A i d to Developing Countries
347
F o r t h o s e v a r i a b l e s m a r k e d b y a n a s t e r i s k , t h e local c u r r e n c i e s w e r e c o n v e r t e d to US d o l l a r s in t h e following w a y : F o r t h e y e a r in w h i c h a figure w a s a v a i l a b l e , t h e c o n v e r s i o n r a t e s to US dollars were examined.
In some cases, these were available on a monthly
b a s i s , s o m e t i m e s o n a six m o n t h l y b a s i s a n d s o m e t i m e s o n l y o n a y e a r l y b a s i s . Either
t h e y e a r l y f i g u r e or t h e
a v e r a g e for t h e y e a r w a s
taken
and
the
calculation made.
The Clustering Procedure O n t h e b a s i s of t h e fifteen i n d i c a t o r s c h o s e n , t h e e i g h t e e n c o u n t r i e s w e r e c l u s t e r e d . G i v e n o n l y e i g h t e e n c o u n t r i e s , it w a s a s s u m e d t h a t n o t m o r e t h a n t h r e e or f o u r c l u s t e r s s h o u l d b e p r o d u c e d belong
to o n e
undertaken.
cluster
only.
They grouped
Two basic countries
and that a country should
types
of c l u s t e r
on the basis
analysis
were
of h i g h s i m i l a r i t y .
It
b e c a m e a p p a r e n t t h a t a l t h o u g h t h e c h o i c e of i n d i c a t o r s d e c i s i v e l y i n f l u e n c e s the clustering,
t h e w e i g h t s of t h e i n d i c a t o r s d o e s n o t .
Calculations
were
u n d e r t a k e n u s i n g v a r i o u s s e t s of d i f f e r e n t w e i g h t s , b u t t h e w e i g h t s did n o t affect t h e c l u s t e r p a t t e r n . T h e final w e i g h t i n g w a s u n d e r t a k e n s u c h t h a t e a c h m a j o r g r o u p of i n d i c a t o r s w a s e q u a l l y w e i g h t e d , a n d t h e w e i g h t s w i t h i n t h e g r o u p s w e r e e q u a l . T h e first a p p r o a c h w a s b a s e d o n m i n i m i z i n g t h e v a r i a n c e between countries within clusters (Ward's approach).
The computer program
e m p l o y e d w a s c o n t a i n e d in t h e SAS c o l l e c t i o n of p r o g r a m s .
The similarity
measure used was the distance derived from the Euclidian norm. are discussed
below.
The second
The results
t y p e of c l u s t e r a n a l y s i s , w h i c h in f a c t
c o n f i r m e d t h e f i n d i n g s f r o m t h e first, w a s b a s e d o n m i n i m i z i n g t h e a v e r a g e distance
between
each
pair
of
observations
(average-linking
process
a p p r o a c h ) . T h e p r o g r a m u s e d w a s SAS C l u s t e r A n a l y s i s . A t e c h n i c a l n o t e a t t h e e n d of t h i s article d e s c r i b e s t h e s e two a p p r o a c h e s in g r e a t e r detail. T h e v e r t i c a l a x i s r a n g i n g f r o m 0 to 0.3 r e p r e s e n t s t h e r e d u c t i o n in t o t a l variance
being
accounted
for b y f o r m i n g l a r g e r
T h a i l a n d a n d M a l a y s i a h a v e a v a l u e of 0 . 0 1 3 .
clusters.
For example,
This indicates that Thailand and
M a l a y s i a a r e t h e m o s t s i m i l a r (least d i s t a n t ) of all c o u n t r i e s a n d a r e t h e r e f o r e j o i n e d to f o r m t h e f i r s t c l u s t e r .
Sri L a n k a
is t h e l e a s t d i s t a n t
from the
c e n t r o i d of t h e first c l u s t e r of M a l a y s i a a n d T h a i l a n d a n d t h e s e j o i n a t a level of 0 . 0 2 6 .
T o n g a c a n b e j o i n e d to t h e s e first t h r e e c o u n t r i e s a t a level of 0.05.
~°
Thailand Malaysia
(b Sri Lanka
t~ Tonga rj) P ~.~
Fiji P
-
-
3 I "o
Philippines o
Maledives ¢o o o r~
o3
Indonesia o
¢3) O.
China
3 c
Singapore Hong-Kong c~ <
(D
Korea S.
o
o -'1
P
Pakistan o
tD
Nepal Afghanistan o
India Bangladesh Burma
:I axn~!a u! p o l u o s ~ d axe as!aaaxa ~u!xalsnla s,p~eA~ aql j o slInsox aq~ a,~!e,'vlq~a/~sod "N ~ pue laqa!a/qa S V
8i7~
Education A i d to Developing Countries
349
By examining t he figure in this w ay it can be seen t h a t the cluster (Cluster 2) of China, Indonesia, Maldives, Philippines, Fiji, Tonga, Sri Lanka, Malaysia a n d T h a i l a n d is different from the cl ust er of S o u t h Korea, Hong Kong a n d Singapore (Cluster 1). B o t h of t h e s e are very different from the c l u s t e r of B u r m a , Bangladesh, India, Afghanistan, Nepal and Paki st an (Cluster 3). This is a t h r e e c l u s t e r solution. If a "more similar" (i.e. lower on the vertical axis) criterion is used, t h e n five c l u s t e r s emerge. T h e s e are: Cluster Cluster Cluster Cluster Cluster
1: 2: 3: 4: 5:
Afghanistan, Bangladesh, Burm a, India, Nepal and Pakistan China, Indonesia, Philippines and Maldives Fiji Malaysia, Thailand, Sri Lanka and Tonga Hong Kong, S o u t h Korea and Singapore
Table 2 p r e s e n t s the m e a n va l ue s of each i ndi cat or for e a c h of t he two sets of clusters. T h e g ener a l i m p r e s s i o n given b y Table 2 is that, w h e t h e r one t a k e s a t h r e e - c l u s t e r g r o u p i n g of a five-cluster grouping, t he h i g h e r the cluster, the m o r e is s p e n t on e d u c a t i o n ; the h i g h e r t he GDP per capi t a growth rate, the lower th e p o p u l a t i o n g r o w t h rate; t he h i g h e r t h e p e r c a p i t a i n c o m e , t he h i g h e r t h e e n r o l l m e n t ratios a n d the p r o p o r t i o n of e n r o l l m e n t s in s e c o n d a r y to p r i m a r y schools, t he h i g h e r t he school size a n d t he l i t eracy rates. The p u p i l - t e a c h e r ratios a n d the a g r i c u l t u r a l and i n d u s t r i a l growth r a t e s are not n e c e s s a r i l y g r e a t e r as one "ascends" the clusters. B e c a u s e t h e r e is a lack of c o m p l e t e l i n e a r i t y over v a r i a b l e s a n d b e t w e e n c o u n t r i e s , t h e i r c l u s t e r i n g becomes necessary. A n o t h e r w a y of p r e s e n t i n g a n d e x a m i n i n g the d a t a in Table 2 is to p r e s e n t in h i s t o g r a m f or m t h e s t a n d a r d i z e d m e a n score v a l u e s for e a c h variable. This is p r e s e n t e d in Figure 2 for t he t h r e e - c l u s t e r solution. An e x p l a n a t i o n of t he figure is desirable. For the first variable ( a n n u a l GDP per c a p i t a in US dollars) C l u s t e r One c o u n t r i e s have a s t a n d a r d score value of n e a r l y 2 (the e q u i v a l e n t of US $ 5,223), C l u s t e r Two c o u n t r i e s of -0.3 (equivalent of US $ 816), a n d C l u s t e r T h r e e c o u n t r i e s of j u s t over -0.5 (the e q u i v a l e n t of US $ 212). The s e c o n d variable ( p e r c e n t a g e of st at e b u d g e t s p e n t on education) varies from 0.85 or 20.4 p e r c e n t for C l u s t e r One, to 0.0 or 14.5 p e r c e n t for C l us t er Two, to -0.4 or 11.8 p e r c e n t for Cluster Three.
