A STATISTICAL APPROACH TO GO-C RATI3
t-POITICS
by-Howard Rosenthal
K
Center for International Studies
Cambridge, Massachusetts
vlay, 1962
*1
In
0
EFRATA
Location
/p. 2, see, 1.11
Corrocted
Incorrect
04., x <
z<
1.13
193
t
p. 3, line 12
p 5, line 18
V
v
V
O
V
section 1.2
to
section 2.2
)
p. 6, line 4i
(see see
p. 6, line 16
of w and e
p.8
p. 13
the equation for the error function should contain 2
~
9
21
2
- 721
P(721)
.2 6.97 P(6.97
Table II A
the growth rate for Brazil is "L"
Table II B
Group II and Group aI
Group II anI Gro'
Figure I
z alogr
x
(see
see. 3.3)
of wande
logy
I
A STATISTICAL APPROACH TO COMPARATIVVE POLITICS
by Howard Rosnthal
. ;roduction
1.1 Among the key economic, d"
nics
nd c
ahic
o
r oad markero of socitl 6oIcncer, there eXits ae
are ttl
membars have
for all practical purpoo,
bo attained.
Exclud- ing aSe
elass includes groea nat
f inite
lnal protductv
p013C
hil
adios
st
t
0o1lq as literacy
o
1
The vti
Onergy, newspaper copies (por capitz, etc.
c.ubd
the distributions of these variables amngnr nations and a ong
of
.
to th
uppr boun
.o
.
n i.Unation ib ono topic of' thi.s Ppoe
ariablev
The basic dJstributioa that characterizes theoe
thet t-normal di
it
of which
ribution (see 1.))
ubsets yield
and moder
On the inCternati
riomal- pIar t;
of log
traditioal.,
an empirica. classfication of the
natiorns.'
i1l be reflected in the three d
Ughon
he oghTh" lo
A i4
,
rnitic
nat;',
Another break down would be betweenu bo stens
ttrowth no-tiofle aI na
-WiU2'
and mature notin
pattern,
oi
p
CAizt
h
tion parmters
apirica1y, the, variables appear to be 6 itribuIted
mong subsets of the nations in log-normal fashion.
the paper portrays a grt;Vh proces under which a 1
would result
cubset
is necessary to divide the population into thee
s choracterized by a deif'Qrent se
f
mn
the ntC
The vecond sectic
og-noma
d i st
Ii.u
In the third section, a body of empirical dta is p
See Daniel Lerner, The Passn
of TrditionaI Sociytv Gnicoe
Aconept
ivtive fromnn tht oft).
Ro sto
h stage
Gtrowth, London (1960o
1
C;
(IV9 8
___-V
dL
W
9
discussed uhile the fourth diccusse3 applications of tho findigs.
broken o
ba h..
graphic-l techniques have been applied.
nly
To aato
According
autom-ated analysis can be developed in the com.ng cunmer.
only a liaited range of possible apolications is presented.
1.11 If for a variable
0
og zz
,
is normally d istribded
tle
say that x is log-normally d istribixted.
1.12 If z
o
log y is log-normaly distributed, then -
normally distributed from vell-mown
properties of the norm'
This implies that if a variable, say persons/vehicles is
importAfnce.
C
r
e
pp10ies
In the physical sciences, thee-nor
lo -noml
also log-normal.
then its reciprocal, say vehicles/ca pita is
1J3
n
ditr
io
Thore is a suggestion of an analogous phenoienon in the socia.
sciences as the investment rate f:Qr tie;alh or birth rate for popui.ation
oealth
tends to be a reasonably constant percentoage of the existing
population.
1.2
grooth'
"Mitles
Among the possible applications staisa the uise od
tics in making inferences about " political deve.opmen
stati
The log
transformation has facilitated an analysis that the author beievos
superior to earlier work based on simple avreraging.
14Te
The objectiva of
section 4 wil be to show that indices cannot be simply "added up" to gi.7e
an "avrage' picture of developmert,
On any given Variable le
position relative to the tir.ld
C
3
Yh
tics
(T
4
the argument runs, the
unctions of the variable
yin
expectation.-ereatIng and eut
must be considered.
