-
U
JUL 23
1964
OF T~y
E\ST.
RA R IE
HETEROGENEITY
IN RESIDENTIAL NEIGHBORHOODS
by
Kenneth E.
Suchan
B. Arch., Carnegie Tech
(1962)
SUBMITTED IN PARTIAL FULFILLMENT
OF THE REQUIREMENTS
FOR THE
DEGREE OF M,'iASTER OF
CITY PLANNING
at the
MASSACHUSETTS IN6TITUTE4
OF
TECHNOLOGY
June, 1964
Author.......I ..............
Department
of City and Regional Planning,
May 22, 1964
...
Thesis Su"_ryjisor
Certified by..
Accepted by....
NV
Department Chairman
~.
m
0 3j
HETEROGENEITY
IN RESIDETIAL 1EIGHBORHOO)S
by
Kenneth E.
Suchan
Submitted to the Department of City and
Regional Planning on May 22, 1964 in partial
fulfillment of the requirement for the
degree of Master of City Planning
'hile heterogeneous,
"lbalanced" urban neighborhoods have con-
stituted a common planning goal, little writing in this area has
clar-ified or quantified this objective. It is therefore the purof this paper to 1) propose one quantifiable definition of
socio-economic heterogeneity, 2) measure the existence of this
heterogeneity in existing cities over a short time span on an
inter and intra-neighborhood level, and for each of a number of
socio-economic variables, 3) finally, to conclude from the study
the probability of heterogeneity, as defined for the study, being
achieved in existing cities at different scales for several variables.
A "cross section" definition of heterogeneity was used for this
study, i.e., heterogeneous neighoorhoods were those which were a
replica of the metropolitan socio-economic profile at both the level
of the neighborhood mean, and in the internal distribution of the
socio-economic characteristics. Applying tais definition to metropolitan Cleveland and Boston for 1950 and 1960, and considering the
variables of income, education level, occupation, ethnicity and
life
cycle stage of the household,
it was found that 1)
with respect
to the individual variables, between 1/2 and 3/4 of all neighborhoods well vithin a miadle range of the total distribution for the
variables for both cities and both census- years. There was little
indication of significance of any one of the variables with respect
to tendencies toward homogeneous or heterogeneous patterning. 2) A
slight decrease in the number of neighborhoods in the middle range
appears evident for both cities between 1950 and 1960 for non-white
popuhtion and occupation, as well as a slight increase for education.
However the changes are not startling. 3) Considering all the
measured variables together, between 1/4 and 1/3 of the neighborhoods
fell within the middle range. 4) At the intr-neighborhood level there
was virtually no correlation of the sub-area distribution with
the metropolitan profile for the variables of income, education, and
non-white population.
The results of this study suggesy that an inter-neighborhood
level of heterogeneity of individual variaoles persists, but these
variables do not reinforce one anotiher in creating many heterogeneous neighborhoods with respect to a numoer of the variables.
However, examination of the intra-neighborhood average was a
poor indicator of internal consistency with the metropolitan profile.
What does this suggest about future study in this araa
and planning objectives concerning heterogeneity and balance?
First, the study suggests that the cross section model is one
which does not appear very often in reality; it is almost nonexistent in both its dimensions. Further, there is some indication that the cross section goal is getting farther from being
achieved. Does this .iean that it cannot be achieved in a planned
neighborhood? No, but it does represent a great gap with respect
to exiding city patterns.
Rather, the results suggest a possible alternate approach for
an objective and corresponding study. As suggested by Herb Gans,
there may be necessary minimum or maximum numbers of persons of
relatively homogeneous characteristics in order to achieve
social equilibrium at a small scale spatial unit like a neighborhood or block. Therefore, a study which examined the
various interactions and scales of neighborhood life might reveal
some insights into these critena. Objectives formulated on the
basis of maximumi or minimum numbers, it is suggested, would be
mor'e liKely to find confirmation in existing city areas, and would
be better suited for implementation than a strict cross section goal.
Thesis Supervisor:
James M1. Beshers
TABLE OF CONTEITS
THESIS ABSTRACT
I.
.
.
2.
0 **Se0e&*00
BACKGROUND FOR STUDY .......................... 1
II. METHODOLOGY .................................. 11
Heterogeneity Defined .......
Case Study Areas ............
Tiie Socio-Fconomic Variables.
Inter-Tract Heterogeneity
11
13
14
15
17
19
20
...
Intra-Tract Heterogeneity
Sources of Data .............
Problems in Data ............
................................... 23
1I1.HYPOTHtSIS
IV.
_ULTS
OF
rACO
25
..........................
inter-Tract Analysis
............
Income
....
Education .
Occupation
Ethnicity .
Life Cycle'
Heterogeneity of All Variables
IntratTract Heterogeneity
V.
....
CONCLUSIONS....................................
I
APPENDIX
70
.....................--
102
BIBIIOGRAPHY ............................-
TABLE I
TABLE II
INTERATRACT HET?EROGENEITY
-
-
'+
INTRA-TRACT HETER,,.GEN'EITY
iii
............
...........
00
61
..
U
MAPS
INCOMEl
-
CLEVELAND
1950
-. -
27
28
29
30
1960
BOSTON
1950
1960
EDUCATION
BOSTON
OCCUPATION
NON-VHITE
-
-
....
32
1960 ....
1950 ....
1960 ....
34
35
CLEVELAND 1950
-
CLEVELAND 1950
1960
1950
BOSTON
1960 ...
j7
38
39
40
..--
44
CLEVELAND
1950
B0ST0 N
1960 ....
1950 ....
1960...
FOREIGN BORN - CLEVELAND 1950 .
1960 .
1950 .
BOSTON
1960 .
% CHILDREN - CLEVELAND 1950 ...
1960 ...
1950 ...
BOSTON
1960 ...
ii
45
46
47
HET.EROGENEITY IN RESIDENTIAL NEIGHBORHOODS
I.
BACKGROUND FOR STUDY
heterogeneity, diversity and "balance" are all words which
have become popular slogans in city planning and housing literature to describe the goals toward which urban residential
neighborhoods ought to strive.
The words and the concepts
which they are attempting to describe are sufficiently vague to
make
them both hard with wiich to argue and to implement.
Nebulous as they are, the goals of heterogeneity and diversity
do sugg;est a direction in
which it
is
proposed that cities
and
their neighborhoods proceed-- i.e., toward a greater mixture
of the various physical and socio-economic characteristics of
the urban population.
From a survey of the contemporary planning literature on
this general subject, it is difficult to determine exactly what
form the "mixing" should iaeally take.
Heterogeneity and diver-
sity have come to wean all things to all mien.
At least three
basic types of diversity can be sorted out from the various
planning proposals:
a small scale, 2)
1)
diversity
t land uses and functions at
diversity of building types and architecture
at the neighborhood scale, 3)
and finally diversity of
the
social and econoiic characteristics of the urban dwellers thewselves at a range of scales.
Any of these three major connotations
of the diversity goal could constitute the basis for a major study.
This paper will limit itself to a discussion of heterogeneity only
with respect to the social and economic characteristics of city
inhabitants.
The terms heterogeneity, diversity and balance will
be used interchangeably, as they are considered to be representative of the same conceptual goal.
WVithin these socio-economic limits there is still a great deal
of ground to probe.
Coming immediately to mind, for example, are
questions of the precise Qefinition of heterogeneity, diversity,
or balance.
Further, at what levl or scale are or should these
goals be operable--the region, the commnunity, the neighborhood,
the block?
There is also the underlying question of the desirability
of a heterogeneous urban environment and/or the degree or amount
of heterogeneity which is desirable.
Is heterogeneity a good in
itself, or is it a means to accomplish
some other planning goals?
Finaily, an important consideration'must be the existing urban
environment and the degree to which it does or does not fulfill
the diversity goal.
If diversity is to be a goal, its limits and
types operationally defined, how different must this new environment be from the existing urban pattern?
The questions of a workable definition for heterogeneity and
discussion of the scale at which it does or ought to exist are
both ones which most writers in this area have avoided.
Whether
this stems from an assumption that "we all know what we're talking
about"
or a lack of interest on their part to delve into this
problem is
hard to discern.
The part of the issue which most
writers have explored or speculted upon is the desirability of
heterogeneity--the answer to the question of why.
Some typical sentiments in planning and housing literature
are expressed in the following excerpts.
These statements were
taken from literature of the 1940's, but their substance has not
varied much from the arguments of the 1960's.
"If democratic health is to be maintained, probably
no neighborhood and certainly no co.imunity, should
consist exclusively of a single income group. How
far diversification may go aepends somewhat on the
size of the neighborhood, its location in relation
to work possioilities, and other variable factors.
The developers tendency to build for only a specific
iincoie group,
based on the theory that people of
varying incomes will not mix and that mixture tends
to force values down to the level of the lowest
group, is not valid in large scale work. The
contrary, in fact, is true for in any investment
program diversification is the essential element of
safety for all
concerned;
the developer,
the owner,
the storekeeper, the municipality, the school system,
and our political system itself..."
(National Committee on housing, 1944)
"There seems no souna reason why a neighborhood
should
contain exciusively one type of housing, one level of
density, or one narrowly restricted group of residents.
The tenuency toward what FHA refers to as 'homogeneity'
may be overplayed, whether it be in the types of houses
or incomes of the occupants, to the disadvantage of
neighuorhood stability and the democratic way of life..."
(Architectural Forum, 1945)
An example of more recent concern over the excessive homogeneity of smAall city areas--nighborhoods or blocks--is the writing
of Elizabeth Wood.
Her major interest appears to be in the problem
of public housing projects--particularly of the low rent variety-and their integration into the city's social pattern.
Miss
Wood's major arguments for heterogeneous mixture in city mighborhoods focus on the need for middle class models to encourage
mobility in lower class persons, and to provide leadership for
neighborhood institutions which will form a backbone and stabilize
the neighborhood.
While her approach is weakened by appealing to
the reader's ability to see the "obvious" necessity of neighborhood
heterogeneity to promote a number of social goals, Miss Wood
does attempt to describe that her balanced neighborhood would
resemble.
She
9 uts
forward a model of city neighborhoods which
retain their socio-economic characteristics while population moves
through them.
"A good mixture is in equiliorium. A balanced neighborhood
is one in which the mixture is not in the process of selfdestruction. A neighborhood rapidly changing from white
U
to all black is not a Oalanced neighborhood nor is one
that is in process of physical deterioration, regardless
of the presence at any one time of all elements of mixture. A neighborhood is in equilibrium when the general
prop ortions of the elements are maintained even thou6h
individual households and buildings change. If rich
people move out, rich people move in; if white persons
iove out, white persons also move in; if a bad building
is demolished, a good one goes up."
