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A STUDY OF HOUSING DISCRIMINATION
AGAINST FAMILIES WITH CHILDREN

IN THE CITY OF SAN FRANCISCO

A Research Paper in Compliance

with Requirements for the M.U.P.

Degree.

Nancy B. Alexander
755 Newell Road

Palo Alto, Ca. 94303
415-328-1776

August, 1975

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133"

T A B L E O F C O N T E N T S

 

Background.............................................x.........1
Purpose..........................................................2
Sc0pe of the Study...............................................3
Data, Assumptions and MethodologY:...............................3
Statistical Testing..............................................5
Chi-square Test, Use and Limitations.............................6
Interpretation...............;..................................ll‘
Findings................................... ....... ..............ll
Conclusion....;.................................................17

FootnoteSOOOOOO ...... 0......OOOOOOOOOOOOOOOOOOOOOOO0.0.000......18

Appendices

 

A. Proposed Ordinance 1974 and Final Ordinance 1975

B. Sample page from U.S. Census of the Population and
Housing,Block Data

C. Details of the Chi-square Method

Dc Sample Calculation of the Chi—square Test on the Data

E. Detailed Summary of Data

Bibliography,

 

Copyright © 1975 by Nancy E. Alexander-

RUST SAN STATE UflJJERSKI
g -’ *w‘iPE

     
 

,

EAST LAHSAG, MICHTGAN 48Q23

BACKGROUND

 

This research was conducted to determine whether or not
_ families with children suffer discrimination in the selection of
rental housing in various neighborhoods in San Francisco.”

Because of the city's increasing white-collar composition1
and attractiveness to adultsz, there exists a high demand for housing
by adults who value in-town living. At the same time, many parts
of the city have a reputation for severe shortages of apartments,
for peOple with children. San Francisco also has an extraordinarily
low housing vacancy rate of 2.6%3, indicating overall high demand
and short supply. Harsh competition for housing, with resultant
high rental rates and high preperty values, imposes a heavy burden
on poor families with children who can neither afford high rents
nor the high costs of commuting from suburban areas.

Concurrent with the extreme competition for existing housing .
due to the changing composition of the labor market (more white
collar tertiary and quarternary functional jobs), newly constructed
housing in the city is increasingly oriented toward relatively
high income adults. Lower and moderate income families with
children are being squeezed into older housing (which being
generally larger is more family oriented) and out to the perimeters
of the city. As usual, poorer families are hurt most by this
squeeze.

Specific reports of landlord discrimination against people

with children have been heard many times by social welfare agencies.

A survey conducted by the City Planning Department reported that

in some areas of San Francisco, 50% of the landlords contacted
indicated that they would refuse to rent to people with children.
Based on this report, the Human Rights Commission and other social
service agencies in the Spring of 1974 supported a preposal for

an ordinance (introduced by San Francisco County Supervisor Quentin
KOpp) Which would bar housing discrimination against people with
children (See Appendix A). This proposal initially failed to pass
because some of the Opposing supervisors thought this type of law
should Originate with the State of California. In the summer of
1975, an ordinance was enacted prohibiting discrimination in the
rental of housing to peOple with children. It should be noted
that during the period of the available data, landlords had the
legal prerogative to discriminate along the line of family compo-

sition.

PURPOSE

This paper specifically examines whether there exists
actual discrimination against peOple with children significant
enough to affect patterns of housing within certain neighborhoods
in the city. Although it may be widely believed that there is
housing discrimination against people with children, the issue
has not been thoroughly investigated” The popular view may in fact
not exist or be due to the actions of a relatively few highly
visible landlords. This paper also examines the extent of housing
discrimination, and locates the areas of high discrimination to a
much greater extent than a study5 conducted by the City Planning

Department.

SCOPE OF THE STUDY

 

This study stresses statistical rigor in locating the actual
discrimination. It does not address itself to either the mechanism
of discrimination or to the methods of alleviation of the discrimi-
nation found. (Regarding the mechanism of discrimination, the San
Francisco Planning Commission 1973 Vacancy Report-Survey indicates
landlord attitudes to be a prime cause.) The emphasis is on the
documentation of housing patterns.

Because it was only possible to systematically study a small

number of neighborhoods in San Francisco, in some of the subject

{neighborhoods no conclusions could be drawn due to the lack of

sufficient units of data for statistical testing.

DATA, ASSUMPTIONS AND METHODOLOGY

 

The most available form of data to study housing patterns
is the 1970 United States Census of the Population and Housing.
(See Appendix B for further details.) It was desirable to use
as Specific data as possible.. Census data, available at the city
block level, includes the following information:

Total P0pu1ation,

Percent Negro,
Percent in group quarters,
Percent under 18 years of age,
Percent over 62 years of age,
Total year-round housing units,
Number of units lacking plumbing,
Number of units in one unit structures, (i.e. number

of houses),

Number of structures with 10 or more units,
Total number of owner occupied housing units,
Number lacking some p1umbing,t A
‘ Average number of rooms per unit,
Average value in dollars,.
Percent Negro,
Total number of renter occupied housing units,
iNumber lacking some plumbing,
Average number of rooms,
Average contract rent in dollars,
Percent Negro,
Total number of units 1.01 or more persons per room,
With all plumbing facilities,
Number of one person households.
Number of households with female heads of family.
Number of units with boarders or lodgers.
jMore Specific census information is available, but it only
covers dwelling units in larger geographical areas, such as block
groups, census tracts, and "areas." There is a tradeoff between
the limited information for the city block and the extensive in-
lformation for the larger geographical area. For the purpose of
this study, information as to specific area or location was more
important than that of quality, so the tradeoff leans in that
direction. Block data census information was used.
Devising a suitable index of the density of children per

block was the next step. Some of the indices available were:

-4;

Percent children per block (18 and under),

Number of children per block,

Average number of children per unit per block,

Number of families with children.
The index, average number of children per unit per block, was
choSen because knowing the number of housing units available
per block reflects the number of children. This index does not
give any indication of the availability of rooms for children on
the block. It would be informative to know whether any overcrowing
exists. The indicator available for checking overcrowding in the
block level census data is 1.01 or more persons per room.

STATISTICAL TESTING

 

Three statistical methods were considered for use in detecting
differences in housing patterns of families with children. The
first was a regression analysis of rents testing whether the density
of children added to the cost of renting housing. The second was.
to test various areas for their variance (block to block) in the
children density index to see whether any two separate areas had
significantly different variances. Both tests were rejected, the
first because of the necessity of access to computer time and
associated costs, the latter, though procedurally simple, was in—
adequate in verifying the existence of discrimination._ (Difference
in variation does not confirm differences in housing patterns.)

The test selected (described in detail below) is a chi-square test
for deviance from an hypothesized probability distribution. This

test was selected for the following reasons:

-5;

1. This test could be performed without the use of the
computer.

2. The test.produces a usable comparison even without
positive outcome.

3. (It is widely known.

4. It is flexible as to the number of points taken in
a sample.

5. It is relatively non—abstract compared to other -
statistical tests.

6. The statistical tables necessary are easily accessible.

_?HE CHI-SQUARE TEST, USE AND LIMITATIONS

 

Chi-square is most simply described as a measure of distance
of a distribution taken from actual experiments (or the real world)
from a distribution expected from the hypothesized distribution.

If the measured distance is too great, it can be said that at some
level of probability that the actual level of distribution is not
the hypothesized one. Unfortunately, this test does not reVeal

at what level of probability the actual distribution could be the
hypothesized one. The test is used to calculate the percentage
.of the time (depending on the chi—square measure) the distribution
is ESE the hypothesized one. Repeating, it can not be learned
from the same test at what probability level the hypotheSis should
be accepted; that is, it cannot be told what percentage of the time
it would be correct to assume that the actual distribution is the
hypothesized one. This feature is critical to correct interpreta-
tion of the results. The test as used certifies to certain proba-

bility levels for the tested areas that the pattern of actual

-5-

. housing is not the one that would be found if no selective process
existed. But the test does not address itself to those areas which,
when tested, were not found to have significant distance from the
hypothesized distribution.

The main hypothesis and the related working assumptions are
stated below. It should be noted that these are limiting assump-
tions but necessary ones in order to maintain a "sense" of rigor
in the study. The assumptions also reflect the limitations of the
data. The assumptions are a result of the balance between an
attempt at rigor and the necessity of working with the available
data.