Instead
-
aWLd2txJ.
log-normaistribution is discussed by G.
ill
on.
comnute the nation G
Then.rse ighti1ng
Hordan, S
Lxnon (1960), pp. 81-106, and Type--Token
pp. 425 and passim.
. Particle Statis
ahematica,
8-aenha5
See the "Concluion" by Jamen-- oloeman in The 1olitics of the De-velopinlpU
and
T:920
do. Princeton
Areas, Gabriel Almond and James Coleman,
=,,vrtt Hagen, "A General Framawork for Arialyiridg Economic and 41olitical
Change" 9 Center for International Studies,.'timeoo,
Cambridge (1961).
a.xpctation-satisfyin~z variables positively and expectation--creating va abl.e
negatiel,
be
a dovelopment or instabilitr
nerato' d
Thic indox
yields a U-shLe~d rolationsh p vitii a batbory 'of indices of potUial d
2.
2,1
S-omo likely conditions for lop:-normality*
The settlement of an area, the introduction of automobilos or rd:Los to
etc. can be thought of av dating from someO
that area
fctive "otarting
time" (the "starting time" will acquire a specific
Assuna
bela)
t
f(t)
t
Tha n fA
(t
.meaiIn
c i0athema
in normally dIstributed smzh
sartiny time t
T- iu
0
t
2
is normal such lthat
-to
2
Where
t
in application, t can be taken as the ti ne 'ofmeasurement6
2*2
lop enat
Assumo for some variable (of the "imitlesa
is logarithmic with time;
log ya
growth" class), growth
rcisel
N
t to
co'. y
Further assume that k is a constant over the population.
Then it
follows that "S
deviation
normal Trlth mean x
kWand standard
X
SiLncc 20s normal, by definition~y)is log-norrnal.*
t
'U
The assumption of a contant growth-parameter, k
Interpretation:
is not as"far £ront reality as might be inagined2
0
In generals the deviation
of
log k sceeris to ba
substantially less tnan the deviation of 10
y
(see 3.3). (ry" refers to the growth variaol
e.g. GNP/capita.
Such a condition would imply that
is the
important variable*
2 .3 A Pieceuise Linear Model
Let us assume that x. the log of the growth variable y, is ro3.atod
to
x,,
by three different constants that apply over different ranges of
That is, lot
X
1
2
2C
k3
+ c
'+
c2
- X---
x
1
+cx
X2
x2
Let us further assume that'Y is normal as In 1.1
Then it folloxs
that the distribution of x is the composite of three different norma
distributions, one of which holds for each k.
Presented in 'tabular fori,
the results may be given as:
Range of x
:k
2;
''
Normal distribution parameters
Mean
S.D.
al.
k~
C3
'3
j;
ki
X2
2'0',
X
x
k a
A graphic illustration of the behavior of x withand the rsulting
density function is presented in figs. 1 and 2.
Emirically, a three-piece "piecewise log-normal" distribution
fits much of our data.
While no assumption has been mDads about the
values of the k's, the k 2 implied by the data is generally larger than
k, and k3
This accords with a traditional., transitional, nodern nodl
with the two breakpoints signifying takeoff" and "maturity.
Of course, any distribution may be approxii#ted throuh a
'ee
of normal segments, and any distribution may bp seg mented to appro::imate
another.
The roason for using the normal is that it has a reasaonable
relation to a growth model.
While each segment does call for three
additional pardkmeters, c, k, and x, these may be taken into account
when pnrforming tests for goodness of fito
2.4
Implications of a b variate log-normal distribution of a gvro- th
variable and growth rate.
To conclude this section on conditions under which log-mormality
can occur, we should like to examine the joint distribution of the
growth variable cx,and the growth parameter k, from section 2.2 and see
if there is a reasonable imnlication about the "starting tiges", to.
In this secbion, V will be a constant within any nation
variable over the set of all nations.
and a random
Givan two times, tl and t2 and corresponding y, and y,, k shbu.
be
r
iven by
log y
-
2.o7 y2
i
Thus,
n o stirmated from empirical daca, o:d it
o
tprs
to approach lo-norial
also
oxnra
2
t.
accord with oit
Lbutions
-,a)
orm.
(so
cc,
in th ln:-
3
Theso lo
noldge of the skewd (aCnd
distribution of irco.mr, mobility,(growth),
c
within r.Aional populations.