This gets closer to a definition of heterogeneity, but the
linking of this goal to an operational policy of implementation
is still not too clear.
Herbert Gans has succinctly gathered together four current
arguments in favor of a heterogeneous environment as follows:
1) Heterogeneity adds variety and demographic "balance" to
an area, thus enriching the lives of the inhabitants. Conversely homogeneity stultifies as well as deprives people
of important social resources.
2) Heterogeneity promotes tolerance of social and cultural
differences, reducing political conflict and encouraging
democratic practices. Homogeneity increases isolation
between smaller area residents and the rest of society.
Heterogeneity provides a broadening educational influence
3)
on children, teaches them about the existence of diverse
groups and how to get along with these people. Homogeneity
limits the children's knowledge of diverse classes, ages,
and races and makes them less capable of association with
others in later years.
Heterogeneity encourages exposure to alternative ways
4)
of life, e.g., providing intellectual neighbors for a child
from a non-intellectual family, or offering mobile working
class families a chance to learn middle class ways of life.
Gans does not quarrel with the ends articulated by these arguments,
but he does raise the question of whether a heterogeneous
commun-
ity or neighborhood is the logical way to achieve the ends, without
unaesirable by-products or consequences.
Gans counters the argu-
aents listed previously with his own realistic appraisal.
For
example:
1) Even if you could get people of diverse backgrounds to
live together, there might be endless bickering, envy,
uneasiness in social relationships because of a lack of
any real foundation for forming friendships. Gans argues
from his experience in studying- suburban areas that propinquity (mere physical nearness) is only a minor cause
of solid friendship-based social relationships. If some
amount of homogeneity of background and interests is not
present, propinquity arely results in polite formalized
cordiality at best.
2) Heterogeneity may not help aemocracy if it sets up such
diverse groups with such intense differences that the normal
democratic processes--fragile as they are--may not be able
to cope with them.
At least some amount of homogeneity can
guarantee sufficient consensus for democratic processes to
work in solving other differences of opinion.
3)
The mere fact that chilaren live in an environment in
which they see diverse types of people is no guarantee that
they will be tolerant of this diversity. Tolerance depends
to the largest extent on parental attitudes.
4)
Concerning the usefulness of heterogeneity in exposing
persons to alternate ways of life, Gans suggests that no
conclusive evidence has been found explaining why lower
class persons adopt middle class ways or whether the presence
of middle class people aias this process. A recent
sociological study showed that some lower class children
in a predominantly middle class school and some middle
class children in predominantly lower class schools adopted
the prevalant life style of the school. Because of the
special social environment of the school and the impressionability of children, the results are not entirely conclusive
Further, Gans
for adults and residential neighborhoods.
sugg ests that success in teaching alternate ways of life really
that the persons involved have
depends on three conditions:
sufficient economic stability and social skills for the new
6
way of life, that the differences in life styles are not
excessively great, and that the teachingc group be sympathetic
and empathetic to the needs and points of view of the aspiring
group.
Gans' evaluation of the most commonly used arguments for
heterogeneity is insightful in pointing out their defects.
His
own suggestions for objectives still lack operational clarity.
He suggests that both homogeneity and heterogeneity are necessary
but at different scales.
At the small scale block or small neigh-
borhood he envisions enough homogeneity to assure consensus among
neighbors sufficient to prevent conflict; positive although not
necessarily intense relations between neighbors with respect to common
needs and obligations; and the possibility for some mutual visiting
and friendship formation for those who want it in the immediate
vicinity.
On the other hand tnere should be enough heterogeneity
for "some diversity"--admnittedly not an operational solution.
At
the community level Gans advocates heterogeneity, not for the four
generally stated reasons, but rather because ours is a pluralistic
society and our communities should be reflictive of this, and
more importantly because, as long as local taxation is used as
the main support for community services, homogeneity at the community
level encourages undesirable inequalities in the ability to provide a high level of services.
Getting to the crucial question of the ideal amount of
heterogeneity Gans admits that
because so little is known about
its ramifications he can only offer two suggestions.
The first
is that enough homogeneity must exist to allow institutions in
the community to function and interest groups to reach workable
compromise.
This suggests that if every small community were
a cross section of a large region, there would result such a
splintering of interest groups and institutions
unworkability and irreconcilable conflicts.
as to lead to
The second suggestion
points out that sufficient heterogeneity ought to exist to ensure
that important community facilities and services be able to be
financed and find sufficient clientele.
Vague as Gans' suggestions are concerning quantifying the
needs for heterogeneity and homogeneity with respect to his particular goal statement, it is at least one of the few attempts to
set forth some criteria for defining these vague objectives and
for judging when the objectives have been reached.
It is an
attempt to consider the question of heterogeneity in a comprehensive
way.
Following that line of thinking, this paper will attempt
to develop an operational definition of heterogeneity and a means
for judging whether existing cities or proposed planning solutions
achieve the operationally
deal with is
defined goal.
What the paper will not
the question of the desirability of heterogeneity
and the relationship of heterogeneity to solving social goals.
As has been outlined in the preceding pages, the question of what
ought to be and why) are each large problems in
their own right.
This paper's concern is the defining of heterogeneity in order
to see how far we nave achieved the goal in existing cities or
how far we must go to achieve it.
The goal is a framework for
analysis which will be tested on case studies in existing cities
and can be tested on planning proposals using specifically defined
goals.
This study will accept the contention that heterogeneity at
every city scale may be a desirable goal for planners to pursue,
and after defining heterogeneity in such a way as to be operational
at all these scales, will determine in case studies in existing
cities the degree and type of heterogeneity existing at present
and immnediate past at various scales, thereby hoping to find a
basis for speculation on the liklihood of a goal being achieved.
Underlying this type of approach are two assumptions:
1)
that people's decisions are more or less based on what they
desire, and 2)
that planners will not be successful in achieving
a goal which is completely out of line with the desires of the
people.
It is of course true that these assumaptions are at best
only generally true.
Many people and groups within the city are
constrained in their desires by
erations.
social or economic status consid-
On the other hand, it may also be possiule for planners
to change the goals of the people through persuasive or educational
techniques, or through offering a new or additional alternative
which the general public had not considered before.
ness of a study of this type,
however,
lies in its
The usefuldefining the
limits of the existing situation based on a particular definition
of heterogeneity and perceived popular aesires--one of the
limitations within which planners' proposals ought to be considered
and formulated.
II. METHODOLOGY
Heterogeneity Defined
To begin a study of heterogeneity, we must first formulate
a definition of this concept which is operational and can be
tested against existing and proposed situations.
There is diffi-
culty in determining quantitatively, from the writing of the proponents of heterogeneity, the desired ends which they had in mind,
e.g., how many families each of low, middle, and high income would
constitute a heterogeneous community or neighborhood?
This study
will explore one rather unsophisticated concept--that heterogeneous
neighborhoods be cross sections of the total city.
Therefore, for
the purposes of this study, the average value over an entire
metropolitan area for each social or economic characteristic shall
be taken as the desired goal to be sought in each smaller unit
of the metropolitan area.
Each sub area should therefore represent
a random sample from the total metropolitan area.
In order to have a consistent measure, the "cross
section"
goal shall apply to each level below the metropolitan scale-through neighborhood ana blocks.
Therefore, in a completely
heterogeneous metropolitan area, each smaller unit within the whole
would be a small scale replica of the metropolitan socio-economic
profile.
It might be argued that by aiming for an ideal in
which all neighborhoods would possess virtually the same average
value for each socio-economic variable, the results could in
fact be a homogeneous metropolitan area.
This might be the case
if the ideal did not also include matching the 'metropolitan distribution curve for the variaoles as well.
area
distribution curve for particular variables were extremely
tightly peaked about
In
Only if the metropolitan
an average value could this charge be made.
fact, the metropolitan distribution for the variables being
measured is not
homogeneous.
Therefore it becomes apparent that only by achieving the
metropolitan average can a small social unit also have a chance
of matching the metropolitan profile for the variable.
Because
the metropolitan profile is composed of diverse and extreme values,
a neighborhood average which is highly divergent from the metropolitan norm indicates a concentration of these relatively extreme
cases in that neighborhood, i.e., relatively homogeneous high or
low value tracts.
This study will primarily be concerned with the statistical
spatial unit most closely approximating a residential neighborhood-that of the census tract.
Census tracts generally contain from
4000 to 6000 persons and were intended by the Census Bureau to
represent "natural areas"
of relatively homogeneous population.
This latter requirement is the one of lowest order and due to shifting
population within rather stable tract boundaries, not considered
to be a built-in bias in measuring heterogeneity.
The use of the metropolitan area as the largest unit from
which to measure heterogeneity is not a constraint on this type
of analysis.
Any average measure, be it national, state, or
region-wide, may be substituted
mind of the planner.
}epending upon the goals in the
The metropolitan norm appeared to the author
to be representative of the goal expressed by current writers on
the subject of heterogeneity.
Heterogeneity may exist on any number of levels--the nation,
the state, the region, the metropolitan area, the neighborhood, the
iLock.
This study assumes a common measure for each level.
This
may, in fact, be misinterpreting what the proponents of heterogeneity have in miind,
but witnout a sound basis to determine the
subtleties of their goals, it appears to be an operational definition
which could be easily modified through coefficients if a comprehensive, quantified goal formulation for heterogeneity at a variety
of scales were proposed.
Case Study Areas
For the case study I have chosen two metropolitan areas-Boston and Cleveland--and will be concerned with two census years
in particular--195O and 1960.
The cities were chosen, first, because
they are representative of two distinctly different types of
American cities which developed in aifferent time periods.
It
is hoped that this will eliminate the problem of drawing incorreat
conclusions from the peculiar circumstances of a single city.
Boston is an eastern city which achieved maturi6/ by the late
19th Century.
Cleveland is representative of the midwestern indus-
trial cities receiving most of its growth at the turn of the 20th
Century and on to the Depression.
They are cities composed of
different primary ethnic stocks--Boston being predominantly Irish
and Italian, with few non-whites, while Cleveland's in-migrants
are mostly Eastern European, with a large minority of non-whites.
4 city economic types they differ.
Boston's economy is based to
a larger extent on office, coiiimercial, aria research and institutional
activity than Cleveland's which is strongly based on manufacturing.
As of 1960 the Boston metropolitan area contained roughly two and
a half million persons.
The Cleveland metropolitan area studied
had a population of about one and two-thirds million.