The main hypothesis is that in a given housing area with a
limited, given range of rent and range of size, the distribution

1. of the index, average number of children per housing unit per block,
is a normal distribution in the statistical sense. (See Appendix
C for further details on the Chi-square method.) Essentially, if
the index were calculated for each city block in the area,_the

distribution of the index will be a "hellishaped" curve.

number
.of
blocks

 

 

children/unit/block

 

Normal distributions are commonly found when there is no selective

process at work distorting "natural" processes. To test the

"D

validity of this hypothesis, the chi-square test was performed

on areas of almost totally owner-occupied housing, where dis-
crimination against families with children is unlikely and unknown.
The findings presented below show no indication of a non-normal
distribution in these areas and qualitatively the distributions
are very, very close to the normal one.

The second assumption is that the quality and type of housing
per block is generally reflected by two indices--average rental
rates and average number of rooms per unit of housing. Rental
price then is the proxy for all the qualitative factors per size
of a rental unit. Some of the factors included in this rubric are:

Distance from the CBD,

Quality of neighborhood, and

Quality of the physical unit of housing.

This assumption is made on grounds that the market values each good
in terms of money. Each block within a particular area that is
similar to the next in average size of unit and average rent is
assumed to be of similar housing quality and that potential

renters would assume this to be true. i

It was assumed that on any particular block there is not
enough variance in the size and rents of rental housing units
to distort the average rent and average apartment size as an
adequate reflection of the type of housing on the block. This
assumption is necessitated by the fact that further breakdowns
of rents indicative of variance from unit to unit is-only avail~

able on a "Block Group" level (an aggregation of about eight

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blocks) in the census data.

As stated above in the description of the chi-square test,

the hypothesis was tested in areas with predominantly owner

, occupied housing. In order to compare the results of the test

from renter occupied housing areas to owner occupied areas, a
method of inferring potential rent in owner occupied areas was
necessary. The gross rent multiplier was used. This is a fraction
of the value of the owner occupied home and transforms the sales
value into the rental value. (1970 is the year of all data used
in the study.) The factor 1/130 was derived after studying areas
which were predominantly owner occupied and totally single family
homes, but which also had rental units, and by dividing the average
rent by the average home values in that area.

Ideally, the chi-square test would compare individual units
of housing with exactly the same rental price and same number of
rooms to test the normality of the distribution. Because the data
are only given in terms of averages per block, there are no two
blocks with exactly the same averages. Therefore, a range of
averages was arbitrarily selected in order to disaggregate and

differentiate between the blocks in an area. All-blocks in a

.particular range were thus considered to be the "same."

' The chi-square test requires a minimum of 15 test blocks

"in order to be effective. The following breakdown was devised

in an attempt to maximize the number of testable categories of
rent-size in a specific area. If the area tested was increased
in size, a more specific breakdown could be obtained. The area
used in this study generally covers two or three census tract

areas. The character of the area would be significantly different

-9-

if more tracts were included, even though finer disaggregation in
the rent and size indices would be permitted. This is the trade—

Off decision mentioned above on page 4.

CATEGORIZATION USED IN THE DATA SHEETS

 

TRACT BLOCK ' % UNDER 18 POPULATION # UNITS AVERAGE AVERAGE
- RENT # ROOMS /
UNIT

 

 

 

Calcu-

lation % rental units # under 18
#1

Calcu- .

lation # under 18/
#2 unit

 

 

 

 

 

 

The categories which did not include a sufficient number Of blocks
in any area were not tested.

The chi-square method for this particular application requires
that the axis of the index be sectioned into at least five parts
with at least five blocks from the sample falling into each section,
and the expected number from the hypothesized normal distribution
being greater than five for each part. _Because the chi-Square
analysis does not dictate the boundaries Of the sections be fixed
from test to test, the boundaries were reset from test to test.

This was Often necessary because there was only a minimal amount

'Of data available.

-10-

INTERPRETATION

 

In interpreting the following results, only very careful and
limited comparisons can be made between any two tested areas, even.
when taking into account the rentrsize levels, because each area
has its Own characteristics in terms of Open space, schools, dis-
tance from the CBD, etc. This chi-square test is designed to
compare one area against an hypothesis, not to compare between
areas. For instance, there can be situations in two categories.
with the same rent-size characteristic that one with a lower mean

number of average children per unit per block will Show no posi4

_tive indication Of housing diScrimination. (It has a low chi—square

value.) But the area with the higher mean value Of average number
Of children per unit per block can show deviance from the hypothesis
indicating discrimination against children. This can occur if the
second area is more desirable to families with children, yet also.
desirable to others and with the resulting competition, discrimina-
tory'practices result.

FINDINGS.

The following are.the results Of the chi-square test described

habove as performed on selected neighborhoods within the City Of

San Francisco.
Map 1 shows the areas of San Francisco that were tested and
the location Of the areas with residential discrimination against

peOple with children.

—11- '

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T A B L E 1

 

SUMMARIZED CHARACTERISTICS OF TESTED CENSUS TRACTS IN 1970

 

Tract % Owner % Single Avg. Value

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Occupied Family Housing Of House (S)

304 82% 86% - $40,000
306 . 88 . 96W 36,800
‘307 86 98 33,100
"328 76 82 29,000
353 78 89 . 29,300
127 _ 12 12

128 27 18

126 ‘ 25 16

129 15 8

130 20 8

131 12 4

135 12 7

133 38 32

134 21 12

154 28 22

401. 27 20

451 34 22

402 25 20

426 36 29

 

 

 

 

 

-13-

SUMMARIZED FINDINGS

T A B L E

2

 

OF THE CHILDREN DENSITY INDEX BY CENSUS TRACT

CHILDREN DENSITY INDEX

 

 

 

 

 

 

 

 

 

 

 

 

 

 

TRACTS nEAN STD. DEV. “X"
F"'304'&’306 " .98899. '.24492" 3.22433 not non-normal
‘““””m”” ".62789' ".20149 .66462 not non-normal”
“P .44466 I21892 2.04546? not non-normal
””T3O7‘" i' .70188 .34014 1.95396 not non-nOrmal
’ 328 " .46255 .16923 3.46953 not non-normal
"“‘353“ ' .77179 .19705 1.62472 not non-normal’
“‘*127 a 128 .12270 ‘.07099 7.19153 non—normala)
126 & 129 .15300 .12996 12.05086 non-normal
t I3o,131,135 .08285 .04898 5.48369 non-normal
‘“‘“‘" *”"‘ ‘112831 .08921 ‘ 2.79956" notT‘non-normalb)
“'"133”& 134 "'§76878 ' .33569""" .15597’ not nOHFnormal”
”“154,401,451 562809 .42908 18.40882 '“ non-normal"
'" "'”"” '.48l69‘ .18363 1.39000" 'not non-normal‘I’
""“402‘E”426'"T'.56567 .18271 2.28900 nOtL nofi?hormalc)

 

 

 

 

 

 

A_-—-——-—-o-. . . . ...u - .

a)
b)

C)

However,

the bias is

...... . ._

families with children.

. a.

-14-

m~ - ...

toward having fewer children.

However, the qualitative bias is toward not having

Note that this tract is biased toward having children.

 

Table 1 summarizes some of the characteristics of each tract,
while Table 2 summarizes the findings of the study. As expected,
there was no evidence Of housing discrimination against families
with children in predominantly owner occupied areas-~tracts 304,
306, 307, 328 and 353. All of these tested areas showed quali-
tatively normal distributions and no evidence of non-normal dis-
tributions were found in the child-density index. However, in
areas Of rental housing, different selection procedures seemed to
be in effect. Evidence of this may be seen in the standard devia-
tions of the index for rental areas which ranged much below and:
much above the deviations over the owner occupied areas. The
number of children per unit per block (the density index) was lower
in the rental areas than in the owner areas. This was expected

1. because as can be seen by the distribution of housing, the owner
areas had significantly larger living units. This occurred because
most owner occupied housing is single family housing, whereas most
rental units are in multi-unit buildings.

Four areas showing evidence of bias were:

Tracts

127, 128 " Marina District
126, 129 iMarina_District
130, 131, 135 Marina District
154, 401, 451 Richmond District

and in addition, tracts 402 and 426 (Richmond District) though
it was not shown to be non-normal, qualitatively there was

‘systematic bias against people with children. Oddly enough, in

‘ V

-15-

Tracts 127 and 128, the bias was toward having children, whereas
the rest of the biases were Opposite in direction.