If k is
lot-normal, then if
we'define w
log k, w is normeal
Lo
joint distribution of w and x is bivariate normal,
us assume th
with correlation peritted, for those nations with large x may tend to
have had a large growth constant as well as an "early" -to
Let us normalize x sich that its marginal distribution is unitnormal.
Then, the joint distribution may be expressed in the bi-
variate normal formp
where
ad
i 4'
of w and 1 is
It
arie the mean and s.d. of the raarginal distribution
the c
variance0
is well-known that the conditional distribution of x given w of the
form
g
)
x
-g
W".
This distribution leads to inferences about the starting times
et
us calculate
Since x
k(t
-
o
t) by assumption and w.l
ey
or since -t
0
I,
x
10
Therefor
lo'
is a simple lindar transformation of iy , the starting
times given the growth constants are normal with the standard deviation
proportional to 10
1/k and mean proprtionalto (l/k)(log k -mlog k)0
Thus, there is the rather reasonable result that for a given growth
constant
growth will "beyin" as a normal random process 0
The behaxior'
of the parameters with k is also reasonable; infinite growth must take
place in a compressed time interval; no
rowth has an indeterminate
distribution
3.0
Examples of log-normal variables
Efforts to find a theoretical basis for the occurrence of a log-,
normal distribution should not dominate our empirical results which
clearly show the log-normal character of growth variables.
Both
graphical andstatistical methods are available for examining data
for log-normality.
This section will begin with the latter, which
has illustrative value, and conclude with the more rigorous statistical
testing,
-SBA
3.1
A preliminary examination for log-normality may be made with the
aid of log-probability graph paoer, a varilant of the more familiar*
probability paper.
On log-probability -ptper, the vertical axis is
logarithmically spaced.
The horizontal axis is spaced according to
the unit normal cumulative or error function, given by
W(x)= (2T)
e
dy
It follows that, if we plot the cumulative percentage up to a
certain va.1e of the variable against that value of the variable of
log-p7.hbability paper and obtain a straight line, then the variable
Is lo:normally distributed.
The value for cumulative percentage
equal to .50 rives an estimate of the mean and the value for cumulative
perciz: -agec 10 and 84 give an estimate-of the range coveredby-The
standard deviation.
If
convenient sub-samples are taken (with N100 for examplo),
no percentaging or other .computation .is necessary, and a very rapid
check may be made as a preiminary to the chi-square test discussed in
As an illustration, the first 100 basic political units in an
alphabetical list were picked and their population density per square
mile for 1950 was taken as the test variable.
In figure 3, we can see
close conformity to a log-normal with mean at log 61 persons/sq
l
miLo
A basic political unit is defined as either a nation or a colony
in
I IIs
.,
the standard deviation extends to log 13 persons/sq. mic and log 290
persons/sq. miD
A linear plot is also obtained for a wide r ange of growth
variables over the set of "developing" countries.
We have used in
these cases the data provided in the appendix to The Politics of the
Developing Areas.
Although we
ill
eventually want to include all
units, a compact and reliable source of data had initial advantagos.
As figures 4-6 disclose, the log-normal distribution holds reasonably
for persons/radio, persons/vehicle, GKP/capita, and persons/docto:,
and daily newspaper copies/capitao
a 1956
unOo
(For the newspapers, we have used
source that also contained data on the developed nationso)
We havi also found a linear fit for persons/telphone and energy.
capit
ne smll number of countries
nvoed (aproximat y 60 in
each case) is offset by the generalty-T the distribution.
In figure 7, the line for each variable in figures 4-6 is
drawn as if all variables had a common mean in order to allow the
reader to compare the similarities In standard deviations0
The
deviations for all variables except O P per capita lie in a narrow
range of o4 to a90 (in log units)o
While this coincidence may,
like a high correlation, reflect the systemic character of development,
we have been unable to develop any firm interpretation*
The fact that a single set of log-normal parameters serves to
describe worlpopulation densities or growth variables in developing
nations doesno
ply any supra-generalityo
1. Almond and Coleman, op. cit.
In the cases where a
-0
single set suffices, it appears that the units must undergo similar
growth processes,
Where, as was mentioned in the introduction
sub-
sistence or saturation levels occur, a single set should not sufficer
Our newsoaper circulation data clearly show a saturation phenomaenon
when the developed nations are included*
For those 25 (mostly
developed) nations that have large newspaper circulations, the lopnormality that obtained with developing units no longer holds,
The
curve of figure 6, with a constantly decreasing slope shows the
development of saturation0
A subsistence bottom is demonstrated by the data on real per
capita GNP for 1961 as presented by Rodan:
While a strict linear
plot is obtained above $120 per capita in figure 8, the lowest 15
to 20% of the nations appear to bottom out.