The Socio-Economic Variables
Five characteristics were chosen to represent the social and
economic makeup of the population and some measure of the life
cycle differentials.
The characteristics and their measure
Income of Families anca unrelated individuals
Years of education for adults over 25
Percent of ,,ales White Collar and Blue Collar
Percent of population non-white
Percent of population foreign born
Percent of population of foreign stock
LIFE Gu LZI Lercent of population 0-16, 0-14, or 6-17
INCOME
EDCATION
OCCUPATION
LT'HICITY
14
include:
'50 and '60
i
i
"
Inter-Tract Heterogeneity
For each of the five measured characteristics, an idex was
calculated for each census tract representing the distance from
the metropolitan norm (being 100).
value.
If
of the tract mean or median
the iietropolitan norm for income is
tract with a median income of 4OO0
$6000 = 100,
a
would be indexed at 8000
600x100 = 1.
We would like to know how many tracts lie in a "heterogeneous"
range at this inter-tract level, and their spatial pattern.
will be the criteria for heterogeneity?
Of course the closer the
tract average comes to the metropolitan average, the
ogeneous the tract (by our definition).
average is tolerable?
What
iore heter-
But how close to the
Because different variables are scaled
aifferently--in dollars, years of education, or percentages of the
total population-- we can cancel the effect of the measuring scale
by calculating the standard deviation (or average deviation where
the average is given as a median rather than a mean) of the range
of indexed tracts and select a measure of heterogeneity in terms
of standard deviation.
Thus for such divergent variables as years
of education (with a range of relatively few years) and one of
percentage of the population which is foreign born or non-white
(with percentages ranging from 0 to 100), the standard deviation
gives some indication of what a comparable range in terms of index
steps for each wiould be,
e.g., aoout 10-14 points for education and
over 50 for percentage foreign born.
The standard deviation is
in terms of index numbers, but oy dividing the standard deviation
by 100 and multiplying by the metropolitan norm for the characteristic, it is possible to find the corresponding distance in termns
of years of education or percentage points, etc.
Further, by dividing the index devation from 100 for each
variable by the maietropoiitan standard deviation for that variable
we can get a set of values for each variale which can be directly
comApared.
A.D. =
S.D.
=
fd
n
tract value for variable
met . mean or median
Zfd
n
met. index
-
tract index
index
=
met. S.D. or A.D.
adjusted
variance
Where f = frequency at each level
d = deviation from mean or median
n = number of values
The values in terms of standard deviations (or average deviations)could then be graphically presented.
A color scheme was chosen,
composed of a neutral shade fr tne middle range of deviations and
graded to two extreme colors representing up to + 5 deviations from
the norm.
This technique hopefully gives a quick idea of the
extremes of the values and their location and patterning.
While tnis is still a rough measure, the middle range of
16
values (those within
1 ;S. D. or A.D.)were considered to
be
more or less heterogeneous with respect to that particular variable
and at this inter-tract level
.
Tracts which fell beyond
2 S.
D.'s,
and certainly those beyond 3, .could be thought of as representing
homogeneously high or low value tracts with respect to particular
variables.
Intra-Tract Heterogeneity
Inter-tract analysis, of course, does not tell the whole story.
Therefore, in addition to the measure of inter-tract heterogeneity,
a test area in the Cleveland metropolitan area was chosen in
Jch to study the relative homogeneity or heterogeneity of the
tract itself.
From U.S. Census figures, it is possible to
measure the interftaldstribution of the variables of income,
education level, and race.
In effect, what we would like to know is 1) how the distribution
curve of the inaividual tract for income and education compares
with the metropolitan distribution, and 2)
how the non-white living
pattern on a block basis compares with the tract average.
The method useful for coiiparing curves, sometimes referred to
as "goodness of fit",
is through the chi square analysis.
formula for calculating x
Where
f
A simple
is:
is the observed
frequency of values in a
distribu;tion; and f is the
e
expected or desired frequency.
X
f
-
fe
2
If we calculate for each census tract what its distribution
should be if it were a random sampling or cross section of
the iaetropolitan area ana use this as f
, we can comnpare the
actual frequency of values reported by the census for each tract
and calculate x2 for the sum of the differences.
A table will
show the probability that the value received for x 2 could have
been from a random sample of the metropolitan area,
(i.e.,
a
heterogeneous aistribution).
As an exataple of how the chi square test vorks let us
consider a simple aistriuution of income levels.
In a census
tract of 100 families, suppose 20 families' income is below $3000,
60 families'
income
5000-7000,
and 20 families at the $7000+ level.
However, in the total mietropolitan area the percentages of the
population at each level are 30%,
40%,
and 30% respectively.
Translated into comparable figures for a tract of 100 families, we
get values of 30,
40, and 30 families.
By squaring the difference
between the expected number of families at each level and the
actual number, and dividing that result by the expected value, we
get a measure at each level of the variance from the "normal" distri"
bution.
The sum
figure 16.67.
of these three variances is x2 , in this case the
A table shows that the probability of this tract
aistribution occurring in a city where every tract contained a
random sampling of the metropolitan profile is less than 1 in 1000.
The tract is not a cross section.
For this study, the census figures allowed comparison at some
14 income levels and 6 levels of educational attainment.
For
the third variable, race, data by blocks was available for each
census tract.
By plotting the percentage of non-whites pegblock
a graphic co:iparison could easily be made with the graphic representation of the percentage of non-whites for the tract as a whole.
The area
chosen for this intm-tract analysis consisted of
24 census tracts in the southeast corner of the city of Cleveland.
The area was chosen because it
see.ued repre-sentative
of the middle
range of values for the socio-economic variables being leasured-in
other words,
a large number of the tracts
were in
analysis.
eous" range as measured by the inter-tract
the "heterogenIt
was
diso a part of the metropolitan area which contained substantial
.iddle
aged housing and neighborhoods and yet still
had extensive
new construction occurring in the decade of the 1950's.
The ethnic
couniodtion, further, was quite varied and in the process of change.
Sources of Data
The primary sources of aata on the social and economic characteristics studied herein were the U.S. Censuses of 1950 and 1960.
Detailed data on social ano econome
characteristics
of the population
was available by census tracts for both Boston and Cleveland
metropolitan areas for 1950 and 1960.
selected housing character-
istics were also available on a block basis for those years for
the central cities of Boston and Cleveland.
19
iviost of the data for the Boston area was gathered not from
the original sources out from the extensive ecological study
of the Boston metropolitan area for the years 1950 and 1960 by
Professor Frank Sweetser of Boston University.
Problems in
Data
In spite of the relative completeness of the data available
for the study, certain problems arose during the course of research
from the lack of comparability between 1950 and 1960 for a few of
the variables.
The 1950 Census measured the median income for
tracts and the metropolitan areas in terms of income of fatailies
and unrelated individuals together.
The 1960 Census refined this
variable into a median for family income and a median for families
and unrelated individuals.
The 1960 family income variable is
probably a much better aieasure for comparability of income levels
across the city, but it has no counterpart in 1950.
used in
family and unrelatea individuals income,
indications of very low income level in
single
areas.
areas occur,
1950 results in
areas of predominantly
.erson resiaence such as extensive
resiaent
The category,
apartment areas or student
Coupled with a knowledge of where such unusual
the variable can be properly
interpreted.
In
order
to have a variable which could ue co.pared for the two census years,
family and unrelated individual income was chosen.
Another _problema occurs with respect
to occupational
groupings.
For the Cleveland data the author grouped the occupation categories
listed in the census into two broad categories with two sub-categories
each--white collar, containing a nigher status white collar
group (professional, technicians, uianagers) and a lower status
white collar group (clerical and sales).
Blue collar consisted
of a higher status group containing craftsmen and operatives,
and a lower status group consisting of laborers, household and
service workers.
The data for Boston gathered by Professor
Sweetser divides the occupational groups into three categories,
a high status white collar group identical with the one used for
Cleveland, a middle status group (presumably white collar in nature)
consisting of clerical, sales, and service and household workers,
and one blue collar group containing craftsmen, operatives and
laborers.
A difference of opinion is evident.
To be sure, the
classification of sepvice workers given by the census is a
vague one and contains a wide variety of skills--from police and
fireien to janitor, waiters, and movie ushers.
This author felt that the predominant nature of the jobs
classified were manual and ought to be included with a blue
collar grouping.
Also the census decision to place this group in
a low position--below operatives in their listing--appears indicative
of its actual status or skill ranking in general.
A second point
of difference with Professor Sweetser is the broadening of the
olue collar category into a high and lower status or skill group.
V
from craftsmen to laborers appears too great in
The range
the
eyes of the author to warrant classification in a single category.
Therefore, for the Boston area the three level classification of
Professor Sweetser is used, and for Cleveland, the four level
system.
The results while not airectly comparable are felt
to be
The differing breakdown
of sufficient similarity for comparison.
for each city is possibly advantageous because each fits the peculiar
economic makeup of each city better.
Finally, the measurement of life cycle tendencies proved to
be a difficult one.
The percent of the population under the age of
18 as a category in the 1960 census seemed to be a useful measurement of the relative youth of families.
however, this category aoes
not appear in the 1950 Census and was not used in the Sweetser
study of Doston for either 1950 or 1960.
Instead the Boston study
used the percent of population in age categories 6-17 as a measure
for both 1950 and 1960.
0-1
It was felt that the 6-17 age group and
breakdown were not sufficiently different in
a change in
the variable.
on children in
Therefore the Cleveland and Boston data
the population is
relative terms is
nature to warrant
not directly comparable
similar enough for aaequate
Data on median school years completea
but in
comparison.
and percent
of the
population which was non-white or foreign born were directly comparable for both cities and both census years.
Additional historic aata,
on ethnic migration in particular, was useful as background information.
,P
III.
HYPOTHESIS
rrior to beginning any research,it is important to define
the direction in which the research is likely to lead and to
estimate what the results of the study might be.
Rather than pre-
determining the results of the research, this practice merely
helps to clarify the issues at stake and to focus attention on
the author's intent in undertaking the study.
What then is the desired result of the research undertaken
for this paper?
First and foremost the study seeks to measure
wrether heterogeneous neighborhoods ao in fact exist in cities.
Are they a comion or unique occurrence numerically?
Secondly,
what has been their direction of change, numerically, between 1950
and 1960?
What different results occur in testing neighborhoods
for heterogeneity with respect to a single social characteristic
and when seeking neighborhoods which are heterogeneous in all repects?
What is the direction or significance of the heterogeneity of the
individual variables?
Thirdly, what spatial patterns do homogen-
eous and heterogeneous neighborhoods exhibit?
these patterns have a predictaoility?
