A STATISTICAL APPROACH TO GO-C RATI3 t-POITICS

by-Howard Rosenthal

K

Center for International StudiesCambridge, Massachusetts

vlay, 1962

EFRATA

Corrocted

/p. 2, see,

p. 3, line

V p 5, line

p. 6, line

v p. 6, line

V p.8

p. 13

Table II A

O V Table II B

Figure I

1.11

12

18

4i

16

04., x < z<

193 1.13

t to

section 1.2 section 2.2

(see see ) (see see. 3.3)

of w and e of wande

the equation for the error function should contain 2

2 21 9 ~- 721 P(721) .2 6.97 P(6.97

the growth rate for Brazil is "L"

Group II and Group aI Group II anI Gro' I

z alogr x logy

In

0

Location Incorrect

*1

A STATISTICAL APPROACH TO COMPARATIVVE POLITICS

by Howard Rosnthal

. ;roduction

1.1 Among the key economic, d" ahic nd c nics

are ttl r oad markero of socitl 6oIcncer, there eXits ae o .

membars have for all practical purpoo, .o uppr boun to th .

bo attained. Exclud- ing aSe f inite 0o1lq as literacy t st

elass includes groea nat lnal protductv adios hil p 013C

Onergy, newspaper copies (por capitz, etc. The vti 1 o

the distributions of these variables amngnr nations and a ong c.ubd

of n i.Unation ib ono topic of' thi.s Ppoe

The basic dJstributioa that characterizes theoe ariablev f

thet t-normal di ribution (see 1.)) On the inCternati

it is necessary to divide the population into thee cubset

of which s choracterized by a deif'Qrent se of log riomal- pIar t;

ubsets yield an empirica. classfication of the traditioal., rnitic ,

and moder natiorns.' Another break down would be betweenu bo stens nat;',

ttrowth no-tiofle aI -WiU2' Ughon Th" lo A i4 pattern, oi CAiztna and mature notin he ogh p h

i1l be reflected in the three d tion parmters

apirica1y, the, variables appear to be 6 itribuIted mn the ntC

mong subsets of the nations in log-normal fashion. The vecond sectic

the paper portrays a grt;Vh proces under which a 1 og-noma d i st Ii.u 1

would result In the third section, a body of empirical dta is p C; d L

See Daniel Lerner, The Passn of TrditionaI Sociytv Gnicoe (IV9 8Aconept ivtive fromnn tht oft). Ro sto h stage ___-V

Gtrowth, London (1960o

9

discussed uhile the fourth diccusse3 applications of tho findigs. To aato nly

graphic-l techniques have been applied. ba h.. broken o

autom-ated analysis can be developed in the com.ng cunmer. According

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 log y is log-normaly distributed, then - o

normally distributed from vell-mown properties of the norm' ditr n

This implies that if a variable, say persons/vehicles is lo -noml

then its reciprocal, say vehicles/ca pita is also log-normal.

1J3 In the physical sciences, thee-nor pp10ies e r io

importAfnce. 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

tends to be a reasonably constant percentoage of the existing oealth

population.

1.2 Among the possible applications staisa the uise od "Mitles grooth' stati

tics in making inferences about " political deve.opmen The log

transformation has facilitated an analysis that the author beievos

14Tesuperior to earlier work based on simple avreraging. The objectiva of

section 4 wil be to show that indices cannot be simply "added up" to gi .7e

an "avrage' picture of developmert, Instead the argument runs, the

expectation.-ereatIng and eut yin unctions of the variable

must be considered. On any given Variable le ill comnute the nation G

position relative to the tir.ld - aWLd2txJ. on. Then.r se ighti 1n g

3 Yh log-normaistribution is discussed by G. Hordan, S . Particle Statistics Lxnon (1960), pp. 81-106, and Type--Token ahematica, 8-aenha5(T pp. 425 and passim.

4 See the "Concluion" by Jamen -- oloeman in The 1olitics of the De-velopinlpUAreas, Gabriel Almond and James Coleman, do. Princeton T:920 and

=,,vrtt Hagen, "A General Framawork for Arialyiridg Economic and 41oliticalChange"9 Center for International Studies, .'timeoo, Cambridge (1961).

C

C

W

a.xpctation-satisfyin~z variables positively and expectation--creating va abl.e

negatiel, a dovelopment or instabilitr d be nerato' Thic indox

yields a U-shLe~d rolationsh p vitii a batbory 'of indices of potUial d lop enat

2. S-omo likely conditions for lop:-normality*

2,1 The settlement of an area, the introduction of automobilos or rd:Los to

that area etc. can be thought of av dating from someO fctive "otarting

time" (the "starting time" will acquire a specific 0athema i c .meaiIn

bela) Assuna t sartiny time t in normally dIstributed smzh t

T- iu tf(t) (t 2

Tha n fA t -to is normal such lthat02

Where t

in application, t can be taken as the ti ne 'of measurement6

2*2 Assumo for some variable (of the "imitlesa growth" class), growth

is logarithmic with time; rcisel

log ya N t to co'. y

Further assume that k is a constant over the population.