Among all of the biased areas, there was evidence of bias
cutting across all rent categories. Tracts 154, 401 and 451
demonstrated bias in the $90 to $149 range while tracts 130,

131 and 135 showed bias in the $150 to $209 range. But, all

Of the biased areas-fell into one size category, 2.7 to 3.8 rooms;
that is, the medium size apartments. There was no evidence of
discrimination in larger, higher priced apartments.

The Marina district had a very low vacancy rate of 1.2% in]
.1969. In the 1973 Vacancy Report, it was reported that 64% of
'all housing units in the Marina did not accept children. Housing
in the Marina is expensive. One-third of San Francisco's total
of 4,478 housing units renting for $300 or more per month were
located in the Marina.6 These factors combine to keep the number
of children in the area low and also to skew the housing pattern
to create areas inhabited almost tOtally by adults.

The Richmond District, like the Marina, had a low vacancy
rate in 1969 (1.5%). Although there is no information available
about landlord acceptance of children, it was noted that children
were acceptable only in apartments vacant for more than two months,
i.e., those Of dubious value.7

In the City of San Francisco, a mere 41.5% Of the housing
units were available to families with children as stated by the
landlords Of those prOperties. Of those buildings, 80.5% actually

8
_had some children living in them. A possible inference is that

-16—

discrimination is more severe than the survey Of landlord attitudes
indicates. This study finds that there is enough bias that the
pattern of housing for families with children is definitely affected
' by the landlords' practices. In order for these tests to reveal
bias, entire areas must be biased. This occurred, even by the con-
servative chi-square test. -

CONCLUSION

 

There exists in areas in the City Of San Francisco evidence
of discrimination against families with children, even when the.
factors Of rent, size of unit and location are cOntrOlled. To-j
gether with the stated preferences of landlords for families
'without children and singles, this study demonstrates the non:

economic, non-market bias against families with children.

 

 

-17-

FOOTNOTES

 

San Francisco 1970 Population Characteristics, Part II,

 

San Francisco City Planning Commission, 1973, page 3.

 

Planning Report, San Francisco Unified School District,
1973, pages 12--l3.

1973 Vacancy Survey, San Francisco Department Of City

 

Planning, p. 11.
ibid., p. 18.
ibig,

ibid., p. 46.
ibid., p. 45.

ibid., p. 20.

-13-

B.

C.

D.

A P P E N D I C E S

 

PrOposed Amendment of Administrative Code introduced by
Quentin Kopp, San Francisco County Supervisor. Final
Ordinance of June 16, 1975.

Sample Page of Census Data Used in the Study.
Chi—Square Method.

A Step-By-Step Sample Calculation of Chi-Square for
Tracts 304 and 306.

Detailed Summary Of Data.

APPENDIX A

 

Proposed Amendment of Administrative Code.

Final Ordinance of June 16, 1975.

r nanAN STATE UNI
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“13:313.? wamzsmrxvt COD! BY ADDING cnu'ran 12C 75123270.
PROHIBITISG DISCRFMXSATION IR TKS LEASIRC CF CLRTLIN RESIDENTIAL
RIM. PROPERTY LECAUSE OP CHILDRER.

to it ordained by the People of the City and County of Ban Pranciaco:
Section 1. Chapter 12C ie added to the San Francisco

 

Adainiatrative Code to read ea iollova:
cmmn 12c.
IPDUIBITXNS DISCRIMINATION I" Tim llASlNC 01' CERTAIN
RZSXD?NTIAL REAL PROPERTY’BBCAUS! OF CHILDREN.
Sec. 12C.l. Prohibited activity.

It ehnll le unlawful for the owner. euhleeaee, real eetato
hrokcr. aaaignee, or other pcraon havin; the right of ownerehip,
the right of poeecaeion, or the right to rent or leaee any
reeidential accoaznodatione, or any agent or‘ employee at auch person.
to refuee to rent or leaee or otherviae deny to or withhold from
any peraon euch accommodationa becauae euch pereon her a child or
children who ehall occupy the leaaed or rented prenieee with ouch
pcraon.

Sec. 12C.2. 55:22:1321. .

Thin ordinance shall not apply to dwellinga containing two or

three apartments. one of which in occupied by an elderly or infirm

pereon for whom the presence of children would constitute a hard-

-_.- .— -'

chip. For the purposes of thia ordinance an "elderly pereon" ahall
been a peraon eixty-iive yeare of age or over. and an "infirn
pereon" ehall nean a peraon vho ia diaahled or auifering from a
chronic illneea and would therehy‘be adveraely atiected by children
living on the prcnieea. -

Sec. 12C.3. Foam occupancy.

Thin ordinance shall nor require the rental of preaiaea for
are contrary to thoee atandarda not out in Section 501.1 of the

 

 

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9

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floueing Code, Part 1!. Chapto: XII of the San Trancieco kanicipal
Code. I
See. 12C.6. Discrimination ix ficenciel obligatio-e p;ohih£ted.
Thia ordinance shall not prohibit the pereon havir; the right
to rent or lease the premiere from requiring the ease linencial
ohligetione of prospective tenants with children aa he or she nay
require of proepective tenanrn without children. However. no
diecrininarion in the amount or cannot of payment of raid financial

ohligationa ahall he perpittcd.

APPROVED AS TO FORK:

THOMAS H. O'CONNOR. City Attorjsy

 

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f

 

PILL 304.1145..—

.Sec. 103. ~Exemptions; Minimum Floor Area.

Sec. 105. Requirements of Financial Obligations Not Prohibited.
'Sec. 106. Penalty.

 

. M
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-- _‘A-h-A ..

8 8 fl 3 2 8

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.-‘_ _ ‘ A—a _fi.‘ - .. , . . O .0

as AMENDED IN some) JUNE 16, 1975

J»

om): NANCE __
mummies "£2212

AHENDING PART II, CHAPTER VIII, SAN FRANCISCO MUNICIPAL CODE (POLICE
CODE) BY ADDING ARTICLE 1.2 TIIERETO, PROHIBITING DISCRIMINATION
AGAINST FAMILIES WITH MINOR CHILDREN IN THE RENTAL OR LEASING OF
CERTAIN RESIDENTIAL PROPERTY: PROVIDING FOR PENALTIES FOR VIOLATIONS
THEREOF; PROVIDING FOR EXPIRATION DATE; PROVIDING SEVERANCE CLAUSE.
Be it ordained by the People of the City and County of San Francisco:

Section I. Part 11. Chapter VIII, San Francisco Municipal Code
(Police Code) is hereby amended by adding Article 1.2 thereto, reading
as follows: '

V ' ARTICLE 1.2

DISCRIMINATION AGAINST FAMILIES WITH MINOR CHILDREN‘LNLHOUSING

Sec. 100. Findings.
Sec. 101. Definitions.

Sec. 102. Prohibited Activity.

Sec. l04.' Tenant Age Policy Not Prohibited.'

t
See. 107. Expiration Date.

Sec. 108. Severance Clause.

SEC. 100. Findings. After public'hearings with the receptioncof

testimony and documentary evidence, we find that discrimination
against families with minor children in the leasing or renting of
housing accommodations exists within the City and County of San Fran-
cisco. He further find that the existence of such discrimination

poses a substantial threat to the health and welfare of a sizable

 

segment of the community. namely families with minor children.

we find that a shortage of housing suitable for families with
minor children exists within the City and County. We further find
that a low vacancy rate exists in all rental housing throughout San

. 1 -

aoaaa 0 “Vin.

IV

 

4.... 1e.

- cu-O 0---0— -

- atfi’

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en‘s-....-— ‘- -.

 

N» e’ween. e an.

‘CQOCQUN-

- - - - - -.
m ‘ U N no 0

lb

.tal unit consisting of one or more rooms in which cooking facilities

 

Francisco. The addition of discrimination against families with
minor children to the above two factors creates an untenable situation
for the children of San Francisco.

The overall effect of such discrimination is to encourage the
flight of families from the City and to further diminish family-
oriented neighborhoods. It has an overall detrimental effect on the
composition of the City, the stability of neighborhoods, the preser-
vation of family life within the City, the living conditions of our
children, the quality of our schools, and the viability of children‘s
activities and organizations. A

This discrimination cuts across all racial, ethnic and economic
levels.