Rodan has included several
remote or specialized areas that Almond and Coleman omitted (Bhutan,
Muscat and Oman, etc.) where the extent of poverty is kept in complete
traditional balance.
Just past the $120 marker lie those nations with
the bevinnings of industrialization and/or export agriculture (Belgian
Congo, Nigeria).
We are led to the sugnestion, with reference to
the theory of section'l, that the breakpoint on the curve emoirically
distinguishes the "traditional" from the "transitional."
Books and paper variables, as shotn in figures 9 and 10, also
exhibit breakpoints although the data is particularly incomplete and
unreliable.
In the case of booka, we have a linear plot for -the first
50% of the nations up to 21 bookr/iO0,OO0 capita. After this point, only
l. P.N. Rosenstein-Rodan, International Aid for Underdeveloped Countries
o, Ca ridge,9.
Center for International Stuies
$urooean -units are included and saturation sets in.
With paper
production, after 50%is passed, an increased slope occurs (Uakeoff?)
followed
by a shar-o saturation with the exception of the United Stateso
With newnrint, a single set of log-normal parameters gives a rough
We notice that both the deviation and mean are maintained over
fit.
an 11 year period,
the pre-orld War II
3.1.1.
This p rhap
eflectS a aen ral read4justment to
levels with some shuffling of position.
To conclude our graphical illustratione of log-normal behavior,
we have two examples using political units within a single nation, the
Unita
Stawcso
In the automobile example of fi-ure 11,
there is
a
clear' saturaztion breakpoint brought about by the depressed levols
of the Southern states
*
A tentative analogy can be drawn betweon
the underdzvoloped character of the South (especially in 19409) and the
undedxveloped nations and their corrosnonding log-normal properties
relative to the developed s tates and nations0
Our second example returns to population density per square
Figure 12 shows the distribution over the 48 continental
states botween 1810 and 19h0.
InitiallyM.Linar pieces must
be used to describe the data, the upper piece for the settled Eastern
Seaboard and the lower piece for the developine interior.
progrresses and as growth becomes more uniform,
As time
the deviation of the
lower pie.ce approaches that of the upper until by 1940 they are nearly
identical.
Here is an excellent example of how presentation of the
logunormal distribution can illustrate a developmental process.
A few highly urbanized states fall below the breakpoint0
This
perhaps reflects the greater availability of public transportationo
There are two further points of interesto
One is that the point
of intersection betwoen the two segments occurs at a higher level
as time orogresses.
The other is that the deviation of the upper
softwnt is naintained constant although its overall growth rate
fluctuates.
Clearly, these facts are at variance with the piece-wise
linear model of 2.3.
ted
They suggest that it will have to be soobistica
to allow for an increasing saturation point as technology progresscs.
Additionaly
there is a suggestion
tIiat
a type of stabilization
occurs There the units maintain nearly constant ratios between each
r the overall growth rate,
other
ate
of ra
i e absorptive capacities
Thse
This implies stablization
problems of
r
uildirng
should not, however, distract us from our'irain task, the presentaticn
of empirical evidence on the log-normal distribution of growth
variables*
3.2.
A more rigorous indication of the presence of log-normality
than graphical methods would be the successful application of a chisquare test for goodness of fit.
Our graphic examination has indicated
that, of the developing units in Rodan s data, those with greater
than $120 real G0JP per capita should form a set over which real GNP
per capita is loc!-normally distributedo
There are 90 nations in this
set for which we have estimated the mean and standard deviation of
thelog at 2.37 and .25 respectively, An eight-class test gives the
observed and expected frequencies contained in Table I; The test
satisfies the 20% level.
.M13 .
-TAlE I
I
III .15
IV
V
VI
12
-10.7'
9
10
10.7
12.6
9.5
12.2
VrI
5
VIII
it
Degroos o.f freedom
91
o-2.11
2.11- 2.21
231
-2.21-
.-
12.2
:5
12o6
10
.