2:
Indicator
3.5
2.9 212
Pop. % growth rate
53.8 29.1
~/o Literacy male
Yo Literacy female
23 248
9
42
Pupil-tchr.ratio (1 st level)
Pupil-tchr.ratio 12nd level)
tw. school size
.07
.3
£nrolment 2nd level/lst level
22.2
18.5
236
5
10
21
Enrolment (2nd level) %
34
67
3.8
Enrolment (1st level) %
3DP per capita US$
1.0
5.2
nd. % .qrowth rate
2.2
3.0
1.8
6.4
.64
sd
~,gric, % growth rate
1
per
1.1
11.8
1.8
x
% or
values
3DP per cap.qrowth %
Ed. % total budget
3urrent exp.ed.% GNP
Table
86.6
91.9
211
20
24
.5
52
107
816
2.0
1.9
4.0
4,9
14.5
3.0
x
(to
6.1
1.8
sd
8.7
4.5
63
9
5
.3
18
9
612
0.6
3.0
4.5
3,6
2
clusters
% or
3
cluster
94.0
97.1
845
27
32
.81
78
105
5233
1.5
4.5
4.4
6.9
20.4
3.2
x
.2
2.4
8.7
.8
8.2
.7
sd
3.4
1.8
180
8
7
.13
14
10
2745
3
decimal
% or
one
.7
11.9
12.7
49.9 23.8
36
6
20 131
13
41
.1
10
26 .4
29
110
1.4
3.7
1.2
.8
75
267
3.3
6.8
2.4
1.7
5.9
2.2 7.3
sd
x
1
point)
84
90
213
25
27
,3
53
113
467
2.3
-0.4
1.8
5.5
8.7
1.4
x
2
8.7
3.6
77
10
28
,2
22
8
178
1,0
3.7
0.1
3,3
1.2
.9
sd
5
87
93
185
2.6
28
,38
78
110
1850
1.5
0
-2
-.3
24
6.3
x
3
clusters
68.0
80.0
271
23
29
.5
33
84
570
2.3
3.4
5.0
3.6
16
2.6
x
4
33.0
23.0
192
3.9
12
.3
19
36
575
0.4
3.0
3.9
4.0
3.8
1.3
sd
94.0
97,0
844
27
31
.8
78
105
5233
1.5
4,5
4.4
6.9
20
3.2
x
,2
2.4
8.7
.8
8
.7
sd
~"
1.8
180
7.0
7.3
.1
14
9.5
2744
5
,,~.. q~
c~ c)
&0 o~ o
Q
vt
(1) L O 0 O3 "0 N "E~ "O (,-
03 O O3 (.-
Or)
L CL
I
I
:1 -m,
I "1--1
~l~l
~
~
II VIII
I~
LV ~
~1~<~1 ~>
penditure on education percentage of total state budget
~I
k..(:]~.'l I.,(:I H I
U,.) ~i
• nber of pupils enrolled in second level sfiitutions divided by number of pupils first level institutions oss enroIIment rat i o cond level of education
VLJI"
Gross enrollment ratio first level of education /~llli~.la~
Annual growth of industrial product Annual growth of agricultural product Annual growth of domestic product per inhabitants in percent Expenditure on educat ion in percentage of GNP per capita i
o
~J
o
Q;
{Q
°M
,M .=
*M
o
o
¢;
Q
Q;
.M
=
Q;
.M
352
A. Sch/eicher and T. IV. Post/ethwaite
F r o m Figure 2 it can be seen t h a t the charact eri st i cs of each cl ust er are as follows in relative s t a n d a r d score terms: Cluster One - (Hong Kong, S o u t h Korea and Singapore) High GDP per capita, high percentage of state b u d g e t for education, high c u r r e n t e x p e n d i t u r e on education, high a n n u a l growth of domestic a n d agricultural p r o d u c t s per capita, a middle level of growth of industrial p r o d u c t s per capita, a low popul at i on growth rate, a relatively high gross e nr ol l m e nt ratio at p r i m a r y level, high s e c o n d a r y level e n r o l l m e n t ratio, a high s e c o n d a r y / p r i m a r y ratio, an average first level an d a high second level p u p i l / t e a c h e r ratio, large p r i m a r y schools and high literacy rates. Cluster Two - (China, Fiji, Indonesia, Malaysia, Maldives, Philippines, Sri Lanka, Thailand, Tonga): Relatively low GDP per capita, average percent age of state b u d g e t spent on education, relatively high c u r r e n t e x p e n d i t u r e on education, average to relatively high a n n u a l growth of domestic, agricultural and industrial production, slightly below average a n n u a l population growth rate, relatively high gross enrollment ratio at p r i m a r y level, slightly above average gross enr ol l m ent ratio at s e c o n d a r y level slightly below average s e c o n d a r y / p r i m a r y ratio, low p u p i l / t e a c h e r ratios at bot h levels, low school size, a nd relatively high literacy rate.
Cluster Three - (Afghanistan, Bangladesh, Burm a, India, Nepal, Pakistan: Low on all finance m e a s u r e s , low a n n u a l growth in domestic and agricultural production, b u t high on industrial p r o d u c t i o n (particularly P ak is tan a nd Burma), high population growth rate, low enrollment ratios, high p u p i l / t e a c h e r ratio at the first level b u t average at the s e c o n d a r y level, relatively low school size, and low literacy rate. Can clustering help devel opm e nt b a n k policymakers ? Clearly, p o l i c y m a k e r s desire a s o u n d information basis for m aki ng their decisions. However, o t h e r factors m u s t influence the final d e c i s i o n - m a k i n g s u c h as m o n e y available, p r e s s u r e - g r o u p force, the governing political party's p h ilo s o p h y of e d u c a t i o n and the like. From the clustering analysis u n d e r t a k e n above, it would a p p e a r to us t hat the Cluster One count ri es are not in need of help a l t h o u g h from t he r e c e n t IEA r e s u l t s (lEA 1988) it would a p p e a r t h a t
Education A i d to Developing Countries
353
H o n g Kong a n d S i n g a p o r e m a y n e e d c e r t a i n i n t e r n a l r e o r g a n i s a t i o n to i m p r o v e t h e p e r f o r m a n c e of less able s t u d e n t s in t he p r i m a r y a n d lower s e c o n d a r y grades. However, the p r o b l e m s in C l us t er T hree c o u n t r i e s are large. In general, it would a p p e a r t h a t m or e m o n e y s h o u l d be s p e n t on e d u c a t i o n . Population g r o w t h r a t e s h o u l d be d e c r e a s e d (but how?), e n r o l l m e n t rat i os s h o u l d be in cr eas ed , th e p u p i l / t e a c h e r ratio (which is not n e c e s s a r i l y t he s a m e as class size) s h o u l d be d e c r e a s e d at t h e p r i m a r y level, a n d l i t eracy r a t e s m u s t be increased. C l u s t e r Two c o u n t r i e s would s e e m to n e e d m o r e hel p in i n c r e a s i n g s e c o n d a r y school enrollments. All of the above m a y s e e m very obvious to t hose working in i n t e r n a t i o n a l agencies. Not all of the above was obvious to us anal yst s and r e s e a r c h workers u n t i l t h e c l u s t e r i n g a n a l y s i s w a s c o m p l e t e d a n d it b e c a m e e a s i e r to d i s t i n g u i s h the wood from the trees. Hence, we believe c l u s t e r analysis to be a helpful t e c h n i q u e . Had d a t a b e e n available for all i n d i c a t o r s m e n t i o n e d in th e c o n c e p t u a l f r a m e w o r k , it is possible t h a t a m o r e detailed a n d possi bl y mo r e u s ef u l clustering would have b e e n produced. It would of c o u r s e be possible within e a c h of the t h r e e c l u s t e r s to r u n o t h e r f o r m s of c l u s t e r a n a l y s e s i n c l u d i n g s u c h v a r i a b l e s as a c h i e v e m e n t , r u r a l / u r b a n differences, b o y / g i r l differences in literacy a c h i e v e m e n t a n d the like, to d i s e n t a n g l e in g r e a t e r detail w hi ch c l u s t e r s of c o u n t r i e s have w hi ch specific p r o b l e m s . In o t h e r words, it is possible to s t a r t with fairly basic variables as was d o n e in th e a n a l y s i s above a n d t h e n p r o c e e d to i n t r o d u c e m o r e detailed variables to refine the first sets of clusters. For gui dance on which actions to initiate for solving t he p r o b l e m s , it is i m p o r t a n t to rely on o t h e r forms of analysis s u c h as p a t h analysis, regression analysis, discriminant analysis within c o u n t r i e s , a n d for a m o r e g e n e r a l p i c t u r e , t h e t y p e s of m e t a - a n a l y s e s u n d e r t a k e n b y Fuller (1985) a n d F r a s e r (1987).
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Conclusion C l u s t e r a n a l y s i s c a n be u s e f u l in i d e n t i f y i n g g r o u p s of c o u n t r i e s w h i c h differ f r o m e a c h o t h e r o n c e r t a i n v a r i a b l e s .
As a n e x a m p l e , a s m a l l c l u s t e r
a n a l y s i s w a s r u n on f o u r t e e n v a r i a b l e s in e i g h t e e n A s i a n c o u n t r i e s .
Three
m a j o r c l u s t e r s of c o u n t r i e s w e r e identified. W h e n d i f f e r e n t w e i g h t s for t h e variables were used,
t h e r e w a s n o d i f f e r e n c e in t h e c l u s t e r s of c o u n t r i e s
which emerged from the analysis.
Had other variables been used, then other
c l u s t e r s of c o u n t r i e s m a y h a v e e m e r g e d . O t h e r v a r i a b l e s c o u l d h a v e i n c l u d e d s o m e of t h o s e given in the c o n c e p t u a l f r a m e w o r k . T h e d a t a u s e d were s e v e r a l y e a r s o u t of date.
T h e v a l i d i t y of the d a t a
c a n n o t be a s s e s s e d a n d h e n c e t h e s t r e n g t h of t h e c l u s t e r a n a l y s i s r e p o r t e d is to s o m e e x t e n t u n c e r t a i n .
W h a t is i m p o r t a n t for this type of a n a l y s i s is to have
u p - t o - d a t e a n d valid d a t a .
For t h e a n a l y s i s , t w e n t y - e i g h t c o u n t r i e s a n d s o m e
twenty variables were originally investigated.
D u e to m i s s i n g d a t a , s o m e
c o u n t r i e s a n d s o m e v a r i a b l e s h a d to be d r o p p e d .
This w a s u n f o r t u n a t e b u t
d o e s p o i n t to the n e c e s s i t y for i n t e r n a t i o n a l a g e n c i e s s u c h as U n e s c o a n d the D e v e l o p m e n t B a n k s to e n s u r e t h a t b a s i c d a t a ( m e a s u r e d in a s t a n d a r d way) are collected.
C l u s t e r a n a l y s i s of this k i n d c o u l d also be of u s e for c l u s t e r i n g
regions, districts, or local e d u c a t i o n a u t h o r i t i e s w i t h i n a c o u n t r y . T h e e x a m p l e given s u g g e s t s o n e w a y of a n a l y z i n g i n d i c a t o r d a t a w h i c h c a n be of u s e to p o l i c y m a k e r s .
O t h e r s will h a v e o t h e r s u g g e s t i o n s .