SEC. 101. Definition: Housing Accommodation. Residential ren-
are available. .

SEC. 102. Prohibited Activity. It shall be unlawful for the
owner, lessor, lessee, sublcssee, real estate broker, assignee, or
other person having the right of ownership, the right of possession,
or the right to rent or lease any housing accommodations, or any agent
or employee of such person to:

(al Refuse to rent or lease, or otherwise deny to or withhold
from any person such accommodations because such person has a minor
child or children who shall occupy the leased or rented premises with
such person;

(b) Represent to any person because of the potential tenancy of
a minor child or children that housing accommodations are not availabll
for inspection or rental when such dwelling is in fact so available; .

(cl Make, print, or publish,or cause to be made, printed or
published any notice, statement, or advertisement; with respect to

the rental of housing accommodations that indicates any preference,

smuaoeumnwwms - 2 o

I

 

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limitation, or discrimination based on the potential tenancy of a mi-
nor child or children;

(dl Discriminate against any person in the terms, conditions '
or privileges of the rental of housing accommodations or in the
provision of services or facilities in connection therewith, because
of the potential tenancy of a minor child or children;

(e) Refuse to rent after the making of a bona fide offer, or
to refuse to negotiate for the rental of, or otherwise make unavailabhz
or-deny, housing accommodations to any person because of the potential
tenancy of a minor child or children;.

I (fl Include in any lease or rental agreement of housing accoma-
dations a clause providing that as a condition of continued tenancy
the tenants shall remain childless or shall not bear children.

SEC. 103. Exemptions; Minimum Floor Area. The provisions of
Section 102 of this Article shall be applicable only to any housing
accommodation which meets or exceeds the following floor area
standards:

' (a\ Each such housing accommodation shall have at least one
room which shall have not less than 120 square feet of superficial
floor area.

(bl Every room which is used for both cooking and living, or
both living and sleeping purposes shall have not less than 144 square
feet of superficial floor area, provided that, when more than one
person occupies such room, it shall have an additional 40 square feet
for each occupant in excess of one. '

(c) Every room used for sleeping purposes shall have not less
than 80 square feet of superficial floor area. i

(d) when more than two persons occupy a room used for sleeping
purposes. the required superficial floor area shall be increased at
the.rate of 50 square feet for each occupant in excess of two.

- 3 .

M 0 WWW

 

 

 

..N..‘HH~

.Hundred Dollars ($500.00).

 

SEC. 104. Tenant Ace Policv Not Prohibited. In residential
buildings otherwise covered by this ordinance, where the owner has
publicly established and carried out a policy of renting exclusively
to persons who are defined herein as elderly, said owner or any other
person enumerated in Section 102 hereinabove shall be exempt from the
provisions of this ordinance, provided, however, that deviation from
or abandonment of said policy shall automatically subject said owner
to all the provisions of this ordinance.

SEC. 104.1. Definition. Elderlv persons. All persons who have
attained the age of sixty-two (62) or more years.

SEC. 105. Reouirencnts of Financial Obligations Rot Prohibited.
This ordinance shall not prohibit the person having the right to rent
or lease the premises from requiring the same financial obligations of
prospective tenants with minor children as he or she may require of
prospective tenants without children. However, no discrimination in
the amount or manner of payment of said financial obligations shall
be permitted.

SEC. 106. Penalty. Any person who violates any provision of
Section 102 of this Article shall be deemed guilty of an infraction,
and upon conviction thereof shall be punished by a fine of not less

than Two Hundred and Fifty Dollars ($250.00) nor more than Five

Any person believing that a violation of said section has been
committed may file a complaint with the District Attorney.

830.107. Expiration. This ordinance shall expire three years
from the effective date hereof, subject to mandatory review by the
Board of Supervisors on the anniversary dates prior thereto for the
purpose of evaluating the experience of operating hereunder and consi-

dering extension of the operative date, amendments or repeal hereof.

sous N wusvuoas

 

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‘ Approved as to Form:

 

 

SEC. 108. Severance Clause. If any article, section, subsection

 

parhgraph, sentence, clause or phrase of this Code, or any part there-
of, is for any reason held to be unconstitutional or invalid or inef-
fective by any court of competent jurisdiction, or other competent
agency, such decision shall not affect the validity or effectiveness
of the remaining portions of this Code or any part thereof. The
Board of Supervisors hereby declares that it would have passed each
Article, section, subsection, paragraph, sentence, clause or phrase
thereof, irrespective of the fact that any one or more Articles,
sections, subsections, paragraphs, sentences, clauses or phrases be

declared unconstitutional or invalid or ineffective.

THOEAS M. O'CONNOR, City Attorney

 

M a “VI“.

 

 

...- -..-_'_‘

--—-a-—-o--_.— .- —<—..-.. .

Passed ior Second Reading
Board of Supervisors San Francisco

............UU~.1.6.1375 ..... . ........... s

Ayes: Supcnisors ' "' . r‘einstein. Pran-
cois. Canaahs. Kopp, Mindtlsohn. W Nel—
der.1’elosi.'l‘amuraa. Von Herold": gen.

Nerd: Supervisor/ ..... . {150118481 ......... '. .
Absent Supervasor/ ....... 8.’ ‘REIAQEU‘JA .......

fl! WKQK» ..... "33?.

42553599257. ... J&VC§065%5.W

File No. ”A pprm.

Read Second Time and Finally Passed

Board of Supervisors. San fiancisco

I O I C IIIIIIIII .u‘U: 2 :0 ::75 OOOOOOOOOOOOOOOOO
Aym SI: punishes Rm Feznstrin. W-

cois. flu-2.212;. Kn; p Me: -.-d.:sohn. mm hel-
der. } ‘eiosa. Tamaras. \oa Btroldmgcc.

Rees: Supervisors . . . B:m 5.3-3.“ ...... ”.3?!” . 91-1
Absent: Saran-350:7 ..... F1. [.3 ............

I hrrcby ccrh'fv fin: Mr [ongoing ordinance was
finally pass“! ay Mr Rmrd o]_ Sumner: n! (he
City and (‘0: «My a] San A terrier...

 

. r- ‘m ......"
...... vgr'y’gp’cffecc’ku‘hczfid
....... .' {14
Mayor
L'

The foregoing measure havin been Finally Passed by the Board of Supervisors
at the meeting of June 23, 975, was referred to his Honor, the mayor, in
accordance with the provisions of Section 2. 303 of the Charter and was

returned by him under date of June 30,
noted theron.

The Board of Supervisors, on July 1a,

1975, with his disapproval and veto

1975, voted to reconsider the foregoing

measure and the Mayor' s disapproval and veto was. overriden by the following

vote:

AYES:' Feinstein, Francois, Gonzales. Kopp, Mendelsohn, Relder,/Pelosi,

Tamaras, von Beroldingen

NOESz Barbagelata, Holinari

 

4342’ 31620214

GILBLRT H. BOREMAN, Clerk

enve- - ‘

 

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-——- fin.

 

 

APPENDIX B

 

Sample Page of Census Data Used in Study

 

 

 

 

 

 

 

 

 

 

 

 

 

‘ 'H 1 I. I In
Unns In- P 0mm MW awful-4m

B'OC"! . 047m».-

0 o l
Wllhln ‘ locl- IocII- loun- '
Census 09 I09 I00 Av«-_

some SIM- some Am- some Am- 099 I5...

TIC"! oroII Iwes oroll 099 Am- 090! 4390 con- ... -
You! In Un- 62 plumb- 000- 47' Numb- mm- coo plvmb- mm- mm, 3144': . “ -
popu- roup do! ”on no on" I007 909 be! who '07- inq bu mu m. “I. N ‘ ‘

Io- Ilo- quor- l3 and Ice-h- stc- not. 'OCIII- oi (doI- «III '0:le 0! Idol- «M I... .51.“ '°
Iioa we Ion mu m9 1090! I45 Ions was low! I-es rooms Ion) More "no! In rooms Ion) Neqvo 7.4.7 ." ,':_ L

305 ...... I35 .. - 22 I3 79 I 53 - 56 I 5.2 30900 - 23 - 4.6 I64 - I I .,

m. ..... ,3 - - ‘. '. 3| - 3' - n " s-‘ M'm " ‘ on. no. on. C - . I.