Does it appear that
How do these patterns relate
to findings by others engaged in social area analysis?
Finally,
what are the implications of these results for pianning goals
or neighborhood heterogeneity and balance--in particular with
respect to the scale or "grain" of heterogeneity?
The expected results of the research
1.
stem from the author's
particular bias concerning the tolerance of t he ordinary citizen
for diversity in his social environment.
It is therefore expected
that,by our definition, very few heterogeneous neighoorhoods will
be found in existing cities and that the tendency toward homogeneous neighborhoods will have increased since 1950.
It is further
expected that homogeneity with respect to income and occupation
will be the most acute, while characteristics such as ethnicity
(for nationality groups) will be tending toward a more heterogeneous
distribution.
On the other hand, it is expected that racial diver-
sity will be virtually non-existent
homogeneous segregation
and an extreme pattern of
with respect to this variable will be
apparent.
The patterning of homogeneous neighborhoods is expected to
follow either a concentric ring model or a sectoral pattern, rather
than following a scattered or checkerboard pattern--further substantiating the Hoyt and Burgess models (sectoral and concentric,
respectively) of urban growth and development.
If these
results are borne out they would seem to suggest a resistance
on the part of city dwellers to a very fine grain mixture of
social and economic characteristics.
This might suggest to the
planner that means other than the residlential neighborhood be
formulated for increasing the city aweller's knowledge of and
tolerance and appreciation for the diversity in his fellow man.
IV.
RESULTS OF RESEARCH
There are three analytical steps which have been used to
test the concept of heterogeneity outlined in the previous
sections.
The first step is a determination of the amount and
pattern of inter-tract heterogeneity or homogeneity present in
the case study cities, with respect to individual variables.
The second step will determine heterogeneous tracts with respect
to all the measured variables.
The third step will determine the
intra-tract heterogeneity for a small sample area in Cleveland with
respect to three of the variables.
Inter-Tract Analysis
The first stage of the study--that of determining inter-tract
heterogeneity--is just that--a first step.
Finding a large number
of tracts which mtch the metropolitan median or mean for particular characteristics does not in itself guarantee that such tracts
are heterogeneous.
The tract would have to be internally consistent
with the metropolitan distribution as well.
Using the first stage snalysis the following results were
obtained for the two case study cities:
Inc o me
Among all the variables measured (with the exception of
race perhaps) income appears to have been the one which has shown
the greatest extremes in
tract average in both cities and for both
2_5
census years.
The 1960 Cleveland figures show the greatest
extremes, e.g. several tracts in the range exceeding +5 A.L.
There seemed to be a slight increase in the extreme values in
the 1960 figures as compared to those for 1950.
High income areas
increased their average income at a greater rate than the overall
rise in income for the metropolitan area.
Conversel,y, low income
tracts remained at very often the same low level as in 1950, and
therefore lost ground as the metropolitan meuian increased.
Much
of this rise in extreme values may be accounted for by the progressive
income tax in the United States.
Because of increasing taxes in
higher brackets, these incomes must incrase at a greater rate in
order to maintain a high take-home pay.
Therefore, a calculation
of income after taxes aiight show a more across-the-board rise in
income at a more or less similar rate.
The "rich get richer and
poor get poorer" first glance conclusion is probably an overstatement.
Within the + 1 A.S. range which this paper is using to indicate
relative heterogeneity, 203 of 320 Cleveland tracts (63%) and 254
of 431 Boston tracts (59%) for 1960 could be classified as heterogeneous.
The 1950 picture is much the same for each city.
Of
2o6 Cleveland tracts, 177 (62%) fell in the heterogeneous range,
while
I82 of Boston's 436 tracts (6>) met that qualification.
Spatially, the "average" tracts arrange themselves in a rough
zonal pattern at a middle distance from the city core in both cities
26
I N CGO0m r..
+3
.
Pr-D.
-3
tCLIVELAND
1M2S3.
S21
I N 60 ME
+4
+3
tAD
-3
-4*
CLIEVELAND
2.8
I NGON\E
'50
INCOME
'%0
for both years.
This zone moved outward from the core soiiewLat
in the decade, centered at the outer areas of the central city(s)
in 1950 and beginning to reach into the first ring of older suburbs
by 1960.
As one moves toward the core, the indices get lower and
lower (homogeneous low income areas) and
as one ioves outward,
generally higher (homogeneous high income areas).
In both cities
the zonal pattern is broken by a pronounced wedge or sector of
very high income reaching from inner city areas to the periphery.
In Boston this is the western sect.or, while in Cleveland the
eastern one (plus a much smaller western sector along the lake).
This predominantly
zonal pattern interjected with a "prestige"
sector is a recurring one in both cities for the socio-econonic
variables of income-education-occupation.
Education
While income may have exhibited great extremes in values, the
analysis for education Jevel ostensibly reveals a much more gradual
uropping away from the norm.
Mandatory education through the
age of 16 in the U.S. has cecreaaed greatly the percentage of
persons with very low educational attainment.
On the other hand
the upper limit of educational attainment appears strongly fike4
at the bachelor's degree for most of the population.
For example,
the range of education extremes was only about 7 years for both cities.
however, by adjusting income and education by the measure of average
Ceviation, the differences are eliminated.
Within +-l
A.D. are in-
cluded slightly fewer tracts than the number in that rarge for the
31
E4DUCATION 'TO
+4
CLliELAKD
BDUCATCCW I(00
+-4
(),
CL1!VELAND
twis.
33
EDU(A110A
3+.
'5D
eDUCAT10A
3 gr
160
income variable.
in
For Clevelaina there were 165 of 3L0 tracts
the heterogeneous
range for 1960 and 165 or 307 (54%)
The Boston figures were 260 of 4356 (60%)
in
in
in
(56%)
19!0.
1960 and 251 of 436 (57%)
1950.
Correlation
high as is
oetween eaucation level and incoie was rather
indicated by the simiilar spatial patterning of the two
variables.
Generally,
only stuaent and somle qpartment
not share the correlation.
with high iioome.
here high education level is
the
heterogeneous zone stretched
from± the edges of the inner city all the
west sector in
not correlated
iine lowest euucation levels were ag--ain in
city core areas ana tne "average" or
for both years.
areas do
way
out to the new suouros
Tie iighest level tracts were sectoral
again--the
boston and ea stern and west-shore sectors in
Cleveland.
Occupation
In the socio-economic triad of income-education-occupation,
the occupational grouping of the population is the variable which
produced the
,reatest number of middle range tracts--though not aif-
fering substantially froni results for the other two variables.
Hovwever the nu-ioer of' middle range tracts for occuational grouping
aecreased in
both cities oetween 1950 and 1960.
the few. c-anges--be
it
the two census years.
This was one of
small--whicn could be noted in
the data for
/0
WWC&-LaOR
150
4-4
S, D
tCLUELPLND
37
% NH- OLCLAR '0
4-
t
A,
CLEVELAND
0%6
W 1A,CDLLA-QP
'5D
016
40
W J4 C OUA
'bo
In
uraer to si.plify
the mapping,
only the white collar ana
blue coiar designations were used (the two sub-categories for
Cleveland being combined and the miadle category for the Boston
data being added to white collar).
The two designations proved
to be more or less mutally exclusive as expected and therefore
only the indices for white collar are mapped.
It would not be
much of an oversimplification to envision a negative of that map
as the picture for blue collar distribution.
The figures on
numbers of occupationally heterogeneous tracts are 211 out of 320
(66%) for Cleveland and 289 of 435 (66%) for Boston in 1960, and
230 of 316 (73%) for Cleveland and 304 of 436 (70%)
in
for Boston
1950.
Relating occupations to income and education we find that the
very high value white coilar tracts are the same ones that were
high in education and income.
A check of the white collar breakdown
also shows a very high percentage of the white collar occupations
for these tracts are in the highest level (professionals, managers, etc.).
Correspondingly the tracts with the lowest white collar employment
are also the ones which containea the highest percentages in the
lowest blue collar trades.
In the middle range of tracts--
those which are heterogeneous or nearly so--the correspondence
between white collar and high income and education,
collar and low income and education breaks down.
and blue
We find that
income levels are much the same for areas of moderately high
white collar employment as those with moderately high blue collar
workers.
But despite this similarity in income levels the white
collar/ blue collar emphasis follows a strong sectoral patterning
which is. approximately
educational level.
the same as that for high income and
These findings appear to corroborate the
occupational studies by Duncan which indicated strong tendencies
toward white collar/ blue collar separation in living patterns
in American cities.
Ethnicity
Persons of foreign birth or stock and non-white persons
constitute the measures of ethnicity for this study.
Both
exhioit, extreme conditions of variation from the metropolitan
average, the racial measure exhibiting by far the greatest ektremes.
in Boston,for example, with only 4.5% of its population in 1960
Ceing non-white, census tracts containing nearly 100% non-whites
would be indexed at over 1000 with respect to the metropolitan
however, when adjusted to a standard deviation measure,
mean.
the absolute numerical extremes are dampened.
The extreme skewness
of non-white distribution results in a large value for standard
deviation.
Therefore a large number of tracts fall within the
oroad middle range.
Trnere is indication in both cities, however,
of a reduction in this aiddle range over the 1950-o0
In
(93%)
Cleveland 270 of 50 tra-cts (64')
trActs wiere in
and in
the heterogeneous range in
period.
Boston 404 of 436
1960 with respect
to this variable.
For 1950 the figures are 275 in
for Cleveland and 414 in
436 (97/)
in
homiogeneousghetto in
one which begins with a concentration in
then iegins a sectoral
pattern outward in
Boston the non-white
ea stward,
it reaehes
wedge
(9)
for Boston.
The pattern of the non-white
is
307
the core
each city
area and
one or two directions.
aioves soutward,
dividing into two segments northeast
while in
Cleveland
and southeast when
tile city oorder.
The foreign born population does not exhibit such extreme
conditions as those
for non-wjhites,
of. concentration in
both cities.
tracts are 224 of 320 (70,O)
for Cleveland.
436 (60;%)
For
o;ton
and 339 of
in
tn
436 (7
out it
The figures for heterogeneous
1960 and 219 of 506 (71%)
in
cures
-4b of
juaing figures are
,atterns.
1950
) for 1960 and 1950 respectively.
The very high oand very low indices for foreign birth in
form distinct
patterns
aoes exhibit
Ooth cities
Tnis is generally a sectoral pattern
with greatest concentration in
becoming more heterogeneous
or near the core area,
as one
moves outward.
the sector
In Boston the
iorthern and southern sectors show this high rate of foreign birth.