But,
i n d i c a t o r v a l u e s of t h e m s e l v e s are of little u s e w i t h o u t a n e x a m i n a t i o n of t h e i r r e l a t i o n s h i p s to e a c h other. Technical note B o t h the a v e r a g e - l i n k i n g a p p r o a c h a n d W a r d ' s a p p r o a c h are b a s e d o n a n a g g l o m e r a t i v e h i e r a r c h i c a l p r o c e d u r e w h i c h identifies h i e r a r c h i c a l c l u s t e r s of countries. E a c h c l u s t e r b e g i n s a s a u n i t in its o w n r i g h t a n d t h e n the two c l o s e s t u n i t s (with r e s p e c t to the s i m i l a r i t y m e a s u r e c h o s e n ) are p l a c e d t o g e t h e r to form a c l u s t e r t h a t on the n e x t h i e r a r c h i c a l level r e p l a c e d t h e two u n i t s . This p r o c e s s is r e p e a t e d b y c o m b i n i n g c l u s t e r s u n t i l all c o u n t r i e s are m e r g e d into o n e cluster.
T h e n the a n a l y s t h a s to m a k e a c u t at a n a p p r o p r i a t e level in
Education A i d to Developing Countries
355
t h e h i e r a r c h y ; t h a t is, at a level w h e r e t h e n u m b e r of c l u s t e r s is s u f f i c i e n t l y s m a l l a n d t h e c l u s t e r s are relatively h o m o g e n e o u s . To d e c i d e this, a f u n c t i o n , t h e s e m i - p a r t i a l s q u a r e d m u l t i p l e c o r r e l a t i o n ( d e n o t e d b y SPRSQ), w h i c h is i n d e p e n d e n t of t h e n u m b e r of c l u s t e r s f o r m e d , is of h e l p . It a c t u a l l y r e p r e s e n t s t h e d e c r e a s e in t h e p r o p o r t i o n of v a r i a n c e a c c o u n t e d for b y t h e j o i n i n g of two c l u s t e r s to f o r m a n e w c l u s t e r . T h e a v e r a g e - l i n k i n g a p p r o a c h a n d W a r d ' s a p p r o a c h differ in r e s p e c t to the functional relation that determines the distance between clusters. They are c o m p u t e d b y t h e SAS S t a t e m e n t 'Cluster' a n d are d e s c r i b e d briefly below: Ward's Minimum Variance Method In W a r d ' s m e t h o d , w h i c h a i m s at m i n i m i z i n g t h e w i t h - c l u s t e r v a r i a n c e , t h e d i s t a n c e b e t w e e n two c l u s t e r s (C(k) a n d C(1) is d e f i n e d b y (see SAS U s e r s G u i d e , Vol. 2): D(k, 1) = B(k, 1) = (~x(k) - x(1) ]]2) / ({1/N(k) + (l/N{1}} W(m) - W(k) W(1) if C(m) = C(k) UC(1) w h e r e B(k,1) = E [] x(i) x(k)~ 2 and W(k) = -
1 ~Ck
x(i)
d e n o t e s t h e v e c t o r of t h e i'th c o u n t r y w i t h the components representing the scores of the v a r i a b l e s
N(k}
d e n o t e s t h e n u m b e r of c o u n t r i e s in c l u s t e r C(k)
K(k)
d e n o t e s t h e a r i t h m e t i c m e a n v e c t o r for c l u s t e r
C(k) T h e c o m b i n a t o r i a l f o r m u l a is t h e n : D(j,m) = {N(j)+N(k)) *D (j,k} + (N{j)+N(1)) *D (j,1) - N(j) *D (k, 1}} / (N(j)+N(m) At t h e h i e r a r c h i c a l level, t h e w i t h i n s u m of s q u a r e s is m i n i m i z e d over all o b t a i n a b l e p a r t i t i o n s b y m e r g i n g two c l u s t e r s f r o m t h e p r e v i o u s level. T h i s m e t h o d is b i a s e d t o w a r d s f o r m i n g c l u s t e r s w i t h a s m a l l n u m b e r of observations.
356
A. Schleicher a n d T. N. Postlethwaite
Average Linking Method: D (k, 1) = X i~C (k) where
X j ~C (1)
d(x(i), x(j))
/
(N(k)*N(1))
d(x(i), x(j)) d e n o t e s t h e d i s t a n c e b e t w e n t h e two c l u s t e r s
i, j.
T h e d i s t a n c e is defined b y t h e E u c l i d e a n d i s t a n c e : d(x(i), x(j))
=
~x(i) -
x0)ll
T h u s it follows t h a t : D(k, 1) = [Ix(k)-
x(1)ll 2 + (xllx(i)- x(klll2 ) / N ( R ) + (E i E c (k)
]l x(j)-x(1)]l 2)/N
j ~:C (i)
T h e c o m b i n a t o r i a l f o r m u l a is t h e n : D(j,m) = (N(k) * D0,k) + N(1) * D 0 , I ) ) / N ( m ) This procedure favours clustering countries with small within-clusters v a r i a n c e a n d is b i a s e d t o w a r d f o r m i n g c l u s t e r s of t h e s a m e w i t h i n - c l u s t e r variance.
References F r a s e r , Barry, J., et al. (1987) Syntheses of Educational Productivity Research, I n t e r n a t i o n a l J o u r n a l of E d u c a t i o n a l R e s e a r c h , Vol. 11, No. 2. (1985) Raising Schools Quality in Developing Countries: What Investment boost Learning? D i s c u s s i o n p a p e r , E d u c a t i o n a n d T r a i n i n g
Fuller, B r u c e
S e r i e s R e p o r t No. EDT7, World B a n k , W a s h i n g t o n , D.C. ILO: Yearbook of Labour Statistics (1986) Statistical Analysis System North Carolina. Unesco
(1986)
UN (1986) UN
(1985)
4 6 t h I s s u e ILO, G e n e v a .
U s e r ' s Guide, V o l u m e 2, SAS I n s t i t u t e ,
Statistical Yearbook, U n e s c o , Paris.
Demographic Yearbook, UN S t a t i s t i c a l Office, N e w York.
(1985) Industry. and Development Global Report, UN I n d u s t r i a l D e v e l o p m e n t O r g a n i s a t i o n , New York.
Education A i d to Developing Countries
357
UN (1986) Statistical Yearbook, 3 4 t h Issue 1 9 8 3 / 8 4 , Statistical Office, United Nations, New York. VIZ: H a n d b u c h f u r Internationale Z u s a m m e n a r b e i t (1985) Vereinigung fur I n t e r n a t i o n a l e Z u s a m m e n a r b e i t , Nomos Verlagsgesellschaft, Berlin. World B a n k D.C.
(1980) Education Sector Policy Paper, World Bank, Washington,
World B a n k (1980) World B a n k Atlas, World Bank, Washington, D.C.
The A u t h o r s ANDREAS SCHLEICHER is a g r a d u a t e s t u d e n t at the University of H a m b u r g an d s t u d i e s physics, m a t h e m a t i c s a nd educat i on. He is c u r r e n t l y working on the scaling of the lEA science data. T. NEVILLE POSTLETHWAITE is a Professor of Com parat i ve E d u c a t i o n at the University of H a m b u r g . He is also c u r r e n t l y working on t he a n a l y s e s of the lEA science data.
0191-491X/89 $0.00 + .50 (~ 1989 Pergamon Press plc
EDUCATIONAL STUDIES
EDUCATION AID TO DEVELOPING COUNTRIES: A GENERAL OR DIFFERENTIATED POLICY? Andreas Schleicher and T. Neville Postlethwaite International Encyclopedia of Education, Institute of Comparative Education, University of Hamburg, Sedanstrasse 19, 2000 Hamburg, F.R.G.
T h i s article e x a m i n e s t h e p o s s i b i l i t y of g r o u p i n g c o u n t r i e s t o g e t h e r on t h e b a s i s of v a r i o u s f i n a n c i a l a n d e d u c a t i o n a l i n d i c a t o r s .
It p r e s e n t s
an
e x a m p l e of a n a t t e m p t to c l u s t e r c o u n t r i e s in t e r m s of t h e s e i n d i c a t o r s a n d d i s c u s s e s t h e u s e of t h e r e s u l t a n t c l u s t e r s for aid a g e n c i e s .
It s u g g e s t s t h a t
w h e n c o u n t r i e s a r e c l u s t e r e d o n t h e b a s i s of i n d i c a t o r s it b e c o m e s e a s i e r to identify the major problems
associated with each cluster.
It a l s o s h o w s
c l e a r l y w h i c h c o u n t r i e s are like e a c h o t h e r a n d w h i c h are not. T h e r e is i n c r e a s i n g e m p h a s i s a t t h e e n d of t h e 1 9 8 0 ' s o n t h e of e d u c a t i o n a l i n d i c a t o r s .
In s o m e c a s e s t h e e m p h a s i s
collection
is o n s y s t e m level
i n d i c a t o r s , a n d in o t h e r c a s e s o n i n p u t , p r o c e s s a n d o u t c o m e i n d i c a t o r s to school systems.
O.E.C.D., a s well a s r e g i o n a l a g e n c y d e v e l o p m e n t b a n k s a n d
s o m e b i l a t e r a l aid a g e n c i e s a r e c a l l i n g for m o r e i n d i c a t o r d a t a c o l l e c t i o n to i n c r e a s e b o t h t h e r a n g e of i n d i c a t o r s a v a i l a b l e a n d t h e a c c u r a c y of the d a t a u s e d for t h e s e i n d i c a t o r s . O n c e t h e d a t a a r e c o l l e c t e d , a m a j o r i s s u e is h o w t h e y c a n b e s t be a n a l y z e d to b e of u s e for p o l i c y - m a k i n g .