”, ...... ‘23 - - a ‘2 3‘ " 3‘ "’ 3? - 5.. 39m .- 2 0 on on. - 3 J .

m ...... ‘64 ‘ - 2‘ 2' 57 ‘ 57 - 53 ‘ 54‘ ‘ l .0 003 000 Ill 0 . ..

”...... q‘ - - m '5 w ‘ n ' 36 ' 5., ‘OIW ' ‘ DO. .00 IO. . - . .

3'0 ...... ‘7 - - - $9 '0 " ‘0 ' q - 56 27m - ‘ on. no on. - s- . .

3II ...... I22 - - I3 I7 53 - 53 — 49 - 56 40300 - 3 - - . ,

3I34..... 32 - - 26 I0 33 - 32 - 27 - 5.6 30I00 - 6 — 4.7 2I5 - . . ,

40I ...... 45 - - 22 29 20 - 20 - 20 - 50 34900 - - - - - - I I .-

402 ...... 26 3 - 3 I9 I4 - I4 - I4 - 5.3 36I00 7 - - - - - - , ,

”a ...... ‘07 1- - 23 23 u - ‘3 " w ’ 6.5 “m - 3 - ‘42 o o o " ' ' H

404.... I05 - - 2I 24 33 — 33 - 35 — 5.7 34900 - 3 - I I I

405 ...... I32 - - I3 39 52 I 44 .. 45 I 5.7 3I000 - 7 - 3.0 m . 2 3 I'

4064.... II6 - - I7 39 54 .. 42 II 35 - 5.I 23700 - I9 - 3.7 763 - I I 3;
_ 407 ...... I37 7 - 22 30 60 - 29 - 3I .. 5.5 23600 - 26 - 4.3 I70 . I2 3 J n

403 ...... 64 - - 23 22 23 — 22 - 2I - 6I 33600 .. I - - . I

m ...... 60 - - n m 23 " ’3 - 22 " ‘0 32m - ' nun 034 one - ‘ ' .

4I0 ...... IOI - - I2 33 40 I 40 - 37 I. 5.9 39500 - 3 .. - - . I

4II4-.... 95 .. - 25 I9 '35 - 25 - 29 - 7.9 5I300 - 5 — 2.3 I33 - - . I

4I2 ...... 40 - - I3 20 in 2 20 - I8 2 5.3 47I00 - 3 . .. - - . I

“3 ...... 5‘ C '- ‘ as 23 " 23 ' 7' I- 5.4 3m " a 2 0-: III .04 - I o .

50I ...... I06 - I - 26 6 32 - 32 — 3o — 6.9 49200 - 2 - .

502 ...... I26 3 - I4 39 53 I 54 - 49 I 6.I 40400 2 3 - 3.3 I67 - - . I-

503 ...... IIo - - I7 23 46 3 33 - 36 2 5.9 36400 - I0 I 3.9 I67 - - . u

504 ...... I20 2 — I3 23 50 — 50 - 44 - 5.7 30300 2 6 — 5.5 I77 - - u

505 ...... II9 3 - 30 I6 46 - 27 - 23 - 5.4 32000 - 22 - 4.2 I47 5 2 7 'I

506 ...... I62 5 - I4 . 25 69 I 42 I2 37 - 5.5 29600 3 32 I 3.9 I69 3 - - 'I

507 .4 ..... I20 - - 9 . 40 50 I 53 - 52 I 5.4 30000 - 6 _ — 3.7 I32 - - . u

503 ...... I07 - - 20 29 43 - 43 - 39 - 5.9 37 - 4 - 3 ' I I

no ...... no 3 - .26 9 33 — 33 - 32 - 7.2 57200 3 ' I I -I I

60I 2‘6 - - 27 3 I0 - 3 - 9 - 619 44400 .. I .. . . - - . I

602 ...... 73 -' - 27 I4 25 — 25 - 24 - . 6.0 40I00 - - - - - - I I I

603 ...... 9o 6 - 29 I3 3I — 3I - 29 - 6.5 49000 3 I .. . . . - . I

604 ...... 3I 3 - I7 I0 33 - 33 - 33 - 5.7 44200 3 — — .. - — - I

605 ...... 60 4 - 9 25 36 I 2I - 23 I 5.4 40I00 4 II — 3.9 I73 - - I'-

606 ...... 39 - .. I3 I3 I7 — I5 .. I4 - 5.4 50200 - 3 .. - - I

607 ...... 20 - - 40 S 5 - S - 3 - 7.0 565-00 - - - — - - - -

6II ...... 39 3 4 I3 I5 24 I 0 - II I 43 30000 - 73 - 3.I I65 3 - . II

6I2..... 2n 3 - 2I . I3 90 3 24 — 32 - 4.9 29300 3 56 3 4.2 I76 5 I . ::

6I3 ...... 63 - - I6 II .27 I 27 — 26 I 5.I 35300 , - I .. - I I I

6I6 ...... 7| - 7 9 45 30 I 29 - 29 I 5.5 37500 - I . - - I

m ...... I03 - — I4 23 45 - 39 - 33 - 6.2 36400 - 6 - 3.7 I50 - - I

702 ...... I43 — - 2I 20 43 - 40 - 44 - 6.0 35600 - 3 . - I I I

703 ._ ..... I50 - - I3 25 62 I 4I - 42 I 5.5 3I300 — I3 — 3.3 I40 - 2 7 I.

704 ...... I43 - — I7 29 57 — 33 - 35 - 5.5 30700 - 2I - 4.0 I63 - 3 I 'I

705 ...... I36 - - I3 33 54 . I 40 - 45 I 5.5 3I700 - 9 - 4.6 I56 - I I I.

706 ...... IOI - - I3 35 42 — 4I - 37 — 5.4 32000 - 5 - 4.6 242 - I I ~‘

707 ...... 63 5 - I3 I3 27 - I3 - I7 - 5.7 4000 6 I0 - 4.I I07 . I I I

700 ...... no I - 26 I6 39 I 35 — 30 I 5.5 34700 — 9 - 5.3 203 II 7 7 _I

709 ...... 67 - - 30 I9 ‘ I9 - I0 - I6 - 5.6 20000 - 3 . - 2 7 I

no ...... I07 - - 22’ I0 46 I 4 — 2I I 5.0 — 23 - 4.7 I72 - - - "

I" -
IV‘.’ . '-

304...’...3 4005 -I - 25 2| I743 22 I505 ~22 um 10 6.2 40000 - m 4 4.6 I74 2 79 7I If
IOI ...... I20 - -' 33. I7 39 I 39 — 37 I 6.0 40500 '- 2 . . . .. - I I '
I02 ...... IIO - - 25 29 30 . - 36 - 37 - 7.I 49Ioo - - - - - - - I
I04 ...... I23 - - 40 I5 34 - 34 - 33 - 7.I 55000 - - - — - - -

I05 ...... ~53 - - 30 26 I0 .- 10 _ I7 - 7.5 49300 - I . . .. - - 5

I06 ...... 52 - - 37 I2 I6 - I6 - I6 - 7.I 40600 - — - - - - - '

.Io74 I55 — - 26 I0 54 3 43 I0 36 3 6.9 43000 - I3 - 4.6 I57 - - f

I03 ...... 77 .. - 34 0 22 - 2I .. I0 - 7.6 54400 - 4 . . . . - -

20I ...... 49 - - 29 I2 I7 - I7 - I5 - 7.2 9300 - 2 . . - I I ‘

-202' ...... m 3 9 32 I3 32 I 32 - 30 I 7.6 52000 - 2 . . . . .. - ’

203 ...... 4I - - I5 . I7 I5 - I5 - I5 .. 7.3 54000 — - - - - - — ’

204 ...... 6o - .. 23 33 20 -I I9 - I9 I 7.4 50000 - I - - f

205 ...... 7I - -. 30 I3 24 - 24 - 22 - 70 40500 - I . - - ;

~207 ...... 64 - - 34 I4 21 - 2o - I7 - 7.7 5Iaoo - 4 . - I ' .

210... .. I00 9 - 34 . I0 27 I 27 - 25 I II 44200 4 2 . . I I ;

30I ...... 70 - - 21 3I 27 - 27 - 25 — 6.0 35900 — 2 . - - ..