Then it follows that "S normal Trlth mean x kWand standard

deviation X

SiLncc 20s normal, by definition~y)is log-norrnal.*

'U

Interpretation: The assumption of a contant growth-parameter, k

is not as"far £ront reality as might be inagined20

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 by three different constants that apply over different ranges of

x,, That is, lot

X + 1 -c X---

2 '+ c2 1 x X2

2C k 3 +cx x 2

Let us further assume that'Y

that the distribution of x is the

distributions, one of which holds

the results may be given as:

Range of x

:k

2; '' X2

X x

2'0',C3 '3 k a

is normal as In 1.1 Then it folloxs

composite of three different norma

for each k. Presented in 'tabular fori,

Normal distribution parametersMean S.D.

al. k~ j; ki

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- thvariable 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 and a random

variable over the set of all nations.

Givan two times, tl and t2 and corresponding y, and y,, k shbu.

be r iven bylog y - 2.o7 y2

i 2

Thus, o o n stirmated from empirical da ca, o:d it in th ln:-

also tprs to approach lo-norial orm. (so cc, 3 Theso lo

oxnra t. Lbutions accord with oit noldge of the skewd (aCnd

-,a) 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

us assume th joint distribution of w and x is bivariate normal,

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 unit-

normal. Then, the joint distribution may be expressed in the bi-

variate normal formp

where i ad 4' arie the mean and s.d. of the raarginal distribution

of w and 1 is the c variance0

It is well-known that the conditional distribution of x given w of the

form

g ) x -g

This distribution leads to inferences about the starting times et

us calculate

Since x k(t - t) by assumption and w.l o I, x 10 Therefor

ey lo'

or since -t is a simple lindar transformation of iy , the starting0

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 process0 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,

W".

-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 miLo

l A basic political unit is defined as either a nation or a colony

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 (For the newspapers, we have used

a 1956 unOo 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 In the cases where a

1. Almond and Coleman, op. cit.

in I I Is .,

-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 lop-

normality 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 CountriesCenter for International Stuies o, Ca ridge,9.

$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

fit. We notice that both the deviation and mean are maintained over

an 11 year period, This p rhap eflectS a aen ral read4justment to

the pre-orld War II levels with some shuffling of position.

3.1.1. 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. As time

progrresses and as growth becomes more uniform, 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 Thisperhaps 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. They suggest that it will have to be soobistica ted

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

other ate r the overall growth rate, This implies stablization

of ra i e absorptive capacities Thse 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 chi-

square 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

Class Observed Expected Range Rane mransformed tounit normal

I 10 12.2 .- o-2.11 -.15 . :5 2.11- 2.21 -141 - 7

III .15 12o6 -2.21- 231 -7 - 3IV 12 -10.7' 231 2.238 -- 0

V 9 10.7 238 - 2,44 0VI 10 12.6 2. - - 7VrI 5 9.5 2,54 2.64 .7 - i1VIII it 12.2 2,64 -1

Degroos o.f freedom 8 el 2 5

del PfR) o(70") o 2091

The combined graphical and statistical results clearly warrant cont ineed

intereet by social scientists in the logp;normal distributiono

- - --- - - - - ,------ ---- --------------- -------- -- 7 - -

- he-

3.3 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. This k also plotted in linear fashion as can

be seen in figure 12 . 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 norm alized scores

has a clear geri6ral preforeic agir g 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

of 5 out of 60 nations, l4oreover, "competitiveness" in practice seems to

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

and on what form it takes. 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 At

one end will lie the familiar examples of "good' deivelooment (India, Turkey). At

the other extreme will li 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 no more

so than the "add 'em all up equally" indices0 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 mediaand vehicle consumption "ave been atypically high,

TABILE IIA

NATIONAL INSTABILITY(Note: The classifications made are ex-trmust eventually be justified, no attempt

Nationbility Index"

AND GROWTH DA.TA,emely tentative. Although th3 m thooogywill be made in this preliminary "udyo)

Leftizrt Large- Lo v row t hTakoover Scale (Inrnal Ra1945-62 Firopriation ars/

1945-62 2opoo,cOOCapita)1946-59

VenezuelaIsraelUruguayNicaraguaEcuadorEl SalvadorColumbiaIndiairgentina,LebanonPakistanBurmaNyasalandPhillipinesThailandTurkeyCongo(Loopoldville),SudanViet-NamPanamaGuatemalaDominican RepublicCosta RicaHondurasIraqCubaBrazilMozambiqueMalayaTanganfkaUnion of South AfricaParaquayIranIndonesia-U.A.R.Libya

15o2.13.011.110.6

9.39.29.08.6'7.97.9,6.56o5.5,35.04As94.8,14.8

3.93.73.73,02.82.62.3.2o22.01.61.6

01.