In
Cleveland it
concon-tration in
is
the northeast
and southeast sector,
the eastern suburbs.
ponas in hoston to the high
Low foreign
plus a
birth corres-
prestige western sector; out in
Cleveland only one of tne two high prestige sectors -- the west shore-shows this low inciuence.
The high stLatus eastern sector is
I/V NON-\N qTBn '50
-'
+35
-3
-4
CLEVELAND
tAl.
S
2,
3
4
-
ITE
%N*NNWR
CLl!VELAND
k
4S-
2,
3
14
6 0
%NAON- W1WTE
7NON- VITE
BO
e
47
%7FOZE16N BW . 15~0
4-3
'4
-3
CLEVELAND
S
2,
3
14
%kFDWZ&MI 9N. 16t
CLEVELAND
EtAIlt
rElM
-3
%Y
FOR9(4
BN 6-A
ISO
'o FoPE01N BN. (U
coa_,osed of
iany persons of eastern European stock and therefore
exhibits traces of the recentness of that iiaigration.
The 1960 Census included a category known as foreign stock,
which included those of foreign birth plus those native born with
one ur both parents of foreign birth.
A breakdown by country of
birth of the foreigh born person in the family gives us a picture
of the
iajor nationality stocks represented in each city.
For
Boston the two groups which are by far the most numerous are the
irish and Italian population.
Since Irish immigration was much
earlier than the Italian, the percentages of Irish stock are not
as high in the population.
Even with this limitation, a distinct
patterning shows up in ethnic stock concentrations.
Italian concen-
tration in Boston is in the northern sector, Irish concentration
in the southern.
There appears to be an inverse relationship
among the two stocks.
,here Italian concentration exceed 20%, Irish
stock is never above 20%, and vice versa.
In Cleveland, four groups still exhibit a strong patterning
of relatively homogeneous nationality grouping.
The Poles occupy
the southeast sector of the city, the Yugoslavs the northeast,
the hungarians a pocket on the east side, and the Italians several
pockets primarily on the east side.
Some remnants of a Czech
community parallelling the Polish one of the east siae is still
evident as well.
These Cleveland patterns have been in existence
for at least 3O years as 1930 aata inaicates.
(geierally Jewish)
Only the iussian
and
community has been noticeably mobile
has dispersea--in the wake of non-white immigration for the most
In ooth noston ana Cleveland the nationality sectors
part.
widen and get more diffuse as they move outward from tie central
It is likely, due to the small amount of immigration in
city.
the past 30 years,
that these ethnic communities will slowly dim-
inish in
size or disappear entirely within a generation.
general,
as previous studies have pointed out,
immigrant
groups (19th centry)
In
the "early"
have become more assimilated into
the total population than the later-arriving eastern and southern
j1uro.eans who still
of th e
mAntain ethnic communities.
,\u ssian Jews,tiese
ith
the exception
ethnic comunities are associated with
olue collar trades.
relatively low eaucation level and
Life Cycle
netermining whether
patterns in
level.
there is
the case study cities
some homogeneity of life
is
cycle
handled at a very superficial
The variable of percentage of the population which is
composed of children was used as the only test.
might have been expected in light of literature
Contrary to what
on the child-eentered
suburbs and childless inner city, the extremes for this variable
are about the same as tnose for the socio-economic variables.
or example , the 19O figures show 241 of _20 Cleveland tracts (73%)
in
the heterogeneous
that range.
in
193
range and
62 of 436 Boston tracts (C03%) in
the corres onding figures are -26
of 307 (74%)
%le C WLDOPEN
'50
O/j(~p~+'I~
I.S, D-
CLEVELAND
M
k.
S2,
3
4
% CAILDdEN
'620
4-3
4-3
-4
_-s'
CLEVELAND
2,
3
14
/H
DW
%/ C-DREAI 'b
97
in Cleveland and
333 of 436 (?6%) in Boston.
To be sure it is
evident that many inner city areas in both cities fell to below
average aaounts of children in 1960 as compared with 1950,
the new suburbs gained chilaren;
ana
but the middle range of tracts
remained very stabie in size.
TLe pattern of heterogeneous and homogeneous tracts with respect to children is primarily a zonal one for the white community,
and appears independant of the sectoral influences evident for
the socio-economic variables of incoae-education-occupation.
high value tracts in the central city generally reflect non-white
population concentration.
Heterogeneity of All Variaoles
Vhen we search for tracts which fall within the middle range
(+ 1 S.D.)
for all variaoles, we find considerably fewer than the
number in that range for any one variable.
There do appear to be
a relatively small numoer of tracts which qualify for the heterogeneous label in
320 (20%)
both cities.
in 196U and 84 in
141 in 436 (32%)
The figures
307 (27%)
in
for Cleveland
1950.
in 1960 and 136 in 436 (31%)
are 65 in
For Boston they are
in 1950.
Is there some rationale oehina the location of these tracts?
hiey au appear to be part of a zonal pattern at a position midway
TABLE I
INTER-TRACT. HETEROGjEITY
(Index)
S.D.
(or A.D.)-5
IhCOME
EDUC.
+2
262(65%)
254(59%)
46
61
'+-)0
- -7
11
18
64
10
11
0
0
1
1
40
29
60
51
251(57%)
260(60%)
82
79
436
456
30
0
0
0
54
304(70%)
52
0
a
436
435
0
0
0
0
0
0
4
0
43
27
339(78%)
34
348(80%)
43
4
42
322(?4%)
57
553(76%)
362(85%)
41
20
'60
22
'50
'6o
30
0
0
412
326
'50
32
'60
46
0
o
0
FOR.ST.
'60
2?
0
0
%/ CHILD.
'50
'6
24
25
62 269(66%)
1
1
436
436
436
5
4
268
165(54%) 80
4
4
0
0
307
21
11
0
0
316
320
5 18
57 0
507
177 (62%)
'60
26
0
203(63%)
'50
'60
14
13
0
0
WH.COLL.'50
'60
59
54
'50
'60
222
203
'50
'60
46
66
F0R.ST. '60
46
% CHILD.'50
27
'60
19
'60
9
9
7
0
ALL VAR.'50
436
436
46
40
22
FOIR.Bi.
436
436
414(97%)
404(-93%)
'50
NON-WH.
64
141( 32%)
'An
EDUC.
431
136(51%)
ALL VAR.'50
IhC0E
+3 +4 +5
15
i\ON-WH. '50
'60
FOR.BNI.
48
TOT-
1i S.D.
16
17
'6u
-2
3
0
'50
WH.CuLL. '50
hUMBER OF TRACTS WITHIN:
-3
5
53
185(58%)
21
0
o
230( /3%)
211( 66%)
41
0
0
275(89O)
9
270(64%)
13
219(71%)
37
6 104
38
320
320
320
308
9
320
224(70%:)
0
0
19
51
226(71%) 41
226(74%)
241( 75%)
64(27%,)
65( 20%)
3
0
0
320
307
320
N
between the central core area and the peripheral suburbs--their location Uetermined to a large extent from the income-educationoccupation variables.
From these socio-economically heterogeneous
tracts are excluded the sectors of tracts with heavy concentrations
of foreign born, non-whites, and those beyond the middle range for
The 1950-60
percentage of the population coiposea of children.
aifferences in the heterogeneous band appear to be more the
'esult
of the metropolitan area growing larger than any other reason.
The zone
ierely
ioved farther out from the expanding low status
core as iore higher status outer suburbs were added.
Intra-Tract Heterogeneity
The test area for intra-tract heterogeneity in Cleveland lies
at about the location of the relatively heterogeneous southeast
side tracts.
Since only a few of the 24 total tracts in, area
exceeded the + 1 A.D. range for the income and education variable
being used in the intra-tract analysis, all the tracts were
analyzed for their "goodness of fit" with the metropolitan distribution.
The chi square test produced very disappointing results if
our goal vas to match the metropolitan profile.
iBone of the tracts
fell within the probability range of 1 in l000(which was the limit
of the table used for analysis) with respect
and for either census year.
to either variable
Of course some tracts came closer
TABLE II
IhTRA-TRACT HETEROGENEITY
IhCOME
EDUCATION
1960
1950
A.D.
CT
x
S3 - -5 173.8 -. 001
Ii
4 + .3
110.2
"
5 +1.9 1988.1
ii
6 + .2 158.4
"
+ .4
112.0
"
8 - .6 210.6
9 41 .1 23.6.
"
T5 + -5 237.5
"
6 - .1 150.3
"
7 + .1 147.6
it
8
9
+
.2
202-.8
+
.4
186.1
Ul +1.1
2 + .6
3
-
-1
4
+
.b
5
+
.5
6
7 +1.8
6
9 +1.3
vi
2
3
-
.o0
301.1
193.6
46.4
3b2. 6
162.9
76 .6
600.3
12_.7
64.9
155.0
221.6
82.1
A.D.
Prob.
-1.1
-
818.8
90.5
1660.6
118.0
0 122.9
.35
+
.6
469.o
-
.3
157.7
-
-
156.o
.6
-..234 249.4
.6
379.4
-
.4
Ii
+
.1
"
- .1
"i
x
"
360.3
83.7
630.0
101.9
+
.2
45-7
-
.1
Ii
+
.2
"i
-
.1
"i
+
.8
84.6
150.5
96.5
195.4
o7.6
77.4
1?7.3
190.6
121.0
"I
"
"
"
"
"
+
.4
-
.5
+ .3
1950
Prob.
A.D.
x'
1960
Prob.
-.00l1
-
.7
553.1 -. 001
ii
-
.6
690.6
II
I,
vi.4 3316.6
-1.0
328.2
.1
1413.4
II
"t
"
ii
"t
"
Ii
ii
Ti
"
ii
"
I,
"i
"
"
"
"
"
"
"I
-
.7
-
.6
-1.1
-1.1
ti
i"
396.5
It
408.1
441.5
i
1416.8
t
It
.9
492.2
.9 1019.1
-1.0
407.9
-. 9 128.8
660.6
.9
.8
199.3
.4
121.3
.?7 196.9
57.3
366.2
+1.1
- 3
37.2
+ .5
-. 35 121.2
37.3
+ .?7
-1.1
434.5
131.2
A.D.
-1.2
+1.0
+1.0
-1.5
-
.7
+ .2
-
-1.3
-1.5.
-1.0
-
ii
"
It
ii
ii
ii
"I
"t
Ii
"
it
.2
.5
-1.0
-1.5
-1.3
-
.9
-1.2
-
.8
-
.1
+
.6
+ .7
- .8
+
+
.1
.1
x
Prob.