.15
--
3
0
0
238 - 2,44
2.
-
-7
7
-
-141
2312.238
-
-
.7
2.64
2,54
2,64 -1
8 el
-
i1
7
5
2
o20
o(70")
PfR)
del
Rane mransformed to
unit normal
Range
Expected
Observed
Class
The combined graphical and statistical results clearly warrant cont ineed
intereet by social scientists in the logp;normal distributiono
-
-
---
-
-
-
-
,------
----
---------------
--------
-- 7
- -
- he3.3 In our worc with American population figures we were also able to compute
a value for k based on the 1890 and 94031 urea.
In both of these years,
one set of lop-normal carameters described the distribution of densities over
nearly the entire set of states.
be seen in figure 12 .
This k also plotted in linear fashion as can
Its deviation differs f rom that of the population
itself by a factor of 2. The result blends with the investigations of section
2*4*
Aplicat-ions to po0litical scienceo
Tho discovery of the generality of the log-normal distribution offors
some inindiate advantages in comparative studies.
Any log-normally distributed
variable may he normalized with respact to the mean and standard deviation.
A d eveloping nation's position relative to other nations is given by its
normalized value which may be comp red to normalized values on a series of
other variables.
Thus, a nation s average position on the international scale
may be computed as well as the variation (balance) in position. While many
results may not be sensitive to the method employed, use of normalized scores
has a clear
geri6ral preforeic
agirg rank orderings and other techniques
that have been applied in the past*
As an illustration of the use of normalized scores, a computation has been
developed to test an hypothesis on the nature of political development
As
mentioned in the introduction, Hagen and Almond and Coleman have computed
some sort of average position on a number of indicos\(1)
and
have attempted to show a form of linear correlation between this position and
"competitiveness" of the political system a
14
0
,
The "competitiveness" concept, in addition to its subjective difficulties,
has the weakness of beinp unstable.
In the year that elapsed between the Almond
and Coleman book and the Hagen paper, Hagen chose to change the classification
l4oreover, "competitiveness" in practice seems to
of 5 out of 60 nations,
place too much emphasis on formalstructure and too little on the crucial
outputs of the system0
An alternative view of the developing nations would emphasize the t ransition
from one type of legitimated and perpetuaing power structure to another with
an intervening crucial period often tormed "Ithe revolution"o
The events in
the revoluti.onary period tend to acquire a defining reference for future
decisionsQ
(The classic example is,
of course, the Soviet Union.)
Ve 'Toul33A
focus primary interost on the conditions under which the "revolution" occurs
takes.
and on what form it
As preliminary indices of "revolutionary" eventa,
we will take leftist takeovers, expropriation of Western property, and internal
wars,
The events in question should occur, in the roughest terms, when the
creation of expectations outruns the satisfaction ofexpectations.
Some develop-
mental variables such as income and medical care tend to satisfy expectations,
Others, such as mass media and transportati.on, we would argue, tend to build,.
more expectations than they satisfy.
It follows that, ihiattempting to predict
the unstable, "revolution" prone subset of nations, some indices must be
weighted negatiyely.
In terms of the normalized scores we have experimented
with an instability index, I, such that
I - 2x GNP/capita + Doctors/capita
-
Radios/capita
-Vehicles/capita
We would epect the unstable nations to lie in the middle of the rangec of
one end will lie the familiar examples of "good' deivelooment (India,
the other extreme will li
Turkey).
At
At
those nations whose (primarily income) levels of |
development have not arrived at revolutionary ootential.
Tnble 2A presents
scores for those units for whom Almond and Coleman have provided a complete.
set of data0
Splitting the ordered vst in thirds
in tablo 2B
e
ind ih osctod
association (no lon er a linear correlation) with the three aforemention'd
indices of "revolutionary" eventsi
While small numbers were involved, -o
did find a preference to straight addition of indices.
This is mainly a
result of the index s classification of some low income countries (India and
Pakistan Cre examoles) into the first class and some high income countries
(Cuba) into the middle group0
As a byproduct, the instability index gives an association to
ates
of economic growth that is superior to using either real GNP levels as the
predictor or the Almond and Coleman indexe.