T h i s article is e x p l o r a t o r y in n a t u r e
a n d p r o v i d e s a n e x a m p l e of h o w e x i s t i n g i n f o r m a t i o n o n i n d i c a t o r s c a n be u s e d in a s e c o n d a r y a n a l y s i s to derive m e a n i n g f u l ~ e l a t i o n s h i p s w h i c h c a n be of u s e to p o l i c y - m a k e r s a t t h e i n t e r n a t i o n a l level.
U n l e s s g r e a t e r u s e c a n be
m a d e of i n d i c a t o r d a t a , t h e c u r r e n t i n t e r e s t m a y w a n e . The
World
Bank
Education
Sector
339
Policy p a p e r in 1 9 8 0 (World B a n k ,
340
A. Sch/eicher and T. N. Post/ethwaite
1980, p. 8 6 - 8 7 ) d e l i n e a t e s five p r i n c i p l e s : to p r o v i d e b a s i c e d u c a t i o n for all c h i l d r e n a n d a d u l t s ; to i n c r e a s e p r o d u c t i v i t y a n d s o c i a l e q u i t y ; to a c h i e v e m a x i m u m i n t e r n a l efficiency of s y s t e m s for i n c r e a s i n g t h e q u a n t i t y a n d q u a l i t y of e d u c a t i o n ;
to
relate
education
and
work
effectively:
and
to
build
i n s t i t u t i o n a l c a p a c i t y to d e s i g n , a n a l y z e , m a n a g e a n d e v a l u a t e p r o g r a m s for e d u c a t i o n a n d training. T h i s is followed b y a s t a t e m e n t t h a t t h e n e e d s of c o u n t r i e s v a r y so m u c h b e c a u s e of t h e i r d i f f e r e n c e s in c u l t u r a l a n d h i s t o r i c a l b a c k g r o u n d s ,
economic
d e v e l o p m e n t , f i n a n c i a l c a p a c i t y a n d so on, t h a t t h e B a n k will n e e d to h a v e a h i g h d e g r e e of d i v e r s i t y in its p r o g r a m m i n g . countries
a r e r e a l l y so d i f f e r e n t a n d
O n e q u e s t i o n is w h e t h e r
a second
question
is w h e t h e r
the it is
p o s s i b l e to i d e n t i f y c l u s t e r s of c o u n t r i e s w i t h e a c h c l u s t e r h a v i n g d i f f e r e n t problems.
T h i s s h o u l d also h e l p d i f f e r e n t i a t e c o u n t r i e s w i t h s e v e r e p r o b l e m s
from those with minor problems. Is T h e r e a Middle P a t h ? It is h o p e f u l l y n o t too n a i v e to t h i n k it u s e f u l to "cluster" c o u n t r i e s w i t h different profiles. the Asian region
E a c h profile h i g h l i g h t s d i f f e r e n t p r o b l e m s . Considering for e x a m p l e , a n d a p p l y i n g .just t h e t w o f a c t o r s of (a)
e n r o l l m e n t in f i r s t g r a d e , a n d (b)
amount
of e x p e n d i t u r e
on e d u c a t i o n in
p e r c e n t a g e of s t a t e b u d g e t , t h e r e a r e c o u n t r i e s t h a t c o u l d b e c l u s t e r e d into four blocks.
Enrollment High E x p e n d i t u r e on E d u c a t i o n in p e r c e n t a g e of S t a t e Budget
In
this
example.
Enrollment/High Expenditure,
Hong
Expenditure,
Bangladesh
first g r a d e Low
High
Hong Kong
Bangladesh
Low
Philippines
Pakistan Afghanistan
Kong
Philippines
might
be
considered
High
might be High Enrolhnent/Low
m i g h t b e Low E n r o l h n e n t / i l i g h
Expenditure,
A f g h a n i s t a n a n d P a k i s t a n m i g h t be Low E x p e n d i t u r e / I , o w E n r o l h n c n t .
and
341
Education A i d to Developing Countries
A Conceptual Framework T h e c l a s s i f i c a t i o n e x a m p l e given a b o v e is b a s e d o n two i n d i c a t o r s only. O t h e r i n d i c a t o r s c o u l d b e a d d e d or deleted.
S i n c e it is c l e a r t h a t t h e c l u s t e r s
of c o u n t r i e s
indicators
f o r m e d will d e p e n d
i n d i c a t o r s is i m p o r t a n t .
on the
used,
the
choice
of
Moreover, p r o p e r l y c o l l e c t i n g t h e n e c e s s a r y d a t a to
m a k e t h e i n d i c a t o r s valid is e s s e n t i a l .
Areas from which other indicators m a y
be s e l e c t e d are listed below: Enrollment:
E n r o l l m e n t d a t a is i m p o r t a n t to c l a s s i f y c o u n t r i e s a s h a v i n g low
or h i g h e n r o l l m e n t s in p r i m a r y a n d s e c o n d a r y school.
It is also d e s i r a b l e to
h a v e t h i s b r o k e n d o w n b y sex. C o u n t r i e s h a v i n g h i g h e n r o l l m e n t s (i.e. h i g h percentages
of a n
age g r o u p in s c h o o l ) n e e d little or n o effort p u t into
increasing enrollments.
However, if girls are enrolled to a m u c h lower e x t e n t
t h a n b o y s , t h e n efforts are n e e d e d to enroll m o r e girls.
If t h e r e is g e n e r a l l y
low e n r o l l m e n t , t h e n efforts are n e e d e d to i n c r e a s e all e n r o l l m e n t s . F i n a n c e available:
I n f o r m a t i o n is n e e d e d o n t h e a m o u n t of f u n d i n g available
for e d u c a t i o n as well as o n the m o n e y p o t e n t i a l l y available.
The l a t t e r c o u l d be
e v a l u a t e d t h r o u g h s o m e i n d i c a t o r of e c o n o m i c g r o w t h . clearly in m o r e n e e d of aid t h a n rich c o u n t r i e s .
P o o r c o u n t r i e s are
Size of c o u n t r y a n d p o p u l a t i o n d e n s i t y : problems
it will
have
in
T h e l a r g e r a c o u n t r y is, t h e m o r e both
the
a d m i n i s t r a t i o n of a n e d u c a t i o n a l s y s t e m a n d the d i s t r i b u t i o n of m a t e r i a l s .
communications,
which
will
affect
For
e x a m p l e , t h i s d i f f e r e n c e c a n be s e e n d r a m a t i c a l l y in t h e d i f f e r e n c e in size between Indonesia and Singapore. solutions. S t r u c t u r e of s c h o o l i n g : or 4 : 4 : 4.
T h e size p r o b l e m c a n r e q u i r e different
S o m e s y s t e m s h a v e a 6 : 3 : 3: s t r u c t u r e , o t h e r s 6 : 6
C o u n t r i e s w i t h similar s t r u c t u r e s m a y be s i m i l a r in o t h e r a r e a s
and m a y have corresponding needs.
S o m e c o u n t r i e s h a v e h i g h p r o p o r t i o n s of
c e r t a i n age g r o u p s in f o r m a l s c h o o l i n g a n d o t h e r s in n o n - f o r m a l e d u c a t i o n ; the h i g h e r t h e p r o p o r t i o n of a n age g r o u p in f o r m a l s c h o o l i n g , the less is the age g r o u p enrolled in n o n - f o r m a l e d u c a t i o n . e d u c a t i o n are h a r d to o b t a i n . and
other
have
many.
B u t a c t u a l figures on n o n - f o r m a l
S o m e c o u n t r i e s h a v e v e r y few p r i v a t e s c h o o l s
Given that
some recent
research
on costs
and
o u t c o m e s in w h i c h p r i v a t e s c h o o l s w o u l d a p p e a r to be m o r e c o s t effective t h a n p u b l i c s c h o o l s , c o u n t r i e s with a h i g h p r o p o r t i o n of w o r t h identifying.
p r i v a t e s c h o o l s are
Finally, the l o c u s of c o n t r o l in t e r m s of h o w m u c h m o n e y is
A. Schleicher a n d 7". N. Postlethwaite
342
s p e n t o n e d u c a t i o n , a n d w h e r e d e c i s i o n s are t a k e n o n w h a t will a c t u a l l y h a p p e n in s c h o o l s , is i m p o r t a n t .
T h u s t h e e x t e n t to w h i c h a c o u n t r y h a s a
h i g h l y c e n t r a l i z e d or d e c e n t r a l i z e d s y s t e m of e d u c a t i o n will be of i n t e r e s t to aid
agencies,
but
the
exact
measure
to
use
for
this
centralization-
d e c e n t r a l i z a t i o n d i m e n s i o n is n o t e a s y to identify. Ethnic homogeneity:
Is a c o u n t r y h i g h l y h o m o g e n e o u s (e.g. one l a n g u a g e only,
o n e religion only, 9 9 % of p e r s o n s b e i n g n a t i o n a l s k n o w i n g t h e c u l t u r e a n d t r a d i t i o n well) or is the c o u n t r y c o m p o s e d of m a n y different ethnic, l a n g u a g e or r e l i g i o u s g r o u p s ?
It is a s s u m e d
t h a t it is e a s i e r to c o n d u c t e d u c a t i o n
p r o g r a m s in a h o m o g e n e o u s r a t h e r t h a n a h e t e r o g e n e o u s society. Literacy and school achievement:
O n the o n e h a n d , a fully literate s o c i e t y
w i t h h i g h s c h o o l a c h i e v e m e n t (on a n i n t e r n a t i o n a l scale) n e e d s n o e x t e r n a l aid.
O n t h e o t h e r h a n d , e x t e r n a l aid w o u l d be n e e d e d in a s o c i e t y with a low
level of literacy.
However, t h e r e are p r o b l e m s in o b t a i n i n g s o u n d d a t a .