946.4 -. 001
"i
393.5
1489.4
1045.2
223.8
It
150.8
it
72.9
472.9
989.5
"t
434.1
388.8
384.4
533.6
338.6
"i
"t
"t
"t
"t
ii
"t
ii
it
245.5
"t
460.7
199.5
86.2
ii
170.9
97.4
137.3
61.3
143.7
63.7
"t
it
it
"I
I"
"i
ii
"t
than others, but none came within the probability range which
would give confidence to a suggestion that it was a cross section
of the metropolitan aistribution.
There did not appear to be
any relationship, either, between the average deviation value for
the tract and its chi square size.
Clearly here is a situation where the tract median did not
represent the whole story.
What appeared to be heterogeneous tracts
in 1950 and 1960 were actually tracts with medians similar to the
metropolitan norm, but with a range of values making up the norm
of considerably different character than was the case for the
A.etropolItan area as a whole.
Getting to the third variable, race, we find that the maapping
of percentages of families which were non-white by block within
a census tract shows a very strong tendency toward concentration of
these non-whites in particular blocks within the tract, rather than
in a random distribution throughout the tract.
There is evidence
of boundary lines for the non-white community which are either
implicit or explicit in the pattern- of non-white migration.
The
very sharp lines separating a predominantly Negro and an all white
area are indicative of such unwritten rules.
1 here
gradations are
softer, the line has probably been broken by a new push of migration
and more than likely a new artificial "containingi
line--a street,
a railraod, or a park--will be set up within which the I\egro
62
community will expLand toward 100% non-white saturation before
another area is "opened up".
The studies by Duncan in the
Chicago 1hegro community show similar patterns.
From this intra-tract analysis it ap pears evident that heterogeneity at a scale below the tract
itself is more difficult to
achieve in most cases than at the tract level.
In fact, if we
may generalize from this study area, a strict cross section goal
is virtually unachievable at this small scale,
63
V.
CONCLUSIONS
Despite the narrow confines of the relatively unsophisticated
uefinition of heterogeneity used in this study, some useful conclusions may be arawn--be they only ones of a negative nature.
First,
from the quantitative results of applying the cross section
criteria to existing cities, it becomes apparent that the criterion
in both its dimensions--both inter and intra-tract level--is virtually unmet in these cities.
By exploring inter-tract and intra-
tract heterogeneity separately, we find that at an inter-tract
level a large and consistent number of tracts fall within a middle
range of values for all variables, when they are adjusted for
scale differentiation through conversion to standard deviation
measure.
It is not so important that the middle range is a crude
and large one.
An important aspect, rather, is the relative
similarity of numbers for all variables.
This is not good support
for a theory which would speculate that certain socio-ec onomic
characteristics were becoming more or less diffused or concentrated
in the metropolitan pattern.
The only possible
contention which may be somewhat substan-
tiated by these figures is the direction of the number of tracts
in th e middle range for the variables of race, occupation, and
educational level.
For occupation and race, fewer tracts fell
within the middle range in 1960 than in 1950;
for education
level, more tracts fell within the middle range in 1960 than in 1950.
Directions of change for other variables were non-existent or
contradictory in the two cities.
The number of tracts which met the inter-tract average
criterion for all the variables taken together was considerably
smaller than the numbers for individual variables.
Furthermore,
there was an apparent downward direction in this number for one
of the cities--Cleveland-- over the 1950-60 decade.
The explan-
ation for this phenomenon is to a large extent the lack of
correlation between the socio-economic variables of income-education-occupation (which produced similar numerical results and
spatial patterning) and the ethnicity and life cycle variables.
These latter two cut across the socio-econonic variables to such
an extent as to cancel out many otherwise "average" tracts on the
basis of excessively high or low concentrations of foreign born,
non-whites, or children.
At the intra-tract level, any hopes of finding cross section
tracts at both dimensions quickly vanished.
Although only three
variables were able to be measured in this dimension--income,
education, and race--the lack of "fit" of tracts in a sample area
with the ietropolitan profile for these variables was virtually
total for ooth census years.
A second conclusion which might be drawn from the data is that
the definition of heterogeneity used herein is indeed too unsophis-
65
ticated and simple.
As well as being too simple a goal for the
complex interactions and interrelationships of human beings, it
would statistically be a "freak".
So fine a grain of mixture among
a large conglomeration of persons would be a rare find.
Like
the mixture of the components of concrete, only constant and incessant moveient of the parts of the whole could be expected to produce
a iixture so devoid of "lumps".
While the analogy may be strained,
there is a glimmer of truth in it.
The Cleveland and Boaton data
suggests that while new suburbs and developments may exhibit
extreme characteristics, the successive movements of population
through them tends to increase their diversity.
Each successive
wave of population may leave a residue of its population to add
"balance" to the new group succeeding them.
This concept does not
hold for social migrations where prejudice plays a part in interrupting this process.
however, the older suburbs of both Boston
and Cleveland, in changing from early homogeneous settlements of
those of high class, became iuch more diversified as succeeding
waves of lower status resiaents passed through them.
It is there-
fore conceivable that many, many more waves of migration through
these areas, in miore than one direction, may result in an even
greater mixing and an even finer grain of mixture.
A third conclusion from this study imiight be its suggestion of
alternative ways of approaching and analyzing the problem.
If,
as we have concluded, very little correlation with a cross section
model exists in today's cities, and if the achievement of such a
fine grain of mixing appears to be tied to mobility patterns and
time, what kind of definition and objectives can we or ought we
to formulate for achieving heterogeneous cities immediately?
We could, of course, attempt to build new cities or neighborhoods
which met the cross section goal--necessarily through coercian and
e xtremely careful control and selection of residents, 'it would
app-ear from this study.
criteria,
Alternatively,
modified cross section
less stringent than those used in
this study, might be
applied with more success.
On the other hand, taking the suggestion of Herb Gans, stated
in the early part of this paper, we dight seek out the apparently
inherent interreiationsLips
i the social life of the block, the
neighborhood, the district, etc.
According to Gans, only when we
fully understand the workings of these interrelationahips can
we mieaningfully propose social planning schemes.
He seems to
suggest that there may be a minimum and/or maximum number of
persons or families of relatively homogeneous characteristics
necessary for social stability in a small area.
Rather than applying
a single nugerical objective for the parts which make up the
mixture--as the cross section goal does--the numerical criteria
would rather be in terms of maxima or minima for various scales
and possibly for individual socio-economic characteristics as well.
It is suggested that future study ought to be at the intra-neighborhood
level, seeking to find the imnortant and relevant interrelationships and their corresponding numerical expression in criteria
by which existing cities can be judged and new ones planned.
The Gans approach is not the only other one which could be
fruitful.
Elizaceth Wood's definition of "balance" was that
of neighborhood equilibrium--a continuous movement through a
neighborhood allowing its socio-economic profile to remain stable.
Although it is. assumed that Miss wood's neighborhood in equilibrium
is also one which is not all of one class or ethnic group (e.g.,
she would not want a low class area to remain low class forever),
the criterion of stability proposed by her could be tested against
existing cities to examine its liklihood of occurence.
Finally, attention might be given not to the traditional
neighborhood units as such but toward the relationship between
neighborhoods--the total configuration of the metropolitan
as a continuous fabric.
area
It might oe argued that while homogeneous
concentrations of extreme characteristics will continue to occur
in our cities, by making the transitions between concentrations
smooth rather than rigid--these areas fluid rather than fixed-the individual may exercise freedom of choice in identifying with
and experiencing greater or lesser diversity of environment on the
basis of his desires or potential.
This final proposal for a concept
of heterogeneity may be the most elusive for study ana need to
be approached from a negative angle, i.e., attempting to eliminate
slharp boundaries and "allow" mixing to take place.
The data
gatherea in this study indicates some evidence of this gradation
at work for many of the variables, the most notable exception,
however, being the pattern for race.
In
aUdition to clarification of the definition of heterogeneity
and standards for its implementation, a very important coacern in
this discussion will need to be the one which this paper has carefully avoided tackling--that of why should our cities, neighborhoods,
or what have you be heterogeneous or balanced.
If the
reasons are based on social goals, should we not examine whether
the physical patterning of people of varying socio-economic characteristics is the correct vehicle for the achievement of these
uals?
With more security in this area of social goals, it may
become more clear which of the several ap roaches to defining and
quantifying heterogeneity will be most fruitful.
APPENDIX I
INTER-TRACT HETEROGENEITY-SELECTED VARIABLES
CLEVELAND
MET. AREA
AVG. VALUE
INDEX
$3451
$6038
10.4yr.
11.0yr
100
100
100
100
35% 40% 65% 60% 11% 16% 13% 10%
100 100 100 100 100 100 100 100
EDUCATION2
INCOME 1
34% 24% 34%
100 100 100
5LIFE CICLE
% FR.BN. %FR.ST5 0-18
(index) (index)
'60 '50 '60
'50 '60
(index)
'60
'50
OCCUATIONS ETNICITY
% BL.CL. % N. WH.
%WU.C1k
(index)
(index)
(index)
(index)
'60 '5o '60 '50 '60 '50 '60
'50
Al
109
85
118
110
169
133
63
28
1
1
72
138
124
41
64
2
90
82
96
87
83
53
109
132
0
3
119
127
110
100
87
3
100
86
103
91
114
80
92
113
4
4
75
136
108
87
83
4
108
104
90
90
91
63
105
125
1
1
129
129
120
87
87
5
101
94
92
93
94
68
103
122
0
4
113
117
113
100
99
6
104
99
94
90
97
65
102
123
0
1
95
149
110
87
88
7
96
93
93
87
91
65
105
123
2
2
89
112
99
87
88
8
92
80
89
82
63
50
120
133
2
12
101
132
100
100
90
9
102
85
92
85
83
63
109
125
0
1
102
155
113
144
98
TRACT NO.