3024... . 6I9 - — 26 II 226 - I94 - I79 - 6.3 0000 - 45 - 4.I I66 - I 3 ,

303. . . no .. - 26 7 37 - 37 - 34 - 6.4 49300 - 3 - . - - ,

307 ...... 63 — - 27 - 22 24 - - 24 - 23 - 74 52300 - I . . . . . - - .

303...- .. 32 I - 33 I2 24 - 24 — 24 - 7.4 50900 - - - - - - -

309 ...... 59 - - 39 I4 I3 I I3 - I7 I 70 50600 - . - - - - ; ;

3Io ...... I23 - - 20 I3 39 - 39 - 30 - 74 53300 — I . .. - - ‘

3II ...... 33 - - 33 I5 9 - 9 - 3 - 69 49000 — I . .. - - ,

40I ...... I35 - - I4 23 53 - 47 - 40 - 50 35000 - I5 - 4.7 I65 - - ,

. 402 ...... 237 2 - 27 I5 36 - 34 - 74 - 57 39500 I I2 - 5.0 205 - - .
403 ...... 54 - . 7 I7 26 - 26 - 25 w 40 33900 I - ~ .
404 ...... I2 - - 25 50 6 - 6 - 5 53 30500 . I .. - - II
405 ...... 64 - . 33 I6 20 20 - 20 ~ 60 41400 - . - - I . ,
406 ..... I02 - - I4 30 44 4I - 30 I 50 35qu - 5 42 I77 - - 2 _
407 ...... IIS - - I7 30 46 - 44 . 43 - 5I 30000 3 .. - 7
403... . HI 4 :II I3 _46 I 40 39 I 59 mm 3 7 60 I96 - 7 1- 2
409. I64 4 20 22 54 3 29 34 2 55 3mm 20 I 40 I54 I5 4 . .
50I .. 73 . . I2 45 31 . 37 30 53 rem-0 3 - - ' .
502. . I50 . . 24 I5 5I . 46 - 43 60 31500 0 - 4| ' I93 - I , ,
503 ..... I05 - III 30 43 I 37 32 I 56 2940) II 55 200 - - .. .
504. I03 - 25 33 30 2 37 33 2 54 31400 5 - 40 - I ' ;
505. I20 - 29 73 43 42 . 4o 59 3:700 2 - . , ~
506.1.... I45 - - I4 33 62 62 57 56 3:900 4 - I

s

CAME—216 SAN FRANCISCO-OAKLAND 000700210 AREA 0...

"7 r'I‘P'I ‘,"T‘ H r" I).
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0 "’"I (‘0' HEB-1N PL. 0 ~- ‘I

APPENDIX C

 

Chi-Square Method

‘0

3

parameters. the number ofthe degrees offreedom in the numerator and the num-

her of degrees of freedom in the denominator. These 100 numbers are usually .

giv en as subscripts of F to ensure proper identification. Thus “0 write
2

(5.10) 5%. ~ n-5,..-»
52

The values for the Fdistribution are available in tabulated form. Usually there
are No tables. one for 5‘72, and one for l‘T’o level of significance. Each table gives
the boundary value of F for a one-tail test. The rows in each table refer to the
number of degrees of freedom in the denominator and the columns to the numv
ber of degrees of freedom in the numerator. For example. in the table for the 5%
level of significanceathe entry in the row labeled “ IO“ and column labeled “15"
is 2.85. This means that “hen we have two independent samples, one of size 16
and the other of size ll, the probability that the ratio (sf/53) would exceed 2.85
is 0.05. That is. the value 2.85 stands for the lower limit of an interval which
extends to +00, and the probability that a value of (sf/53) would fall within this
interval is'0.05.

These tests concerning population variances are strictly true only for normal
parent populations. There are some indications, however, that the results apply
to a large extent also to other types of parent populations, providing they do not
differ from the normal population too markedly.6 But if there are good reasons
to suspect that the parent p0pulation is highly skewed or U-shaped, then the
tests cannot be applied with much confidence.

Coodness-of-F it Test

1 he goodness-01:17: test Is applicable to problems of deciding whether a sample
frequency distribution is compatible with some given theoretical distribution. It
would be used. for instance. to test the assumption that some variable is normally
distributed. In general. the null hypothesis is the proposition that a certain
variable has a specified probability distribution, while the alternative hypothesis
states that the proposition is not true. To test the null hypothesis, we use the fre-
quency distribution obtained in the sample as the evidence concerning the form
of the distribution in the population. The test statistic commonly used in this
case is '

fim—mfi
I=1 e.

wheref, is the sample frequency in the ith interval, e. is the frequency expected
in the theoretical (hypothesized) distribution, and m is the number of intervals.
it can be shown that this test statistic has a distribution which for large samples
can be approximated by the viii-square distribution. In particular. if the sample is
large. then

M“ (II '- (I)?
(5.11) 21 e‘

‘ For a discussion on this topic see, e.g.. G. Udny Yule and M. G. Kendall. An Introduction
to the Theory of Statistics (London: Griffin. 1950), p. 486.

2
~ Xm-k-II

-‘~- v.5 w~'-Qn~.m-w.n.v~—w . j ‘

 

.‘H'. 5~2l Distribution of Selected Tent Statistic-4 149

II here the subscript (m -— k -— l) refers to I’I: number of degrees of freedom.
1 he sample frequenciesj} are observed. and III: theoretical frequencies e. can be
calculated by using the distribution l'orInulI specified by the null hypothesis.

. 1 his formula will involve some unknown parameters which have to be replaced

by their respective sample estimates. For instance. if the null hypothesis specifies
that the population distribution is normal. It will be necessary to estimate the
mean and the variance oftltis distribution from the sample. (Actually, if(5.l l) is
to hold, the estimates must be ofa certain kind. Specifically, the estimates should
be of“maximum likelihood" type—a term that will be explained in Section 6—2.
At this stage it is sufficient to note that X’ is a maximum likelihood estimate, and
3’ is approximately so in large samples.) The number of the degrees of freedom Is
determined as followzs

m = number ofintcrvals;

k = number of parameters that had to be replaced by sample estimates.

For the test to be reasonably satisfactory, it is required that m 2 5 and e. 2 5
for each i.

If the null hypothesis is true,f. can be considered as a sample estimate of 0.,
and the expression in (5.1!) will differ from zero only because we observe a
sample rather than the entire population. Therefore, if we observe a sample for
which the value ofthc test statistic (SJ l) is large, we consider it as evidence against
the null hypothesis. To carry out the test vsc have to determine the boundary
between the acceptance and the critical region. This depends on the number of
degrees of freedom and the chosen level of significance and can be looked up in
the chi-square table. Note that since the statistic (5.11) cannot be negative, evi-
dence against the null hypothesis can only take the form of very large values (and
not very small ones) so that the appropriate test is a one-tail test.

EXAMPLE Economists are often interested in the distribution of personal incomes.
Let us consider the hypothesis that family incomes are normally distributed. To test
this hypothesis we may use the data in Table S -I. These data may be considered as a
sample from a population that includes all possible incomes that could have been
received during I962 in the United States. The statistic to be used for the test is

i (ft - ct)” _ [26] 2(_________77Ifl - In)“

I-I e. IOII

where p. = observed percentage frcquchIeI. and 17. == expected percentage f rc-
quencics. The expected frequencies have to be calculated by titling a normal distribu-
tion to the observed data. To do that we base to estimate two parameters—the mean
and the variance—from the sample. For this purpose we shall use the sample mean
and the sample variance whose values are -

.9 I- 6507 and 6’ - 4920’.

I».... m..- .'

.¢

TESTS or nvrururasrcs ten. 5

ISO
Table 5-1
Interval Mid; I-int‘ Percent of
Familiesf
Under $2,000 1.! 30 12.7
$2,000 to $2.999 “2.90 9.4
$3,000 to 83.999 3.440 10.8
$4,000 to $4.999 4.5l0 ".7
$5,000 to $5,999 5.490 11.4
$6,000 to $7,499 6.690 14.4
$7,500 to $9,999 8.570 13.9
$10,000 to $14,999 11.960 10.5
$l5,000 and over 22.780 5.2
Total 100.0

Total number $7,890,000

 

‘ Midpoints were calculated by dl~t~ltng total income (after tax)
in each income class by the number o1 recipient families in that class.