0o4

'2

+ 4-.

+

+ 7

+-

+ .

+

1471,8.

02,11,91.3

0,14

2.5031.0nodo0 .9O70-6

1.1n,,d42.72o11.02,51.81052.2048'n.d.1..10.11052.11o40.51431.9

L

LSL

HH-11 GROUP

H

L

L

S

SSI

L

SS

LL GROUP

L

LnLd

L-SL4*

?

TABLE IIA (Continued)

I ("Ins a Leftistbility Index") Takeover

1945-62

Large- LogScale (Interna

Expropriaton Wars/i0,C00,000Capita)1946-59

CeylonGhanaNigeriaSo. RhodesiaJordanPeruAlgeriaMexicoEthiopiaFrench Equitorial AfricaHaitiChileFrench 'West AfricaTunisiaKenyaAngolaMoroccoBolivia

-1 7-2.0

-h ~h-4 4-4.6-5.5

-548

-8o2-8.2-

-10.1-10 _7-14.6 +7?

0.n.d.1.6

0.9100028n0.6

250O1 3n,d1.31,141,20.k1.32.0

L

LH

LL GROUPL III

L

L

L

L

L

L

0

Nation GrowthRate

Key: Countries include all with full set of GNPp radio, doctor, and vehicledata 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 0places it lowest in rank order.

-- Egypt is low, Syria stationary0*N* Source: Harry Eckstein "Internal Wars: The Problem of Anticipation,"

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 ofthe classifications

Group IGroup IIoroup III

TABLE 11I

GROUP DIFFERENCES IN STABILITY

Takeover Expropriation Internal WarMeans

0 1.277 6 1,52 1 l2

* All +, +?, 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 levelaCases with no data excluded,

TA BLE IIC

COMPARISON OF GROWTH RATES AFD INDEX CLASS

I index(4 basicindices)

GrowthGroup

IIIII

H L S

6 10 20 1i 5.2 1 2

-32 3,

S81718

*Reai

Capita

Growth

Group

III

H

323

L S

1211

/

j-c)

AlmondandColeman(11 indices)

Growth

roupH{ L S

3

III 159,

* Groups formed from rank-order

102320

1 0

b

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 expctat c

creation va satisfaction is crucial to political stability These tests

would include varying, the parameter of the instability index and lookins at

tre~nd dat With trend data, we could look more closely at s-ubsience an

tur k fcts as variants of the eeral lor-normal case The bi

to in ." Orwth and the ability, to c tch up to developed nations Ihou be

of si lcr importance as n6sition relative to other developing nations

9d data on developin nations c an be explored quickly w th an

d penage of comuter rograms The sv cz ing step will be to turn

to eetern Eurone and the UnitedZtatos where detailed lon term data is

av~alale on socio-economic variablez. After trying to estinate the rela'ic hio

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*

V. ... L- s 0 Relstinsy bcit,,cu :F und 6c c1~ 1!

~AiIAkX

'~1

ci~

(p t-to

I/

0 cj)

FJGRnE 2 a MltttiollO o12'sIty functioa, for tbre-Yiece mdel

/, 11 10/

FIGCURE3

Log-normal cumulative distribution of prsona/dqo d . in"basic political units,"i 19509

10,000

PersonsSq. Di.

1.,000

CUNHiATIVE PERCENTAGE

indicates approximate location of actual dataPositions of some units indicated for illustration.

. IGURE1.

Log-normal cumulative distribution of13ersons/doctor, persons/radio, persona/veh::

iOOC O

10,

PersonsUnit

01

Source; Almond and Coleman

Doctors x-65.adios Ns26Vehicles N-62.

50 99099CUULATIVE PERCENTAGE

o Points from doctors dataPoints from vehicles data

( Points from radios data

~pi~: hg~o~iiicurhftive diirytribution

'Sou rceo Aiyaord' and~ C o lema n 6

NU~L~~EE PERCETRIAC:E

1000

3.00

it

IF

A

FiGruRr, 6) I

Sourco: V1NESCO

copicS. - 10

:16

GtJIUTATIVE PER MC M-1TAGE.?