The
l i t e r a c y f i g u r e s of U n e s c o are u n r e l i a b l e b e c a u s e t h e y are b a s e d in p a r t on g r a d e levels r e a c h e d or o n g u e s s t i m a t e s .
It is q u e s t i o n a b l e to u s e r e a d i n g a n d
w r i t i n g a s a m e a s u r e of l i t e r a c y in c o u n t r i e s w i t h a n oral l e a r n i n g t r a d i t i o n . L i t e r a c y is o f t e n d e s i g n a t e d in t e r m s of c o m p e t e n c e in t h e official n a t i o n a l l a n g u a g e w h i c h m a y be different f r o m c o m p e t e n c e in a local l a n g u a g e , often m a s t e r e d b y m a n y m o r e p e r s o n s t h a n are literate in t h e i m p o s e d n a t i o n a l language.
N e v e r t h e l e s s , d e s p i t e all t h e s e c a v e a t s a b o u t t h e U n e s c o l i t e r a c y
figures, t h e y are the only figures available for m a n y c o u n t r i e s . The
International
Association
A c h i e v e m e n t (lEA) h a s m e a s u r e d
for
the
Evaluation
of E d u c a t i o n a l
a c h i e v e m e n t in s e v e r a l s u b j e c t a r e a s in
m a n y c o u n t r i e s , b u t t h e l a r g e s t n u m b e r of c o u n t r i e s p a r t i c i p a t i n g in a n y one s u b j e c t a r e a p r o j e c t w a s t w e n t y f o u r (in t h e S e c o n d I n t e r n a t i o n a l S c i e n c e Study).
Until the n u m b e r of c o u n t r i e s in t h e s e s t u d i e s i n c r e a s e s , it will n o t
be p o s s i b l e to u s e s c a l e d a c h i e v e m e n t b e s t s c o r e s in specific s u b j e c t s in cluster analyses.
B u t it w o u l d be h i g h l y desirable to do so.
E n r o l l m e n t is no p r o x y m e a s u r e for a c h i e v e m e n t .
T h e p e r c e n t a g e of a n
age g r o u p g r a d u a t i n g f r o m 12th g r a d e m a y be t h e s a m e in two c o u n t r i e s , b u t t h e i r a c h i e v e m e n t in m a t h e m a t i c s or s c i e n c e m a y be v e r y different.
T h a t is
w h y b o t h t h e e n r o l l m e n t a n d the a c h i e v e m e n t i n d i c a t o r s are n e e d e d . B y u s i n g all of the v a r i a b l e s in a c l u s t e r a n a l y s i s it s h o u l d be p o s s i b l e to identify different clusters
of c o u n t r i e s
a c c o r d i n g to o n e or m o r e of t e n
Education A i d to Developing Countries
variables.
Once the clusters
would be whether
343
have been identified, the next consideration
t h e c l u s t e r s a r e u s e f u l in t h e d e v e l o p m e n t of d i f f e r e n t i a l
p o l i c i e s for c o u n t r i e s l o c a t e d in d i f f e r e n t c l u s t e r s a n d of s i m i l a r p o l i c i e s for countries within the same cluster. An Example W h a t follows is a n a t t e m p t to e x a m i n e t h e p o s s i b i l i t y of f o r m i n g c l u s t e r s of c o u n t r i e s
using
example because
a v a r i e t y of e d u c a t i o n a l
indicators.
It is a n i m p e r f e c t
it h a s n o t b e e n p o s s i b l e to o b t a i n a n d u s e d a t a on all t h e
variables mentioned above. F o u r m a j o r g r o u p s of v a r i a b l e s w e r e identified: 1. F i n a n c i a l (5 v a r i a b l e s ) ; 2. E x p e n d i t u r e o n e d u c a t i o n (10 v a r i a b l e s ) ; 3. E n r o l l m e n t (17 v a r i a b l e s ) ; a n d , 4. l i t e r a c y r a t e s (8 v a r i a b l e s ) . T w e n t y - e i g h t A s i a n a n d Pacific c o u n t r i e s were considered. In o u r a t t e m p t to i d e n t i f y v a r i a b l e s a n d c o u n t r i e s in w h i c h d a t a w e r e a v a i l a b l e it s o o n b e c a m e o b v i o u s t h a t t h e r e w e r e s e v e r a l c o u n t r i e s for w h i c h some indicator data were missing.
G i v e n t h a t c l u s t e r a n a l y s i s d o e s n o t allow
for m i s s i n g d a t a , it w a s c l e a r t h a t e i t h e r c o u n t r i e s
or v a r i a b l e s h a d to b e
d r o p p e d or m i s s i n g v a l u e s e s t i m a t e d . T h e following s t e p s w e r e t a k e n : S t e p 1.
If t h e d a t a w e r e for l a t e r t h a n 1983, t h e y w e r e a c c e p t e d .
If,
h o w e v e r , t h e r e w e r e f i g u r e s for t h e t i m e b e t w e e n 1981 a n d 1983 a n d t h e difference b e t w e e n t h e l a s t two y e a r s a v a i l a b l e w a s l e s s t h a n 15%, t h e v a r i a b l e w a s r e t a i n e d .
If t h e f i g u r e s for 1980
a n d 1981 differed b y l e s s t h a n 10%, t h e n t h e v a r i a b l e w a s S t e p 2.
retained. O n t h e b a s i s of S t e p 1, a n y c o u n t r y w i t h m o r e t h a n t h r e e v a r i a b l e s missing was dropped.
S t e p 3.
A n y v a r i a b l e w i t h d a t a m i s s i n g for f o u r or m o r e c o u n t r i e s w a s
S t e p 4.
dropped. G i v e n t h a t t h e r e still r e m a i n e d c o u n t r i e s a n d v a r i a b l e s w i t h m i s s i n g d a t a p o i n t s (those u n d e r l i n e d in T a b l e 1), a p r o c e d u r e w a s u s e d to e s t i m a t e t h e v a l u e s . T h i s c o n s i s t e d of r u n n i n g a c l u s t e r a n a l y s i s of c o u n t r i e s w i t h o u t t h o s e v a r i a b l e s w i t h m i s s i n g data points.
For one variable, cluster mean values were inserted.
344
A. Schleicher and T. IV. Post/ethwaite
T h e n a n o t h e r c l u s t e r a n a l y s i s w a s r u n a n d v a l u e s inserted.
This
iterative p r o c e d u r e w a s u s e d until all m i s s i n g v a l u e s h a d b e e n inserted.
This is n o t a n ideal p r o c e d u r e a n d it m u s t be s t r e s s e d
t h a t it w o u l d h a v e b e e n h i g h l y desirable to have h a d a c c u r a t e a n d c o m p l e t e data.
However, after m i s s i n g v a l u e s h a d b e e n e s t i m a t e d
a n d inserted, the s t a n d a r d deviation for a variable w i t h i n a c l u s t e r w a s n o t m o r e t h a n 10%.
This implies t h a t t h e e s t i m a t i o n
p r o c e d u r e u s e d p r o v i d e d r e a s o n a b l e e s t i m a t e s for the m i s s i n g d a t a points. T h e r e s u l t of the a p p l i c a t i o n of t h e s e f o u r s t e p s w a s t h a t t h e d a t a set c o n t a i n e d e i g h t e e n c o u n t r i e s a n d fifteen v a r i a b l e s :
F o u r i n d i c a t o r s of wealth,
t h r e e i n d i c a t o r s of e x p e n d i t u r e o n e d u c a t i o n , six i n d i c a t o r s of e n r o l l m e n t , a n d literacy rates.
The d a t a set is p r e s e n t e d in Table 1.
E x p l a n a t i o n of i n d i c a t o r s : Note 1 :
F i g u r e s in bold a n d u n d e r l i n e d were s u b s t i t u t e d b y the withinc l u s t e r m e a n s as explained in Step 4 above.
Note 2:
The t e r m s e c o n d level e d u c a t i o n (Unesco definition) refers to s e c o n d a r y s c h o o l s t h a t provide g e n e r a l or specialized i n s t r u c t i o n b a s e d u p o n at least four y e a r s of p r e v i o u s i n s t r u c t i o n at the first level, a n d w h i c h do n o t aim at p r e p a r i n g the p u p i l s for a given t r a d e or o c c u p a t i o n .
Note 3:
Public e x p e n d i t u r e on e d u c a t i o n does n o t i n c l u d e foreign aid received for e d u c a t i o n .
Note 4:
C u r r e n t e x p e n d i t u r e on e d u c a t i o n i n c l u d e s e x p e n d i t u r e on a d m i n i s t r a t i o n , e m o l u m e n t s for t e a c h e r s a n d s u p p o r t i n g t e a c h i n g staff, s c h o o l b o o k s a n d o t h e r t e a c h i n g m a t e r i a l s a n d m a i n t e n a n c e of s c h o o l b u i l d i n g s .
SRI-LANKA
THAILAND
FK~G-KC~G
KOREAIS.
SINGAPOFE
TONGA
13
14
15
16
17
18
3.3
3.2
3.8
2.5
3.1
2,3
1.2
0.6
MALEDIVES
PHILIPPINES
11
5.2
6.3
2,3
1.6
1.6
2.1
3.0
2.3
1,5
1.2
MALAYSIA
12
10
FIJI
9
PAKISTAN
6
BURMA
NEPAL
5
CHINA
INDIA
4
6
INDONESIA
7
BAN~ESH
3
AFGHANISTAN
2
No.