These results are presented in Table 2 Cc
11 the instability index appears to be '-ulled from a hat" it is
so than the "add 'em all up equally" indices0
no more
In fact, there is perhaps
more logic to weighting income double than to leaving it equal to the others.
What we wish to offer, in any case, is not that the present research offers
any solid proof but that it extends the point that some forms of growth are
clearly preferred and that growth on any one dimension does not always make a
positive contribution to a nation's stability.
The succesu1-tiiMh growth
rate, low violence rate nation perhaps must e-tz its cargo before the media cult
arriveso
1
The third class alsO includes aznumbez. of "settler" colonies in which media
and vehicle consumption "ave been atypically high,
TABILE IIA
NATIONAL INSTABILITY AND GROWTH DA.TA
(Note: The classifications made are ex-tr ,emely tentative. Although th3 m thooogy
must eventually be justified, no attempt will be made in this preliminary "udyo)
Nation
bility Index"
Leftizrt
Takoover
LargeScale
1945-62 Firopriation
1945-62
Lo v
(Inrnal
row t h
Ra
ars/
2opoo,cOO
Capita)
1946-59
Venezuela
Israel
147
15o2.
13.0
11.1
10.6
El Salvador
9.3
1,8.
0
2,1
1,9
1.3
Columbia
India
9.2
9.0
0,14
irgentina,
8.6'
7.9
7.9,
6.5
6o5.
Uruguay
Nicaragua
Ecuador
Lebanon
Pakistan
Burma
Nyasaland
Phillipines
Thailand
Turkey
Congo(Loopoldville),
Sudan
Viet-Nam
Panama
Guatemala
Dominican Republic
Costa Rica
Honduras
Iraq
Cuba
Brazil
Mozambique
Malaya
Tanganfka
Union of South Africa
Paraquay
Iran
Indonesia
-U.A.R.
Libya
'2
5,3
5.0
4As9
4.8,
14.8
4-.
+
3.9
3.7
3.7
3,0
2.8
2.6
2.3
.2o2
+
+ 7
2.0
1.6
1.6
?
01.
++.
+
0o4
2.5
03
1.0
nodo
0 .9
O7
0-6
L
L
S
L
H
H
-11
H
L
1.1
n,,d4
2.7
2o1
1.0
S
2,5
I
S
1.8
105
2.2
048'
n.d.
1..1
0.1
105
2.1
1o4
0.5
143
1.9
GROUP
L
S
L
L
L GROUP
L
nLd
L
L-S
L4*
TABLE IIA (Continued)
Nation
I ("Ins a
Growth
LargeLog
Rate
(Interna
Scale
1945-62 Expropriaton Wars/
i0,C00,000
Capita)
1946-59
Leftist
bility Index") Takeover
0
Ceylon
Ghana
Nigeria
So. Rhodesia
Jordan
Peru
Algeria
Mexico
Ethiopia
French Equitorial Africa
Haiti
Chile
French 'West Africa
Tunisia
Kenya
Angola
Morocco
Bolivia
Key:
-1 7
-2.0
0.
L
n.d.
-h~h
1.6
-4.6
0.9
-5.5
100
L
028
n0.6
L GROUP
L III
-4 4
H
L
-548
250O
1
3
n,d
1.3
-8o2
-8.2-
1,14
-10.1
0.k
1.3
1,2
-10 _7
-14.6
+7?
L
L
L
L
L
2.0
Countries include all with full set of GNPp radio, doctor, and vehicle
data per Almond and Coleman, opo cit.
nod.: Sources cited had no report on these urits, No data,
H,LS,: High, Low, and Stationary growth rate.. per Rodan, op. cita
* Uruouay had no incidences of internal war, The arbitrary score of 0
places it lowest in rank order.
Egypt is low, Syria stationary0
-Source: Harry Eckstein "Internal Wars: The Problem of Anticipation,"
*N*
A rep.,rt for the Smithsonian Institution, mimeo., Washington (196?),
We have used the total incidence of Eckstein's "Unequivocal Cases."
This category includes "Warfare, Turmoil, Rioting, Terrorism,ating,
and Coup."