O0-01 314 99099

\01

EoTwoouI

asded9aqq

!L7aam po7,-, 0 a Vinourx indmo sadOT13 Tv=,Ou-'Oq

U

Figue 8:RealG/Cpt

Source: Rodan

-. 100 yd:us I., Virgin I., Grenland, Canal gone arbitrarily excluded

4

C-)

Ha

* S

""-

~

~

-(9

. I

0A

-'

'I j

"'6'.,.

ii

V.'

£

rill Co

~5

Jo '-A p4 C> C;

0 4-; K) 12

)

Cd

S.

4. .0 (21

I 4 4

"5

C (3

~,

44

C C

4 ('03

I fl r~

k.

lx

) "'"6

I *

,% --

'1-~ '-3

c:~

f~3u

C

t*~

tn

C'

H

~ 0

4.,'

44

'I --

4%

I

0~

4fl

4

"'''.

4

P

4 kt4

*'tJ

'2

.4

;..i

6?

) 'ti

~2

3K

9rt

IU

l..

4

' 4-J

b

I.

-I

$

Figurc jrCpnuption

Cumulative distributions for newaprint and papel ic1Sor: TJESCO

1000

Kg/head

100

2.

1939

1950

Cu ATIVE PEFENTAGES

$ A

.0

Auomobile regictration/capitS 19h0. Source: Sttistic2 - Abstract 'of the UOBS

;99

CUIt7LATIVR PERCENTAGES

( ?)

FIGUREf 12

Cutiu2ative di.stribuuiono of poptilection density in thL3ic~

Source: Sttfistical pr t CAP,- Uiltod Stcetas

ID2flsity

Poqson

4lo 64

0001

'/sq, rnio

.990)9916 S- - ".0 deviations-of' actua]. data

b a V

*

p *

First draft-not for circula tion

Txhis appendix adds statitical data to the graphical e:ination dv

in thu text.;0 Distribution parametcr! ar, presentcd alon- 'ith th r

for chi-souare tests for goodness oCf ri The oigt-class chiquE

discumd in tne text was usod in alcs. Comrtatio;

na2tur.l lor arithm (not the log oss in th b t t)~' 10

Rodan data 90 countries: abovo 1I20 real. GN/capita~

Variable

in p

iea njti -logoficn

4235,,5

6329 h5.59

Almnond and Coleman data: 66 coutries

Mean AnAm sean

GNP/capita 0178o7ln(GNP/capita) 695

Perons/doctor 8682o,ln(persons/doctor) 9o06

313o6in(persons/vehicle) 5.16

Persois/telephone 5462In(Persone/telephone) 5o571

Parsons/radio 371,4ln(Persons/radio) 4173

Persons/newspaper copy 322h.4ln(Persons/newspaper copy) 4.4?1

2 This work wlas done in part at the2. All data per capita

8600,

174

264

13

85

.I.T.

137o8M66

25238~1o29

137o81010

626,31.32

506.3lo7

819,7io,6o

Ch -Squarc Lvel

7 32

18 8 3

io0 83

Corputation Center

S. D4

322.90,66

330.70,.,56

6o97

8 OtI

atisfied

* -

080

o02

00

........... .

""*.L75

10

Almond and Coleman data: 66 countries (continued).

MIean Anti-log Chi-Souaroe LevelSaet 13fie d

onergfl3y convo/capitaln(onergy/capita)

O32-1.87

OO4545 1o22

4

a

pE 0 &

Variable

15o03 01

S.D.

Interpratation of Rlsults

While the chi. esquare results for veihicles and dgatprs are extremely

satisfying and the results for income atisfac"ory, there is a poor result

for the remaining variables. 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 hne

correlation matrices oresented below. That the logs ive substantial and

uniform increases in corielation between variables suggests that the variables

are pot-er funct.ions of one another. This has been tentatively confirmed b5

the exairination of scattergrams.

.

CORRELATION MATRICES FOR PER CAPITA DEVELO? PM ARIABLIES AND LOGARITIiU 0FTIE VARIABL3

Untransfor3d variablos

GNP -Doctors Yohicles -Telephonos

ONP

~-Doctr ~

-Tele phones

GNP Doctors

,72

Vehicles Telephones

,,73.

o70

.81

,84

,81

Radios Newspapers

072

087

o74

089

482

W01

.78

'80

54 6

GNP and Energy ar "per capita" All others are "persons per."**All variables "per capita."

037 ,37

.40 168

438

.69

38

.69

27

.30

'32

,32

q42

S33

.22

GNP

Docto:rs

VehiCle 3

TOlph e -,

.2

;75

(W81

)77

------ ------ ........ ..... ......

Energy