Country
3ountry
set
of
18,0
11,0
24.2
26.0
19,1
12,0
8.0
8.0
21.0
24.0
10.0
15.0
5.0
2,9
14,0
10.1
19,0
15.0
11.8
7.8
6.6
6.2
4.2
2.9
2,6
9.1
3.8
-0.3
4.8
3.0
2.5
1.0
1.6
13.7
-1.8
10.5
7.5
3.5
5.3
1.7
1.8
3.8
-0.2
3,0
6.6
1.2
3.6
2.5
3.8
0.5 4.9
0.5 3.3
-2,1
0,4
2.3
7,1
4.2
5.6
t .0
2.3
-3.0
2.4
1,2
1,6
1.6
2.1
1,4
2.6
470
7260
2110
6330
860
360
660
1860 430
2.3
5.5 3.2
1850
9.1 1.5
380
3.1
3,4
160
4.3
180
260
2.0
310
54O
2.2
1.2
130
2.8
160
2.6 2.2
105
115
96
105
97
103
1 07
99 108
110
118
102
42
93
90
118
60
14
0.84 0.94 0,68 1.05
94 71 78
0.59
53
69
0.38
78
0,30
0.36
37
0.64
0,26
24
61
0.37
15
30
0.26
30
0.08
0.44
34
(; 38
0.25
39
68
0.34
50
0.29
7 18
GDFUH ENR1FM ENR2FM EFF21
3.4
9.4
4,6
4.3
1.7
1.4
2.1
AGRICGRP INDUSGRP ~
indicators
E)~=EDCF EXFEDTB ~
I: F i n a l
Table
19,63
27.08
39.93
27.33
20.43
15,91
30.72
~
24.06
28,13
25.25
44.83
31,13
37,60
55.45
26.44
46.97
36.73
PTQ1
21,35
20.45
35.08
25.10
25,76
23 90
32.11
22.00
22 16
2.64
17,86
28 45
15.52
26 68
18.40
15.85
26.23
21.16
PTQ2
147.11
1049.54
772.2l
712.00
172.41
233.39
268.03
217.00
330.62
185.47
158.80
170,78
88.99
149.90
152.93
188.59
201.91
724.08
PSQ1
99.83
96.33
99.07
99.80
94.03
97.43
90.60
95.30 95.77
89.50
97.22
91.33
87.17
76.67
86.87
74.67
70,03
21.77
13.07
36,50
77.83
24.53
8.90
LF
92.06
90.30
85.77
88.00
92.80
92.93
86.97
43,80
41.40
64.43
88.13
44.33
41,74
LM
~,
,,~
r0 -<
~
~"
~z
346
A. Schleicher and T. N. Postlethwaite
The m e a n i n g of each indicator label in Table 1 is given below: Educational Expenditure EXPEDCP EXPEDTB
C u r r e n t e x p e n d i t u r e on e d u c a t i o n as a p e r c e n t a g e of GNP. E x p e n d i t u r e on e d u c a t i o n as a percent age of total state budget.
Financial GDPGRPH AGRICGRP INDUSGRP POPGRP GDPUH
A n n u a l growth of domestic p r o d u c t i o n per i n h a b i t a n t in percent. A n n u a l growth of agricultural p r o d u c t i o n in percent. (Def. see UN Statistical Yearbook 1986). A n n u a l growth of industrial p r o d u c t i o n in percent. (Def. see UN Statistical Yearbook 1986). A nnual population growth rate. (Average of first four year s for which dat a were available). A nnual GDP per capita in US $. (Scaled on scale 4 - 100 for all count ri es in d a t a set).
Enrollment ENR 1 F MP ENR2FMP EFF21 PTQ 1 PTQ2 PSQ 1
Gross e nr ol l m e nt ratios male and female first level of education. Gross e nr ol l m e nt ratios male and female second level of e d u c a t i o n Total n u m b e r of pupils enrolled in second-level i n s t i t u t i o n s divide by total n u m b e r of pupils enrolled in first level institutions. P u p i l / T e a c h e r ratio first level. P u p i l / T e a c h e r ratio second-level. (Computed from total figures). Pupils per school first level. (Computed from total figures).
Literacy LM
LF
Literacy of males from fifteen to thirty four years. (Computed from weighted p e r c e n t a g e s of illiterate people of the age g r o u p s 15-19, 20-24, 25-34 years). Literacy of females aged from fifteen to thirty four years. (Computed from weighted p e r c e n t a g e s of illiterate people of the age g r o u p s 15-19, 20-24, 25-34 years).
Education A i d to Developing Countries
347
F o r t h o s e v a r i a b l e s m a r k e d b y a n a s t e r i s k , t h e local c u r r e n c i e s w e r e c o n v e r t e d to US d o l l a r s in t h e following w a y : F o r t h e y e a r in w h i c h a figure w a s a v a i l a b l e , t h e c o n v e r s i o n r a t e s to US dollars were examined.
In some cases, these were available on a monthly
b a s i s , s o m e t i m e s o n a six m o n t h l y b a s i s a n d s o m e t i m e s o n l y o n a y e a r l y b a s i s . Either
t h e y e a r l y f i g u r e or t h e
a v e r a g e for t h e y e a r w a s
taken
and
the
calculation made.
The Clustering Procedure O n t h e b a s i s of t h e fifteen i n d i c a t o r s c h o s e n , t h e e i g h t e e n c o u n t r i e s w e r e c l u s t e r e d . G i v e n o n l y e i g h t e e n c o u n t r i e s , it w a s a s s u m e d t h a t n o t m o r e t h a n t h r e e or f o u r c l u s t e r s s h o u l d b e p r o d u c e d belong
to o n e
undertaken.
cluster
only.
They grouped
Two basic countries
and that a country should
types
of c l u s t e r
on the basis
analysis
were
of h i g h s i m i l a r i t y .
It
b e c a m e a p p a r e n t t h a t a l t h o u g h t h e c h o i c e of i n d i c a t o r s d e c i s i v e l y i n f l u e n c e s the clustering,
t h e w e i g h t s of t h e i n d i c a t o r s d o e s n o t .
Calculations
were
u n d e r t a k e n u s i n g v a r i o u s s e t s of d i f f e r e n t w e i g h t s , b u t t h e w e i g h t s did n o t affect t h e c l u s t e r p a t t e r n . T h e final w e i g h t i n g w a s u n d e r t a k e n s u c h t h a t e a c h m a j o r g r o u p of i n d i c a t o r s w a s e q u a l l y w e i g h t e d , a n d t h e w e i g h t s w i t h i n t h e g r o u p s w e r e e q u a l . T h e first a p p r o a c h w a s b a s e d o n m i n i m i z i n g t h e v a r i a n c e between countries within clusters (Ward's approach).
The computer program
e m p l o y e d w a s c o n t a i n e d in t h e SAS c o l l e c t i o n of p r o g r a m s .
The similarity
measure used was the distance derived from the Euclidian norm. are discussed
below.
The second
The results
t y p e of c l u s t e r a n a l y s i s , w h i c h in f a c t
c o n f i r m e d t h e f i n d i n g s f r o m t h e first, w a s b a s e d o n m i n i m i z i n g t h e a v e r a g e distance
between
each
pair
of
observations
(average-linking
process
a p p r o a c h ) . T h e p r o g r a m u s e d w a s SAS C l u s t e r A n a l y s i s . A t e c h n i c a l n o t e a t t h e e n d of t h i s article d e s c r i b e s t h e s e two a p p r o a c h e s in g r e a t e r detail. T h e v e r t i c a l a x i s r a n g i n g f r o m 0 to 0.3 r e p r e s e n t s t h e r e d u c t i o n in t o t a l variance
being
accounted
for b y f o r m i n g l a r g e r
T h a i l a n d a n d M a l a y s i a h a v e a v a l u e of 0 . 0 1 3 .
clusters.
For example,
This indicates that Thailand and
M a l a y s i a a r e t h e m o s t s i m i l a r (least d i s t a n t ) of all c o u n t r i e s a n d a r e t h e r e f o r e j o i n e d to f o r m t h e f i r s t c l u s t e r .
Sri L a n k a
is t h e l e a s t d i s t a n t
from the
c e n t r o i d of t h e first c l u s t e r of M a l a y s i a a n d T h a i l a n d a n d t h e s e j o i n a t a level of 0 . 0 2 6 .
T o n g a c a n b e j o i n e d to t h e s e first t h r e e c o u n t r i e s a t a level of 0.05.
~°
Thailand Malaysia
(b Sri Lanka
t~ Tonga rj) P ~.~
Fiji P
-
-
3 I "o
Philippines o
Maledives ¢o o o r~
o3
Indonesia o
¢3) O.