1 Includes unattached individuals.

Source: Statistical Abstract of the ('nited States. I965, U.S. De-
partment of Commerce, Table 467.

To obtain the frequencies of the normal diSllll‘llllon with the above mean and vari-
ance, we shall follow the procedure described In Section 4-2 and illustrated in Table
44. First, we form the standard normal variable

X -- (.507
z = 7630“—
(where X = income), and recalculate the interval limits in terms of this variable.
Then we find the normal probabilities for cat h income class from the table of areas

.under the normal curve. The results are presented in the Table 5-2. Using these

 

results, we find that

_ _-.__..~_——-—

———.__.

 

 

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

D 2

2 ————U‘ " "l ... 9.454.950.

t-x 9‘ .

The tabulated value of chi-square with 9 -- 2 - 1 = 6 degrees of freedom at 1‘7o
level of significance is l6.8l2. Values smaller than that would fall into the acceptance
region and values that are larger into the critical region. Since in our case the value
of the test statistic far exceeds the boundary value of 16.812, the null hypothesis is to
be rejected. That is, the data do not appear to be consistent with the proposition that
family incomes are normally distributed. -

Conclusion

This brings us to the end of the present section containing the description of
several basic tests. There was a twofold purpose to it. First, we wanted to illus-
trate the development of test procedures in general so that the reader could see

53

See. 5-2] lli-trilrutiurt of Selected Test Statistics 15'

in Concrete terms the kind of problems involved and the method of handling
them. Actually, the specific problems and related tests riven in this section are
not very frequently encountered in enconornetrics. This rs because the statistical
models used are too simple to satisfy the usual demands of economic theory. In
particular. the concentration on one variable to the exclusion ofall other factors

 

 

 

 

 

Table 5-2
Cumulative Normal
Intervals ' Normal Probabilities
Probabilities

x z [(2) Percent
Under 2.000 —oo to -0.92 0.1788 0.1788 17.9
2,000 to 2,999 -0.92 to -0.71 0.2388 0.0600 ‘_6.0
3,000 to 3.999 -0.71 to —-0.51 0.3050 0.0662 6.6
4,000 to 4.999 —0.51 to -0.31 0.3783 0.0733 7.3
5,000 to 5,999 —0.31 to —0.11 0.4562 0.0779 7.8
6,000 to 7,499 —0.11 to 0.20 0.5793 0.1231 12.3
7,500 to 9,999 0.20 to 0.71 0.7612 0.1819 18.2
10,000 to 14,999 0.71 to 1.73 0.9582 0.1970 19.7
15,000 and over 1.73 to +00 1.0000 0.0418 4.2
1.0000 100.0

 

does not do justice to the complexity of economic relations. There is, however,
one common feature between the simple tests discussedin thissseetion_and—,
the tests applicable to more complex situations. Thrs common feature is the

’ ‘ if" use ofdistributions described on the preceding pages: the normal, the chi-square,

the t and the Fdistributions. This was the second and the more important pur-
pose of this section. The discussion of the simple tests enabled us to introduce
these distributions in a natural way, and gave us an opportunity to highlight
their main characteristics and to relate them to each other. For this reason this

section is really indispensable for a complete understanding of econometric
methods.

EXERCISES
5-1. Let X ~ NQu,81). The null and the alternative hypotheses are

”0: ll. '3 10,
lb: p > 10.

The test statistic is to be based on a sample of size 9, and the chosen level of signifi-
cance is to be 57.. Draw a diagram of the power function for this test.

Source: Kmenta, Elements of Econometrics,
MacMillan, 1971, pp. 148-51.

APPENDIX D

 

A Step-By-Step Sample Calculation of Chi-Square

for Tracts 304 and 306

A P P E N D I X D

 

SAMPLE CALCULATION OF THE MEAN, STANDARD DEVIATION AND

CHI-SQUARE VALUES FOR CENSUS TRACTS 304 AND 306.

Steps
(1) Look at the census by block (see xerox of page).

(2) Calculate inferred rent from average value of homes

 

for each block.

For example, Block 101 of Tract 304

 

 

 

Inferred Average Rent = Average Value
130
$373- = $48,500
130

(This procedure is used for predominantly owner occupied tracts
only. On other tracts which are predominantly renter occupied,

use "average rent.")

(3) Classify into Rent-Size categories.

'For the above block: ' Rent

$373

Average Number of Rooms 6.8

so that this would be classified into category (613 to 7.4

average # rooms) and ($330 or more in average rent).

 

 

 

 

 

 

Average Rent ($/month)

Avg. # n . '
Rooms to 89 90--l49 150--209 210--269 270--329 330 up
to 2.6

2.7--3.8

309--500

5.1-46.2

6.3-—7.4 'x

 

 

 

 

 

 

 

 

 

(4) For each category with 15 or more blocks falling into it,

do a Chi-square test.

For tracts 304 and 306 there are three categories to be tested:

a

. (a) ($330 up) and (6.3 to 7.4 rooms)
(b) ($270 to $329) and (5.1 to 6.2 rooms)

(c) ($210 to $269) and (5.1 to 6.2 rooms)

 

 

 

 

 

 

Average Rent ($/month)

Avg. #

Rooms to 89 90--l49 150--209 210--269 270--329 330 up
to 2.6 0 0 0 ' 0 '0 0
2.7--3.8 0 0 0 0 O. 0
3.9--5.0 O 0 0 0 O 0
5.l--6.2 0 0 0 23 15 l
6.3--7.4 0 0 0 0 2 27

 

 

 

 

 

 

 

 

 

(5) For each of the blocks of any one category, calculate

the child density.

 

 

For Block 101 of Tract 304

Density = (% under 18) x (Population)
(# of housing units)

 

.33 x 120 = 1.02
39

 

(6) Calculate the mean and variance for the densities of each

 

category.

Mean = [sum of all densities in a category- = i
¥ of blocks in a category

Variance = Sum of all 'squares' of:

(densities of each block minus the mean)
2
==O’ (square of standard deviation)

for category ($330 up) and (6.3 to 7.4 rooms)

.98899 (child per unit)

i
0' = .24492 (standard deviation)(child per unit)
The values i and.a’ fully describe the hypothesized

probability distribution, that is, the normal distribution.

(7) Set up the boundaries of the sectors along the density
index to be tested so that for each section both the expected
value of the section and the actual are greater than 5.
(In practice for any size-rent category, arrange the

blocks in increasing order of child density. Then

(8)

(9)

experiment with values of child density which would divide

the samples into sections so that the above constraint holds).

For rent-size category ($330 up) and (6.3 to 7.4 rooms)

Actual . 7 7 5 8

 

Expected 5.34 8.154 8.154 5.34

 

 

 

 

 

 

 

\
’ Density Index

(SGUII BurpIAIp)" \L
T808L'
66886'
LTL6I°T

The expected can be calculated from the hypothesized

I'normal' distribution. (See any statistics book.)

Do the chi-square sum.

Chi-square = Sum of all [Actual in a seétor-Expected]2
Expected

The parameter of the chi-square table to be used to see

whether the chi—square sum is significant is the number

of sections minus 2. We can check for various significance

levels.

(5% significance level means that the actual distribution

is the hypothesized one only 1/20 of the time.)

For the category ($330 up) and (6.3 to 7.4 rooms):

2
2 (parameters)

Chi-square =‘X 3.22433

II
N

Parameters = 4 (sections) - 2

APPENDIX E

 

Detailed Summary of Data

DATA FOR TRACTS 304 and 306

 

 

OWNER OCCUPIED

 

DISTRIBUTION OF BLOCKS INTO AVERAGE RENT-SIZE CATEGORIES

 

Average Rent ($/month--inferred)

 

 

 

 

 

 

Rzgms# to 89 90--l49 150--209 210--269 270--329 330 up
to 2.6 0 0 0 O 0 0
2.7--3.8 0 0 0 0 0 0
3.9--5.0 0 0 O O 0 0
5.l--6.2 0 -0 0 23 15 l
6.3--7.4 0 O 0 O 2 27

 

 

 

 

 

 

 

The categories

were tested.