? These symbols are to indicate the degree of appropriateness of
the classifications
1 0
TABLE1 1I
GROUP DIFFERENCES IN STABILITY
Takeover
All +,
*
1.27
0
Group I
Group II
oroup III
*
Expropriation Internal War
Means
7
2
6
1,5
1
l2
+?, and ? cases from Table IIA have boen c6unted
A t-test of the hypothesis that the difference between the means of
Group II
and Groupts I and III is positive was successful at the .01
levela
Cases with no data excluded,
TA BLE IIC
COMPARISON OF GROWTH RATES AFD INDEX CLASS
Growth
Group
I index
(4 basic
indices)
II
III
H
L
S
6
0
2
10
1i
1
2
-32
3,
Almond
and
Coleman
(11 indices)
5.b
2
Growth
Group
S8
17
18
Growth
roup
* Groups formed from rank-order
Reai
3
III
3
*
2
III
Capita
H{
1
L
H
S
10
5
9,
23
20
3
L
12
11
S
/
j-c)
a.
5
For the day after
The imimdiate task is to buttreess where pocsible, our data on
undordovelooed countries and further toot the hypothesio that
creation va
satisfaction is crucial to political stability
would include varying, the parameter
tre~nd dat
tur
to in
of si
These tests
of the instability index and lookins at
With trend data, we could look more closely at s-ubsience an
k
fcts as variants of the
."
eeral lor-normal case
The
Orwth and the ability, to c tch up to developed nations
bi
Ihou
be
lcr importance as n6sition relative to other developing nations
9d
data on developin
d penage of comuter
to
expctat c
nations c an be explored quickly w th an
rograms
The sv cz
ing step will be to turn
eetern Eurone and the UnitedZtatos where detailed lon
av~alale on socio-economic variablez.
term data is
After trying to estinate the rela'ic
of those variables to expectations in n particular time period and us n tr
dat
or parameter estimation, we might try to predict which sociological
strata (locality, class, etc*) are in a state of high expectation frustration
and to test this prediction by an appropriate survey*
hio
V.
...
L- s
0
Relstinsy bcit,,cu
und
:F
6c
c1~
1!
~AiIAkX
'~1
ci~
(p
t-to
I/
0
cj)
FJGRnE 2 a
/,
/
MltttiollO o12'sIty
11
10
functioa, for tbre-Yiece mdel
FIGCURE3
Log-normal cumulative distribution of prsona/dqod
"basic political units,"i 19509
. in
10,000
Persons
Sq. Di.
1.,000
CUNHiATIVE PERCENTAGE
indicates approximate location of actual data
Positions of some units indicated for illustration.
.
IGURE1.
Log-normal cumulative distribution of
13ersons/doctor, persons/radio, persona/veh::
iOOCO
Source; Almond and Coleman
10,
Doctors x-65
.adios Ns26
Vehicles N-62.
Persons
Unit
01
50
CUULATIVE PERCENTAGE
o Points from doctors data
Points from vehicles data
( Points from radios data
99099
~pi~:
hg~o~iiicurhftive diirytribution
6
'Sou rceo Aiyaord' and~ C o lema n
NU~L~~EE PERCETRIAC:E
1000
3.00
it
IF
A
FiGruRr, 6
) I
Sourco: V1NESCO
copicS. - 10
O0-01
:16
314
M-1TAGE.?
GtJIUTATIVE PER MC
99099
\01
EoTwoouI
asded9aqq
!L7aam po7,-,
Vinourx
a
indmo0 sadOT13 Tv=,Ou-'Oq
U
Figue 8:RealG/Cpt
Source: Rodan
-. 100
4
yd:us I.,
Virgin I.,
Grenland,
Canal gone
arbitrarily excluded
rill
"'6'.,.
Co
a
* S
I.
ii
A-'0
(9.
H
""-
~
~5
V.'
~
£
I
j
'I
I
-
*
4
(21
Cd
S.
4.
.0
12)
K)
4-;
0
C;
C>
p
Jo
'-A
-
H
0
~
t*~tn
'-3 c:~
f~3u
'1-~
-
,%
44
4.,'
C'
C
4
4
I
'4-J
b
--
'I
4%
~,
0
fl
"'''.4
lx
t
P
4
)
"'"6
k.
('03
4
I
r~
C
C
44
(3
C
"5
;..i
*'tJ
~2
6?)
Ul..