China
3 c
Singapore Hong-Kong c~ <
(D
Korea S.
o
o -'1
P
Pakistan o
tD
Nepal Afghanistan o
India Bangladesh Burma
:I axn~!a u! p o l u o s ~ d axe as!aaaxa ~u!xalsnla s,p~eA~ aql j o slInsox aq~ a,~!e,'vlq~a/~sod "N ~ pue laqa!a/qa S V
8i7~
Education A i d to Developing Countries
349
By examining t he figure in this w ay it can be seen t h a t the cluster (Cluster 2) of China, Indonesia, Maldives, Philippines, Fiji, Tonga, Sri Lanka, Malaysia a n d T h a i l a n d is different from the cl ust er of S o u t h Korea, Hong Kong a n d Singapore (Cluster 1). B o t h of t h e s e are very different from the c l u s t e r of B u r m a , Bangladesh, India, Afghanistan, Nepal and Paki st an (Cluster 3). This is a t h r e e c l u s t e r solution. If a "more similar" (i.e. lower on the vertical axis) criterion is used, t h e n five c l u s t e r s emerge. T h e s e are: Cluster Cluster Cluster Cluster Cluster
1: 2: 3: 4: 5:
Afghanistan, Bangladesh, Burm a, India, Nepal and Pakistan China, Indonesia, Philippines and Maldives Fiji Malaysia, Thailand, Sri Lanka and Tonga Hong Kong, S o u t h Korea and Singapore
Table 2 p r e s e n t s the m e a n va l ue s of each i ndi cat or for e a c h of t he two sets of clusters. T h e g ener a l i m p r e s s i o n given b y Table 2 is that, w h e t h e r one t a k e s a t h r e e - c l u s t e r g r o u p i n g of a five-cluster grouping, t he h i g h e r the cluster, the m o r e is s p e n t on e d u c a t i o n ; the h i g h e r t he GDP per capi t a growth rate, the lower th e p o p u l a t i o n g r o w t h rate; t he h i g h e r t h e p e r c a p i t a i n c o m e , t he h i g h e r t h e e n r o l l m e n t ratios a n d the p r o p o r t i o n of e n r o l l m e n t s in s e c o n d a r y to p r i m a r y schools, t he h i g h e r t he school size a n d t he l i t eracy rates. The p u p i l - t e a c h e r ratios a n d the a g r i c u l t u r a l and i n d u s t r i a l growth r a t e s are not n e c e s s a r i l y g r e a t e r as one "ascends" the clusters. B e c a u s e t h e r e is a lack of c o m p l e t e l i n e a r i t y over v a r i a b l e s a n d b e t w e e n c o u n t r i e s , t h e i r c l u s t e r i n g becomes necessary. A n o t h e r w a y of p r e s e n t i n g a n d e x a m i n i n g the d a t a in Table 2 is to p r e s e n t in h i s t o g r a m f or m t h e s t a n d a r d i z e d m e a n score v a l u e s for e a c h variable. This is p r e s e n t e d in Figure 2 for t he t h r e e - c l u s t e r solution. An e x p l a n a t i o n of t he figure is desirable. For the first variable ( a n n u a l GDP per c a p i t a in US dollars) C l u s t e r One c o u n t r i e s have a s t a n d a r d score value of n e a r l y 2 (the e q u i v a l e n t of US $ 5,223), C l u s t e r Two c o u n t r i e s of -0.3 (equivalent of US $ 816), a n d C l u s t e r T h r e e c o u n t r i e s of j u s t over -0.5 (the e q u i v a l e n t of US $ 212). The s e c o n d variable ( p e r c e n t a g e of st at e b u d g e t s p e n t on education) varies from 0.85 or 20.4 p e r c e n t for C l u s t e r One, to 0.0 or 14.5 p e r c e n t for C l us t er Two, to -0.4 or 11.8 p e r c e n t for Cluster Three.
2:
Indicator
3.5
2.9 212
Pop. % growth rate
53.8 29.1
~/o Literacy male
Yo Literacy female
23 248
9
42
Pupil-tchr.ratio (1 st level)
Pupil-tchr.ratio 12nd level)
tw. school size
.07
.3
£nrolment 2nd level/lst level
22.2
18.5
236
5
10
21
Enrolment (2nd level) %
34
67
3.8
Enrolment (1st level) %
3DP per capita US$
1.0
5.2
nd. % .qrowth rate
2.2
3.0
1.8
6.4
.64
sd
~,gric, % growth rate
1
per
1.1
11.8
1.8
x
% or
values
3DP per cap.qrowth %
Ed. % total budget
3urrent exp.ed.% GNP
Table
86.6
91.9
211
20
24
.5
52
107
816
2.0
1.9
4.0
4,9
14.5
3.0
x
(to
6.1
1.8
sd
8.7
4.5
63
9
5
.3
18
9
612
0.6
3.0
4.5
3,6
2
clusters
% or
3
cluster
94.0
97.1
845
27
32
.81
78
105
5233
1.5
4.5
4.4
6.9
20.4
3.2
x
.2
2.4
8.7
.8
8.2
.7
sd
3.4
1.8
180
8
7
.13
14
10
2745
3
decimal
% or
one
.7
11.9
12.7
49.9 23.8
36
6
20 131
13
41
.1
10
26 .4
29
110
1.4
3.7
1.2
.8
75
267
3.3
6.8
2.4
1.7
5.9
2.2 7.3
sd
x
1
point)
84
90
213
25
27
,3
53
113
467
2.3
-0.4
1.8
5.5
8.7
1.4
x
2
8.7
3.6
77
10
28
,2
22
8
178
1,0
3.7
0.1
3,3
1.2
.9
sd
5
87
93
185
2.6
28
,38
78
110
1850
1.5
0
-2
-.3
24
6.3
x
3
clusters
68.0
80.0
271
23
29
.5
33
84
570
2.3
3.4
5.0
3.6
16
2.6
x
4
33.0
23.0
192
3.9
12
.3
19
36
575
0.4
3.0
3.9
4.0
3.8
1.3
sd
94.0
97,0
844
27
31
.8
78
105
5233
1.5
4,5
4.4
6.9
20
3.2
x
,2
2.4
8.7
.8
8
.7
sd
~"
1.8
180
7.0
7.3
.1
14
9.5
2744
5
,,~.. q~
c~ c)
&0 o~ o
Q
vt
(1) L O 0 O3 "0 N "E~ "O (,-
03 O O3 (.-
Or)
L CL
I
I
:1 -m,
I "1--1
~l~l
~
~
II VIII
I~
LV ~
~1~<~1 ~>
penditure on education percentage of total state budget
~I
k..(:]~.'l I.,(:I H I
U,.) ~i
• nber of pupils enrolled in second level sfiitutions divided by number of pupils first level institutions oss enroIIment rat i o cond level of education
VLJI"
Gross enrollment ratio first level of education /~llli~.la~
Annual growth of industrial product Annual growth of agricultural product Annual growth of domestic product per inhabitants in percent Expenditure on educat ion in percentage of GNP per capita i
o
~J
o
Q;
{Q
°M
,M .=
*M
o
o
¢;
Q
Q;
.M
=
Q;
.M
352
A. Sch/eicher and T. IV. Post/ethwaite
F r o m Figure 2 it can be seen t h a t the charact eri st i cs of each cl ust er are as follows in relative s t a n d a r d score terms: Cluster One - (Hong Kong, S o u t h Korea and Singapore) High GDP per capita, high percentage of state b u d g e t for education, high c u r r e n t e x p e n d i t u r e on education, high a n n u a l growth of domestic a n d agricultural p r o d u c t s per capita, a middle level of growth of industrial p r o d u c t s per capita, a low popul at i on growth rate, a relatively high gross e nr ol l m e nt ratio at p r i m a r y level, high s e c o n d a r y level e n r o l l m e n t ratio, a high s e c o n d a r y / p r i m a r y ratio, an average first level an d a high second level p u p i l / t e a c h e r ratio, large p r i m a r y schools and high literacy rates. Cluster Two - (China, Fiji, Indonesia, Malaysia, Maldives, Philippines, Sri Lanka, Thailand, Tonga): Relatively low GDP per capita, average percent age of state b u d g e t spent on education, relatively high c u r r e n t e x p e n d i t u r e on education, average to relatively high a n n u a l growth of domestic, agricultural and industrial production, slightly below average a n n u a l population growth rate, relatively high gross enrollment ratio at p r i m a r y level, slightly above average gross enr ol l m ent ratio at s e c o n d a r y level slightly below average s e c o n d a r y / p r i m a r y ratio, low p u p i l / t e a c h e r ratios at bot h levels, low school size, a nd relatively high literacy rate.
Cluster Three - (Afghanistan, Bangladesh, Burm a, India, Nepal, Pakistan: Low on all finance m e a s u r e s , low a n n u a l growth in domestic and agricultural production, b u t high on industrial p r o d u c t i o n (particularly P ak is tan a nd Burma), high population growth rate, low enrollment ratios, high p u p i l / t e a c h e r ratio at the first level b u t average at the s e c o n d a r y level, relatively low school size, and low literacy rate. Can clustering help devel opm e nt b a n k policymakers ? Clearly, p o l i c y m a k e r s desire a s o u n d information basis for m aki ng their decisions. However, o t h e r factors m u s t influence the final d e c i s i o n - m a k i n g s u c h as m o n e y available, p r e s s u r e - g r o u p force, the governing political party's p h ilo s o p h y of e d u c a t i o n and the like. From the clustering analysis u n d e r t a k e n above, it would a p p e a r to us t hat the Cluster One count ri es are not in need of help a l t h o u g h from t he r e c e n t IEA r e s u l t s (lEA 1988) it would a p p e a r t h a t
Education A i d to Developing Countries
353
H o n g Kong a n d S i n g a p o r e m a y n e e d c e r t a i n i n t e r n a l r e o r g a n i s a t i o n to i m p r o v e t h e p e r f o r m a n c e of less able s t u d e n t s in t he p r i m a r y a n d lower s e c o n d a r y grades. However, the p r o b l e m s in C l us t er T hree c o u n t r i e s are large. In general, it would a p p e a r t h a t m or e m o n e y s h o u l d be s p e n t on e d u c a t i o n . Population g r o w t h r a t e s h o u l d be d e c r e a s e d (but how?), e n r o l l m e n t rat i os s h o u l d be in cr eas ed , th e p u p i l / t e a c h e r ratio (which is not n e c e s s a r i l y t he s a m e as class size) s h o u l d be d e c r e a s e d at t h e p r i m a r y level, a n d l i t eracy r a t e s m u s t be increased. C l u s t e r Two c o u n t r i e s would s e e m to n e e d m o r e hel p in i n c r e a s i n g s e c o n d a r y school enrollments. All of the above m a y s e e m very obvious to t hose working in i n t e r n a t i o n a l agencies. Not all of the above was obvious to us anal yst s and r e s e a r c h workers u n t i l t h e c l u s t e r i n g a n a l y s i s w a s c o m p l e t e d a n d it b e c a m e e a s i e r to d i s t i n g u i s h the wood from the trees. Hence, we believe c l u s t e r analysis to be a helpful t e c h n i q u e . Had d a t a b e e n available for all i n d i c a t o r s m e n t i o n e d in th e c o n c e p t u a l f r a m e w o r k , it is possible t h a t a m o r e detailed a n d possi bl y mo r e u s ef u l clustering would have b e e n produced. It would of c o u r s e be possible within e a c h of the t h r e e c l u s t e r s to r u n o t h e r f o r m s of c l u s t e r a n a l y s e s i n c l u d i n g s u c h v a r i a b l e s as a c h i e v e m e n t , r u r a l / u r b a n differences, b o y / g i r l differences in literacy a c h i e v e m e n t a n d the like, to d i s e n t a n g l e in g r e a t e r detail w hi ch c l u s t e r s of c o u n t r i e s have w hi ch specific p r o b l e m s . In o t h e r words, it is possible to s t a r t with fairly basic variables as was d o n e in th e a n a l y s i s above a n d t h e n p r o c e e d to i n t r o d u c e m o r e detailed variables to refine the first sets of clusters. For gui dance on which actions to initiate for solving t he p r o b l e m s , it is i m p o r t a n t to rely on o t h e r forms of analysis s u c h as p a t h analysis, regression analysis, discriminant analysis within c o u n t r i e s , a n d for a m o r e g e n e r a l p i c t u r e , t h e t y p e s of m e t a - a n a l y s e s u n d e r t a k e n b y Fuller (1985) a n d F r a s e r (1987).