1Income of Families and Unrelated Individuals
3 Years
of Education of Persons over 25
Males in Profess., Tech. Manag., Clerical, Sales
Serv. Occup. in Boston)
4 (Also those in
Males in Craftsun, Operatives, Laborers (also
Serv. Occup. in Cleveland)
5Foreign Born plus Native Born of
6oreign or Mixed Parentage
0-15 Group in 1950 for Cleveland
6-17 Group in '50 and '60 for Boston
Bl
109
104
98
94
100
80
100
113
1
1
129
159
132
87
83
2
118
108
104
95
117
90
91
107
1
1
114
130
128
87
97
3
105
100
99
92
97
63
98
125
0
2
108
146
118 100
91
4
107
99
92
89
94
73
103
118
0
2
101
122
110 100
97
5
104
90
91
81
66
40
118
140
2
1
99
124
104 114
103
6
95
87
87
80
60
40
122
140
0
0
115
129
103 114
126
7
106
92
85
81
66
50
118
133
1
0
1-14
97
104 114
99
8
100
90
88
81
60
50
115
133
0
1
127
153
126 114
92
9
100
94
85
80
74
58
114
128
1
1
167
205
160 100
96
Cl
89
77
86
83
66
58
118
128
6
1
157
200
117 100
102
2
71
64
85
77
49
38
128
142
5
3
87
98
59 100
102
3
60
33
86
79
63
45
120
137
9
20
64
105
87 144
105
4
88
83
86
83
60
48
115
135
0
5
104
148
103 100
99
5
88
82
87
79
57
28
123
148
1
3
119
135
90 100
101
6
71
60
86
78
57
43
123
138
5
5
130
111
80 100
91
7
58
65
77
75
29
30
138
153
63
8
136
107
96 114
119
8
93
89
88
80
63
40
120
140
1
1
136
137
94 100
104
9
94
A80
84
79
57
40 ~123
140
1
0
145
140
102 100
106
Dl
83
74
85
79
51
40
126
140
1
1
139
174
114 100
115
2
85
83
84
79
54
45
125
137
2
1
171
242
149 114
109
3
77
72
82
75
40
25
139
155
3
1 200
248
133 114
119
4
94
90
87
80
60
48
122
135
2
3
162
229
144
5
91
78
84
77
57
30
123
147
0
0
191
261
159 114
6
87
87
88
81
77
48
112
135
0
5
122
129
122 100
99
7
77
61
89
80
63
45
120
137
1
11
128
150
110 144
127
8
109
91
86
80
69
55
117
130
1
6
132
167
136 100
109
87
97
119
9
94
92
84
80
69
48
117
135
0
4
138 187
133
100
85
El
106
97
87
86
66
53
118
132
0
1
133 133
120
100
88
2
110
88
84
83
83
48
109
135
0
0
142 194
145
87
91
3
105
93
88
83
80
55
111
130
0
0
130 156
146
100
88
4
100
97
92
88
89
63
106
125
1
1
96 135
118
87
93
5
101
88
97
88
100
80
100
113
1
1
82 155
119
87
113
6
92
88
89
90
66
68
120
122
20
19
106 118
110
87
92
7
123
114
93
92
88
75
108
117
0
0
108 126
122
100
101
8
106
92
90
86
88
65
108
123
5
2
120 135
130
100
88
9
110
108
94
90
89
90
106
107
0
0
102 133
134
100
85
130
118
96
100
111
133
94
78
0
0
100 125
145
100
77
2
116
111
98
95
94
78
103
115
1
1
101 114
126
144
97
3
103
102
87
89
97
83
102
112
0
1
110 177
142
87
90
94
91
91
83
63
109
125
0
0
135 152
123
100
99
Fl
4
5
122
110
88
89
91
85
105
110
1
0
141 202
164
87
80
6
109
102
86
83
91
80
105
113
1
0
154 170
152
87
85
7
131
115
94
110
146
128
75
82
0
0
98 102
129
87
80
G5
61
50
83
73
43
73
131
118
60
85
143 185
103
114
94
8
54
35
88
84
83
70
109
120
68
67
79 114
94
41
26
9
52
32
87
83
117
115
91
90
133
138
75 101
86
100
84
H2
90
72
82
77
46
60
129
127
1
1
180 260
159
114
94
3
92
85
83
77
51
38
126
142
16
22
147 223
129
100
95
4
86
72
82
78
46
45
129
137
40
32
138 186
112
114
100
6
76
55
83
80
54
43
125
138
36
100
116
82
72
114
88
7
58
44
78
75
51
40
126
140
665
534
18
12
14
100
103
8
51
40
86
76
63
53
120
132
647
490
27
18
16
41
73
1
m
M
50
35
86
78
26
48
140
135
879
631
2
0
1
144
158
13
56
27
71
76
20
15
143
157
811
444
16
26
21
144
126
5
52
42
69
70
26
28
140
150
503
431 105 112
60
114
94
6
41
29
61
70
20
3
143
165
794
612
34
13
8
114
119
7
47
80
65
100
17
73
145
118
888
608
5
0
1
144
121
8
47
36
89
81
37
25
134
150
895
640
0
0
1
144
155
9
54
40
72
66
20
18
143
155
894
634
6
6
3
114
131
J4
80
73
80
78
34
45
135
137
35
57 118 127
99
114
123
5
78
68
84
80
57
40
123
140
5
2 135 148
114
100
90
6
90
72
81
75
46
28
129
148
5
3 123
83
85
114
114
7
114
98
85
80
40
45
132
137
22
8 102 119
121
114
109
8
91
80
82
80
49
55
128
130
1
0 141 142
131
100
96
9
95
90
84
80
54
63
125
125
2
0 139 158
150
100
92
KI
86
72
80
78
51
48
126
135
0
1 201 226
143
87
93
2
88
81
85
80
51
55
126
130
9
67 161 206
127
87
96
3
91
88
82
78
51
53
126
132
21
0 178 215
149
100
95
4
98
85
90
90
77
53
128
132
5
56
46
100
111
5
101
86
85
80
57
83
123
112
1
0 190 292
186
87
83
6
97
84
83
80
66
60
118
127
1
0 184 254
166
87
84
7
102
93
83
83
60
55
122
130
1
1 171 216
161
87
85
8
101
90
90
82
77
33
112
145
1
38 147 229
149
87
96
9
90
79
87
85
69
65
117
123
155
117 122 146
118
87
88
Li
93
72
85
80
69
30
117
147
6
371 123
78
58
100
122
2
101
69
95
82
83
40
109
140
5
519 105
32
21
87
116
3
80
60
84
79
51
28
126
148
73
539
90
18
12
100
131
90
62
89
82
74
20
114
153
47
586
86
13
10
87
142
-
474 142
~w
5
82
59
98
82
80
28
111
148
47
573
83
12
12
41
119
6
85
66
101
84
89
23
106
152 107
571
70
13
10
87
131
7
64
51
86
84
57
15
126
157 139
413
62
17
26
87
108
8
76
56
98
83
83
30
109
147
40
441
68
24
20
41
97
9
57
44
83
77
29
13
138
158 842
624
7
3
2
87
107
M1
71
50
102
86
86
58
108
128 357
457
41
29
26
41
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Ni
67
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Si
61
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87
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81
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125
23 229
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140
115
100
101
Ti
86
90
7
101
85
87
77
58
112
128
73 355
173
121
83
87
94
8
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89
93 100
58
100
128 225 534
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59
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102
87
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182
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123
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132
12
28
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100
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7
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3
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3 156
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133
CHI
153
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173
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ECI
118
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L02
1
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119
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101
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132
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124
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101
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142
179
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223
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18
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362
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233
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136
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92
101 120
114
107
2
149
134
119
110 197
170
48
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109
184 164
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96
BAl
156
160
122
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200
34
33
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41
43
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BD1
110
125
115
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115
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112
117
116
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103
0
2
74
65
87
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107
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102
108
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113
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1
102
85
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107
BEl
110
103
119
110 109
110
95
93
64 132
12
26
50
144
147
2
117
125
117
113 140
155
78
63
5
3
39
38
65
114
119
3
48
54
121
113 151
130
72
80
41
39
31
49
64
100
BKl
117
121
109
102
97
80 102
113
0
0
50
77 111
144
114
CC5
98
109
97
103
91
80 105
113
1
4
62
40
68
144
121
6
-
129
119
112 177
153
58
65
0
0
38
35
54
114
123
7
-
128
-
110 106
105
97
70
0
0
-
40
74
114
124
9
-
155
-
111 147
145
74
70
0
0
-
47
83
144
114
11
98
116
109
110 100
85 100
110
13
1
47
28
64
144
143
12
121
143
113
110 117
128
91
82
6
1
70
61
96
144
118
13
107
123
97
109 109
105
95
97
2
1
55
42
73
100
125
14
-
120
98
109
94
88 103
108
0
0
69
33
72
144
122
18
115
116
97
109
86
105 108
97
0
0
83
56
98
114
111
103
80
82
19
-
125
102
109
94
85
103
110
0
0
74
48
85
100
125
20
10 1
102
86
83
69
50
117
133
0
0
120
128
146
87
91
22
-
116
98
63
53
120
132
0
0
-
103
122
100
95
23
-
128
115
110 114
93
92
105
1
0
57
46
100
144
108
24
-
146
101
109 103
115
98
90
0
0
103
84
126
114
110
25
12 4
133
102
105 126
118
86
88
0
1
75
64
120
114
113
26
11 4
131
93
94
123
103
102
1
8
83
56
97
114
110
27
12 7
157
118
113 160
165
68
57
9
3
44
51
93
41
71
28
11 0
119
119
115 177
168
58
57
8
12
121
172
107
114
116
CC29
-
108
100
100
74
63
114
125
10
6
59
18
86
114
116
30
-
143
113
109 114
115
92
90
1
2
104
87
136
144
113
35
-
245
124
116 229
223
31
18
11
4
54
100
135
144
116
36
-
107
113
-
2
-
56
82
113
4
127
113
2
1
65
79
113
107
40
99
93
95
137 192 172
56
56
64
144
114
41
98
143
92
42
-
43
109
80
99
82
110 120
128
89
87
71
45
115
110
57
118
120
88
96
5
62
68
114
144
121
141
110
94
113
103
92
0
1
-
68
105
114
118
-
144
112 160
148
68
68
0
4
-
52
115
144
110
45
-
171
122
120 186
210
54
27
10
13
73
67
76
100
91
46
-
242
125
120 209
203
42
32
5
4
47
66
97
144
104
49
-
142
115
111 131
135
83
77
5
1
111
84
116
100
109
50
14
132
114
111 123
130
88
80
9
0
69
57
96
144
118
-
203
122
128 189
208
52
28
5
2
55
45
89
114
118
02
118
119
115 160
168
68
55
0
1
40
43
47
100
101
37
52
55
12
14
00
FP1
138
136
118
112 174
160
60
60
0
1
61
66
87
144
103
LHl
143
157
119
114 169
170
63
53
1
0
65
76
100
144
122
2
-
138
-
-
140
-
73
-
2
-
106
124
-
103
MYl
124
126
115
110 120
128
89
82
2
1
69
105
123
144
117
2
-
129
-
-
125
-
83
-
1
-
89
127
-
110
N01
127
129
114
110 126
130
86
80
1
1
71
66
86
144
117
2
121
131
111
110 -126
128
86
82
0
1
59
60
85
114
120
PH1
124
129
118
110 157
145
69
70
4
0
62
74
111
144
113
2
-
141
-
-
135
-
77
-
0
-
72
94
-
125
RR1
194
183
122
119 237
205
26
30
3
1
41
51
65
100
102
2
150
144
119
114 203
185
45
43
2
1
64
73
84
114
91
UH1
WL1
176
118
144
138
121
114 246
210
22
27
8
1
111
140
157
114
97
116
111 140
140
78
73
1
1
76
65
88
114
112
111
110
112
BOSTON
MET. AREA
AVG. VALUE
- 16%
100
'50
13%
100
'60
41%
100
'60
16%
100
'50
20%
100
6
117
115
131
94
100
0
31
103
100
117
106
95
148
5
0
119
123
134
125
105
128
142
5
2
125
123
127
113
100
62
138
140
8
0
143
146
141
113
100
58
68
142
146
8
0
138
192
153
106
90
76
54
62
146
140
0
10
144
154
149
118
95
75
76
58
45
142
161
8
4
144
192
161
125
90
55
81
77
66
79
134
123
5
28
81
108
107
175
140
74
75
74
75
56
50
144
155
5
0
144
277
235
113
95
5A
87
83
77
76
52
47
148
159
0
0
156
231
173
106
100
5B
90
89
79
78
60
69
140
134
22
4
118
131
134
118
105
C2
87
73
90
90
80
69
120
134
8
21
75
85
85
156
125
3
90
82
95
94
82
84
118
117
5
4
68
69
83
137
115
Dl
80
73
85
78
76
83
124
119
35
0
75
69
95
132
120
2
96
71
85
81
58
69
142
134
5
87
85
105
132
120
3
87
85
91
90
72
81
128
121
8
6
4
75
69
88
113
115
4
93
89
88
83
72
56
128
148
5
4
75
77
97
137
115
El
77
80
79
85
62
73
138
129
117
23
82
69
88
118
100
2
83
83
90
94
80
77
120
125
13
13
87
77
107
94
95
F1
67
67
65
78
52
79
148
123
74
80
175
169
117
94
55
50%
100
'50
47%
100
'60
90
102
111
0
78
86
122
115
84
60
56
140
79
87
72
62
75
79
78
62
80
82
77
76
B1
80
82
74
2
80
75
3
83
4
50%
100
'50
53%
100
'60
96
98
87
91
94
80
93
92
5
87
6
c0:
1l.2yr.