K9r t
'ti
I
$
3
.4
4
I
'2
k
4
~4fl4
-I
$
Figurc jr
A
Cumulative distributions for newaprint and papel
Cpnuption
ic1Sor: TJESCO
1000
Kg/head
1939
1950
100
2.
Cu
.0
ATIVE PEFENTAGES
Auomobile regictration/capitS
19h0.
Source: Sttistic2
- Abstract 'of the UOBS
;99
CUIt7LATIVR PERCENTAGES
( ?)
ba
FIGUREf 12
V
Cutiu2ative di.stribuuiono of poptilection density in thL3ic~
pr t CAP,- Uiltod Stcetas
Source: Sttfistical
ID2flsity
Poqson
4
lo 64
'/sq,
0001
-
16
-
S
".0 deviations-of' actua]. data
.990)99
rnio
*
p
*
First draft-not for circula tion
data to the graphical e:ination
Txhis appendix adds statitical
Distribution parametcr! ar, presentcd alon- 'ith th
in thu text.;
0
for chi-souare tests for goodness oCf ri
Comrtatio;
~'
Rodan data
Variable
p
abovo
90 countries:
iea
1I20 real. GN/capita~
njti -log
oficn
""*.L75
6329 h
GNP/capita
ln(GNP/capita)
0178o7
695
Perons/doctor
ln(persons/doctor)
8682o,
9o06
5.16
5462
5o571
Parsons/radio
ln(Persons/radio)
371,4
4173
322h.4
Persons/newspaper copy
4.4?1
ln(Persons/newspaper copy)
2
2.
6o97
8
This work wlas done in part at the
All data per capita
OtI
Ch -Squarc
137o8
M66
7 32
25238~
8600,
10
66 coutries
AnA
sean
m
Lvel
atisfied
*080
1o29
137o8
313o6
Persois/telephone
In(Persone/telephone)
322.9
0,66
0,.,56
Almnond and Coleman data:
Mean
S. D4
330.7
5.59
in(persons/vehicle)
t)
b
10
4235,,5
in
t
in th
oss
(not the log
r
The oigt-class chiquE
discumd in tne text was usod in alcs.
na2tur.l lor arithm
dv
174
1010
626,3
264
o02
1.32
506.3
13
85
lo7
18 8 3
819,7
io,6o
io0 83
.I.T. Corputation Center
00
pE
0
&
Almond and Coleman data:
Variable
MIean
66 countries (continued).
Anti-log
S.D.
Chi-Souaroe Level
Saet 13fie d
onergfl3y convo/capita
ln(onergy/capita)
4
a
O32
-1.87
OO45
45
1o22
15o03
01
Interpratation of Rlsults
While the chi. esquare results for veihicles and dgatprs are extremely
satisfying and the results for income
for the remaining variables.
atisfac"ory, there is a poor result
Whether thais revults from bias in reportin
communications and production data, saturation effects at the t ails of the
distribution, or theoretical deficiencies is a topic for future invuestiga ion
In any casei there seers a clear oreference to using log values in place o0
the untransf ormed values.
The standard deviations of the untransforrod
variables range over nerative values of persons/doctor, telephone etc. Cnd
thus reflect the high y skewed nature of the basic distribution.
-~
jaare
r~ther reinforced in our argument for the log-normal by
correlation matrices oresented below.
That the logs
hne
ive substantial and
uniform increases in corielation between variables suggests that the variables
are pot-er funct.ions of one another.
the exairination of scattergrams.
This has been tentatively confirmed b5
.
CORRELATION MATRICES FOR PER CAPITA DEVELO? PM ARIABLIES AND LOGARITIiU
TIE VARIABL3
0F
Untransfor3d variablos
Yohicles -Telephonos
GNP -Doctors
ONP
~-Doctr
~
27
438
,37
037
.40
168
.69
.30
,32
'32
q42
38
.69
-Tele phones
S33
.22
Energy
GNP
Doctors
,72
GNP
Telephones
Vehicles
Docto:rs
Radios
,,73.
.81
072
o70
,84
087
Newspapers
.2
482
;75
W01
,81
VehiCle 3
TOlph
-,
089
e
(W81
o74
.78
'80
54
GNP and Energy ar "per capita"
**All variables "per capita."
6
All others are "persons per."
)77