354
A. Sch/eicher and T. N. Postlethwaite
Conclusion C l u s t e r a n a l y s i s c a n be u s e f u l in i d e n t i f y i n g g r o u p s of c o u n t r i e s w h i c h differ f r o m e a c h o t h e r o n c e r t a i n v a r i a b l e s .
As a n e x a m p l e , a s m a l l c l u s t e r
a n a l y s i s w a s r u n on f o u r t e e n v a r i a b l e s in e i g h t e e n A s i a n c o u n t r i e s .
Three
m a j o r c l u s t e r s of c o u n t r i e s w e r e identified. W h e n d i f f e r e n t w e i g h t s for t h e variables were used,
t h e r e w a s n o d i f f e r e n c e in t h e c l u s t e r s of c o u n t r i e s
which emerged from the analysis.
Had other variables been used, then other
c l u s t e r s of c o u n t r i e s m a y h a v e e m e r g e d . O t h e r v a r i a b l e s c o u l d h a v e i n c l u d e d s o m e of t h o s e given in the c o n c e p t u a l f r a m e w o r k . T h e d a t a u s e d were s e v e r a l y e a r s o u t of date.
T h e v a l i d i t y of the d a t a
c a n n o t be a s s e s s e d a n d h e n c e t h e s t r e n g t h of t h e c l u s t e r a n a l y s i s r e p o r t e d is to s o m e e x t e n t u n c e r t a i n .
W h a t is i m p o r t a n t for this type of a n a l y s i s is to have
u p - t o - d a t e a n d valid d a t a .
For t h e a n a l y s i s , t w e n t y - e i g h t c o u n t r i e s a n d s o m e
twenty variables were originally investigated.
D u e to m i s s i n g d a t a , s o m e
c o u n t r i e s a n d s o m e v a r i a b l e s h a d to be d r o p p e d .
This w a s u n f o r t u n a t e b u t
d o e s p o i n t to the n e c e s s i t y for i n t e r n a t i o n a l a g e n c i e s s u c h as U n e s c o a n d the D e v e l o p m e n t B a n k s to e n s u r e t h a t b a s i c d a t a ( m e a s u r e d in a s t a n d a r d way) are collected.
C l u s t e r a n a l y s i s of this k i n d c o u l d also be of u s e for c l u s t e r i n g
regions, districts, or local e d u c a t i o n a u t h o r i t i e s w i t h i n a c o u n t r y . T h e e x a m p l e given s u g g e s t s o n e w a y of a n a l y z i n g i n d i c a t o r d a t a w h i c h c a n be of u s e to p o l i c y m a k e r s .
O t h e r s will h a v e o t h e r s u g g e s t i o n s .
But,
i n d i c a t o r v a l u e s of t h e m s e l v e s are of little u s e w i t h o u t a n e x a m i n a t i o n of t h e i r r e l a t i o n s h i p s to e a c h other. Technical note B o t h the a v e r a g e - l i n k i n g a p p r o a c h a n d W a r d ' s a p p r o a c h are b a s e d o n a n a g g l o m e r a t i v e h i e r a r c h i c a l p r o c e d u r e w h i c h identifies h i e r a r c h i c a l c l u s t e r s of countries. E a c h c l u s t e r b e g i n s a s a u n i t in its o w n r i g h t a n d t h e n the two c l o s e s t u n i t s (with r e s p e c t to the s i m i l a r i t y m e a s u r e c h o s e n ) are p l a c e d t o g e t h e r to form a c l u s t e r t h a t on the n e x t h i e r a r c h i c a l level r e p l a c e d t h e two u n i t s . This p r o c e s s is r e p e a t e d b y c o m b i n i n g c l u s t e r s u n t i l all c o u n t r i e s are m e r g e d into o n e cluster.
T h e n the a n a l y s t h a s to m a k e a c u t at a n a p p r o p r i a t e level in
Education A i d to Developing Countries
355
t h e h i e r a r c h y ; t h a t is, at a level w h e r e t h e n u m b e r of c l u s t e r s is s u f f i c i e n t l y s m a l l a n d t h e c l u s t e r s are relatively h o m o g e n e o u s . To d e c i d e this, a f u n c t i o n , t h e s e m i - p a r t i a l s q u a r e d m u l t i p l e c o r r e l a t i o n ( d e n o t e d b y SPRSQ), w h i c h is i n d e p e n d e n t of t h e n u m b e r of c l u s t e r s f o r m e d , is of h e l p . It a c t u a l l y r e p r e s e n t s t h e d e c r e a s e in t h e p r o p o r t i o n of v a r i a n c e a c c o u n t e d for b y t h e j o i n i n g of two c l u s t e r s to f o r m a n e w c l u s t e r . T h e a v e r a g e - l i n k i n g a p p r o a c h a n d W a r d ' s a p p r o a c h differ in r e s p e c t to the functional relation that determines the distance between clusters. They are c o m p u t e d b y t h e SAS S t a t e m e n t 'Cluster' a n d are d e s c r i b e d briefly below: Ward's Minimum Variance Method In W a r d ' s m e t h o d , w h i c h a i m s at m i n i m i z i n g t h e w i t h - c l u s t e r v a r i a n c e , t h e d i s t a n c e b e t w e e n two c l u s t e r s (C(k) a n d C(1) is d e f i n e d b y (see SAS U s e r s G u i d e , Vol. 2): D(k, 1) = B(k, 1) = (~x(k) - x(1) ]]2) / ({1/N(k) + (l/N{1}} W(m) - W(k) W(1) if C(m) = C(k) UC(1) w h e r e B(k,1) = E [] x(i) x(k)~ 2 and W(k) = -
1 ~Ck
x(i)
d e n o t e s t h e v e c t o r of t h e i'th c o u n t r y w i t h the components representing the scores of the v a r i a b l e s
N(k}
d e n o t e s t h e n u m b e r of c o u n t r i e s in c l u s t e r C(k)
K(k)
d e n o t e s t h e a r i t h m e t i c m e a n v e c t o r for c l u s t e r
C(k) T h e c o m b i n a t o r i a l f o r m u l a is t h e n : D(j,m) = {N(j)+N(k)) *D (j,k} + (N{j)+N(1)) *D (j,1) - N(j) *D (k, 1}} / (N(j)+N(m) At t h e h i e r a r c h i c a l level, t h e w i t h i n s u m of s q u a r e s is m i n i m i z e d over all o b t a i n a b l e p a r t i t i o n s b y m e r g i n g two c l u s t e r s f r o m t h e p r e v i o u s level. T h i s m e t h o d is b i a s e d t o w a r d s f o r m i n g c l u s t e r s w i t h a s m a l l n u m b e r of observations.
356
A. Schleicher a n d T. N. Postlethwaite
Average Linking Method: D (k, 1) = X i~C (k) where
X j ~C (1)
d(x(i), x(j))
/
(N(k)*N(1))
d(x(i), x(j)) d e n o t e s t h e d i s t a n c e b e t w e n t h e two c l u s t e r s
i, j.
T h e d i s t a n c e is defined b y t h e E u c l i d e a n d i s t a n c e : d(x(i), x(j))
=
~x(i) -
x0)ll
T h u s it follows t h a t : D(k, 1) = [Ix(k)-
x(1)ll 2 + (xllx(i)- x(klll2 ) / N ( R ) + (E i E c (k)
]l x(j)-x(1)]l 2)/N
j ~:C (i)
T h e c o m b i n a t o r i a l f o r m u l a is t h e n : D(j,m) = (N(k) * D0,k) + N(1) * D 0 , I ) ) / N ( m ) This procedure favours clustering countries with small within-clusters v a r i a n c e a n d is b i a s e d t o w a r d f o r m i n g c l u s t e r s of t h e s a m e w i t h i n - c l u s t e r variance.
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The A u t h o r s ANDREAS SCHLEICHER is a g r a d u a t e s t u d e n t at the University of H a m b u r g an d s t u d i e s physics, m a t h e m a t i c s a nd educat i on. He is c u r r e n t l y working on the scaling of the lEA science data. T. NEVILLE POSTLETHWAITE is a Professor of Com parat i ve E d u c a t i o n at the University of H a m b u r g . He is also c u r r e n t l y working on t he a n a l y s e s of the lEA science data.