$3112
$5561
100
1n
100
TRACT NC.
'50
'60
'50
Al
112
98
94
2
106
102
3
103
4
T XT1V
11.4yr.
100
'60
5%
2%
100 100
'60
'50
'60
80
oz
73
72
74
68
73
132
129
0
2
182
224
173
106
3
58
78
106
114
132
86
64
35
76
82
177
124
100
65
4
77
88
74
70
79
130
123
5
0
100
246
176
100
85
5
74
73
72
70
62
130
140
5
10
182
239
173
100
85
6
48
96
97
134
124
66
72
39
36
118
139
124
25
10
Gi
38
75
66
158
171
42
19 2296 1384
57
385
188
57
60
2
48
75
68
134
130
66
66 1130 1054
137
284
173
63
60
3
65
89
106
138
113
62
85
83
450
137
224
137
13
35
4
45
91
74
112
139
88
56
904
626
113
208
115
87
100
Hi
74
78
83
94
77
106
125
48
8
163
185
163
100
90
2
74
75
118
-
26
0
182
154
49
113
60
3
45
101
106
128
173
72
17
117
284
132
77
85
82
20
4
61
79
80
100
100
100
100
18
13
156
215
146
63
45
Ii
45
77
75
102
115
98
83
569
469
156
215
119
94
90
2
58
75
72
86
122
114
74 1226
786
132
331
151
113
75
3
46
76
75
112
106
88
93
266
306
168
185
127
63
60
4
41
78
83
86
75
114
127
243
806
118
92
68
113
135
Ji
48.
88
82
132
130
68
66
113
97
175
208
137
43
25
2
38
81
94
124
122
76
74 2961 1328
57
108
71
50
45
3
61
108
105
134
139
66
56
78
73
113
146
110
31
20
4
54
105
100
116
120
84
77
474
571
106
131
105
57
45
5
54
109
106
134
130
66
66
213
145
100
154
110
25
20
K1
74
110
110
136
139
64
56
61
56
106
108
1o3
50
25
2
70
116
134
176
173
24
17
22
22
87
92
76
25
20
82
oc
3
54
60
116
128
178
167
22
23
26
34
82
77
73
25
10
4A
38
15
114
125
164
162
36
29
65
58
75
69
71
19
20
4B
87
64
112
110
146
141
54
53
26
58
87
131
110
31
15
5
65
60
115
120
174
162
26
29
26
32
94
92
78
19
15
Li
38
33
84
78
112
113
88
85
505
534
150
200
117
43
40
2
51
46
83
82
110
83
90
119 3274 2002
31
69
39
50
45
3
45
42
79
78
84
79
116
123 2052 1580
87
115
64
57
50
4
51
39
73
73
98
73
102
129
400
363
137
215
131
68
60
5
48
44
100
103
116
92
84
108
52
136
82.
131
112
87
55
6
48
33
79
78
108
100
92
100
165
132
94
161
115
63
30
M1
83
58
79
96
63
33
132
174
0 126
137
39
49
132
30
2
78
64
78
78
62
54
138
151
5
4
113
123
105
125
110
3
90
66
110
93
94
83
106
119
0
39
13
39
51
87
160
4
67
48
74
77
58
58
142
146
0
0
137
115
127
132
95
Ni
80
76
82
89
70
75
130
127
13
28
106
92
95
118
90
2
100
100
94
98
96
86
104
115
18
6
94
108
117
106
105
3
103
94
102
104
88
88
112
113
0
6
106
108
127
100
85
4
90
96
90
95
80
84
120
117
0
6
106
115
117
118
100
01
87
87
88
94
80
79
120
110
0
0
118
146
122
100
95
2
96
69
98
90
84
73
116
129
5
0
68
69
85
144
115
3
87
73
80
79
66
62
134
140
5
2
125
115
107
118
110
4
80
67
79
81
54
60
146
144
0
0
113
146
117
132
120
PlA
77
87
79
89
66
86
134
115
5
0
132
123
90
113
105
lB
83
55
107
90
104
106
96
93
5
0
50
61
83
182
110
iC
106
96
89
91
76
75
124
127
13
0
106
100
112
132
105
2
109
92
90
95
80
81
120
121
5
2
125
123
134
100
100
3
100
89
83
89
88
88
112
113
30
158
113
92
97
118
105
4
90
69
87
83
78
56
122
148
57
369
100
115
97
118
105
5
87
85
88
83
82
75
118
127
161 1102
132
77
66
137
125
6
90
75
95
96
90
75
110
127
5
54
125
131
119
75
75
Ql
74
64
79
75
52
58
148
146
104
50
87
131
122
156
95
2
65
48
78
75
70
86
130
115
704
495
68
77
73
156
120
3
80
58
87
87
78
77
122
125
579
726
87
100
88
137
130
4
87
69
85
79
76
73
124
129
61
339
113
139
81
113
95
5
87
75
81
79
64
49
126
157
73
276
113
123
103
144
105
R1
48
39
78
76
80
81
120
121 3987 2080
6
46
36
113
90
2
67
44
89
78
88
58
112
146 2161 1193
43
92
66
125
90
3
58
39
80
77
78
62
122
140 2509 1817
43
61
36
118
120
26
19
112
106
132
126
68
71
57
691
94
61
58
31
80
2
77
50
91
89
94
94
106
107
52
4
75
100
100
187
130
3
80
67
86
82
70
62
130
140
374
669
118
115
97
118
95
4
77
73
100
100
96
102
104
98
161
195
106
131
112
100
75
5
77
69
101
106
112
113
88
85
34
93
118
161
127
94
75
6
77
85
93
87
98
96
102
104
34
45
137
192
144
100
95
96
60
100
95
84
83
116
119
8
184
82
61
78
100
145
103
102
92
90
92
79
108
123
5
8
118
131
122
113
100
3A
87
89
100
104
102
96
98
104
8
6
106
115
119
75
80
3B
109
96
100
95
96
88
104
113
8
4
113
123
124
100
95
4A
103
98
96
95
84
79
116
123
0
0
113
131
124
118
100
4B
116
110
98
102
98
83
102
119
0
2
118
131
124
118
105
00
Si
Ti
2
oc,
90
77
110
125
5
10
113
123
107
113
105
96
106
86
94
115
13
17
113
123
115
113
95
89
89
102
66
98
138
248 1773
200
77
54
113
115
83
105
91
120
73
80
129
13
680
163
177
122
100
90
100
83
105
81
124
88
76
113
22
526
206
192
134
100
95
8A
106
80
107
96
126
96
74
104
18
86
200
192
141
100
95
8B
100
92
107
96
100
83
100
119
22
45
132
139
122
100
85
9
109
105
103
99
104
92
96
108
8
6
106
108
119
106
100
10
106
114
109
106
114
112
86
87
0
4
94
115
124
94
90
Ul
87
67
93
87
86
81
114
121
661 1389
106
100
76
100
105
2
80
60
95
84
92
67
108
136 1613 1708
82
54
39
113
105
3
80
58
88
79
78
62
122
142
369 1119
94
92
64
106
105
4
77
78
90
89
82
73
118
129
748 1260
94
77
64
137
115
5
87
71
100
95
110
132
90
64 2435 1934
87
85
56
100
100
6A
93
75
104
91
114
90
86
111 1069 1784
137
92
58
94
95
6B
109
82
108
106
154
79 1123
187
169
100
94
75
83
69
97
91
98
2
80
60
96
88
3
96
89
88
4A
93
87
109
107
93
5B
100
98
106
6
87
62
7A
109
7B
vi
102
46
89
69
102
134
187
389
125
154
107
100
80
80
79
120
123
82
295
94
77
88
150
40
86
72
73
128
129
0
36
113
139
122
118
100
108
106
112
113
88
85
13
6
113
100
122
87
75
110
4B
112
98
107
101
98
90
102
111
5
21
113
161
131
94
90
5
100
92
108
104
104
102
96
98
13
17
106
131
122
100
80
6
103
96
95
91
86
73
114
129
18
34
125
154
122
106
95
W1A
109
108
109
108
134
130
66
66
0
6
94
108
105
100
100
lB
112
123
110
108
130
120
70
77
5
6
82
92
122
100
LI
901
001
LZT
811
001
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