(1) ($330 up)
(2) ($270--329)

(3) ($210--269)

For the density index:

 

(1)

The mean of the children

x =

The s

.98899

tandard deviation

The chi-square

x§=

and (6.3 to 7.4 rooms)
and (5.1 to 6.2 rooms)

and (5.1 to 6.2 rooms)

density index

7" = .24492

3.22433 (not non-normal)

 

Actual 7 7 5 8

 

Expected 5.34 8.154 8.154 5.34

 

 

 

 

 

 

(2)

Density Index

LTL6I'I //

L; {o
(I) co
0 (I)
O) \D
H m
The mean
i = .62798 ‘

The standard deviation
'0’: .20149

The chi-square

 

'Xi = .66462 (not non-normal)
Actual 5 6 4
Expected 5.175 4.650 5.175

 

 

 

 

 

(3)

Density Index

8L?S'

/ \

The mean

i = .44466

The standard deviation
0" = .21892

The chi-square . ;.::;flm;mgxsh;&LWLu.:

2
‘XZ = 2.04546 (not non-normal)

 

Actual 6 7 3 7

 

Expected 5.566 5.934 5.934 5.566

 

 

 

 

 

 

 

 

 

 

. . - Density Index
1» ob Ch
uh ‘0 sh
g—a J:- \l
b m C
N Ch 0
Characteristics of Tracts 304 306
% Owner Occupied Housing 82.0% 88.0% -
% One Unit Housing 86.0% 95.5%
Average Value of a Home ($) $40,000 $36,800

 

 

 

 

 

DATA FOR TRACT 307

 

 

OWNER OCCUPIED

 

DISTRIBUTION OF BLOCKS INTO AVERAGE RENT-SIZE CATEGORIES

 

Average Rent ($/month)

 

 

 

 

 

§§§§s# to 89 90--149 150--2o9 210--269 27o--329. 330 up
to 2.6 o o o o o o
2.7--3-8 o o o o o o
3.9--5.o o o 4 3 1 1
5.l-~6.2 o o 3 3o 5 1
6.3--7.4 o o o o o 4

 

 

 

 

 

 

 

The category ($210-—269) and (5.1 to 6.2 rooms) was tested.

 

For the density index:_

 

The mean

i = .70188

The standard deviation
a’= .34'014

The'chi-square

 

 

 

 

 

 

 

 

 

 

 

 

jKi = 1.95396 (not non-normal)
Actual 5 8 4 5
Expected 5.13 5.22 9.30 5.22 5.13
_,.—””/// .——-
\
. . . f“ " Density Index
w 01 co 0
\l m N N
(0 U1 \l (II
\J m w O
U! N ah pa
Characteristics of Tract 307
% Owner occupied housing 85.8%
% One unit housing 97.5%
Average value of a home ($) $33,100

 

 

 

 

 

. DATA FOR TRACT 328

 

OWNER OCCUPIED

 

\

DISTRIBUTION OF BLOCKS INTO AVERAGE RENT*SIZE CATEGORIES

 

 

 

 

 

 

Average Rent ($/month)
Avg. #
Rooms to 89 90--149 150--209 210--269
to 2.6 0 0 0 0 0 0
2.7--3.8 O 0 0 0 0 0
3.9--5.0 0 0 2 1 0 0
5.1--6.3 0 0 9 38 0 0

 

 

 

 

 

 

 

The category ($210-~269) and (5.1 to 6.2 rooms) was tested.

(That is, 38 blocks.)

For the density index:

 

X2 = 3.46953
4

The average of the children density index over the blocks in

the category

X = .46255 Children
unit

The standard deviation of the density index

0": .16923

The chi-square

Actual 5 10 5 6 8. 4

 

Expected 6.498 6.612 5.890 (5.890 6.612 6.498

\

 

 

 

 

 

 

 

 

5Density
Index

8LTO€° \\\\

98V66'
SSZ9?‘
fZOES'

ZEEZ9' I

The average rents here have been inferred by using the

multiplication factor 1/130 from the average rents.

 

 

 

 

 

 

 

Characteristics of Tract 328

% Owner occupied housing 76.1%
% One unit housing 81.5%
Average value of a home ($) $29,000

 

 

DATA FOR TRACT 353

 

 

OWNER OCCUPIED

 

DISTRIBUTION OF BLOCKS INTO AVERAGE RENT-SIZE CATEGORIES.

 

 

 

 

 

 

. Average Rent ($/month)
Avg. # .
Rooms to 89 90--l49 150--209 210--269 270--319 320 up
to 2.6 0 0 0 0 0 0
”N 2.7—-3.8 o o o o o o
3.9--5.0 0 0 2 ll 0 0 ‘
5.1—-6.2 o o 2 25 1 1 '|

 

 

 

 

 

The rent category ($210 to 269) and size (5.1 to 6.2 rooms) was tested

(25 blocks).

 

For the density index:

 

The average of the child density index over the blocks in

the category

x = .77179

The standard deviation of the density index

0" = .19705

The chi-square

12 1 62472
2 - 0

(not non-normal)

 

 

M) .

Actual 4 10 6 5

 

Expected 5.3 7.2 7.2 5.3

(Hypothesis)

 

 

 

 

 

 

 

 

 

 

3‘ L, ‘0 )r Density Index
H ~3 N
A +4 w
H ~3 p
m \o w
Characteristics of Tract . 353
% Owner occupied housing 78.2%
% One unit housing 88.5%
Average value of a home ($) $29,300

 

 

 

 

DATA FOR TRACTS 127 and 128

 

 

RENTAL AREAS

 

DISTRIBUTION OF BLOCKS INTO AVERAGE RENT-SIZE CATEGORIES

 

Average Rent ($/month)

 

 

 

 

 

 

$3315# -to 89 9o—-149 150--209 21o-—269 27o—-329 330 up
to‘ 2.6 o 1 1 o o o
2.7--3.8 o 6 27 o o o
3.9--5.o o 1 13 5 o o
5.1--6.2 o o o o o o
6.3--7.4 o o o o o o

 

 

 

 

 

 

 

 

The category ($150--209) and (2.7 to 3.8 rooms) was tested.

For the density index:

 

The mean value
§ = .12270

The standard deviation

 

0’= .07099
The chi-square

2 .
11 = 7.19153 (non-normal at 99% accuracy)
Actual 4 8 15

 

Expected 8.802 9.396 8.802

/ \

 

 

 

 

 

" Density Index

SL060°
S9VSI'

Notice that this tract is biased toward having children.

 

 

 

Characteristics of Tracts 127 128
% Rental housing _ 78% 72.5%
% Single family housing 12% 18.0%

 

 

 

 

 

DATA FOR TRACTS 126/129

 

 

RENTAL AREAS

 

DISTRIBUTION OF BLOCKS INTO AVERAGE RENT-SIZE CATEGORIES

 

AverageRent ($/month)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

$3345# to 89 9o--149 150--209 210--269 27o--329 330 up
to 2.6 0 0 l 0 0 0
—2.7--3.8 0 10 34 l 0 0
3.9-~5.0 0 4 5 4 0 0
_5.l--6.2 0 0 0 0 0 0
6.3--7.4 0 0 0 0 0 0
The category tested was ($150-~209) and 2.7--3.8 rooms).
For the density index:
The mean
E = '.15300
The standard deviation
0"= .12996
The chi-square
‘x3 =12.05086 (not normal at 99% accuracy)
Actual 6 11 7 5 5
EXpected 8.772 5.270 5.916 5.270 8.772
A
‘6 L, L3 L, > Density
$_ 2 '03 4': Index
31 S {I 2
Characteristics of Tracts 126 129
% Rental housing 75% 85%
% Single Family housing 16% 7.6%

 

 

 

 

 

 

3 Ngtg that the bias is against having families with children.

DATA FOR TRACTS 130/131/135

 

 

RENTAL AREAS

 

DISTRIBUTION OF BLOCKS INTO AVERAGE RENT-SIZE CATEGORIES

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Average Rent ($/month)
AVg. # ‘ .
Rooms to 89 90--149 150--209 210--269 270--329 330 up
to 2.6 2 0 0 0 0 0
2.7--3.8 1 7 23 16 O O
3.9--5.0 0 0 8. 5 0 0
5.l--6.2 0 0 0 0 0 0
”\ 6.3--7.4 O 0 0 ' 0 0 O
1The categories (1) ($210-~269) and (2.7--3.8 rooms)-
and (2) ($150-—209) and (2.7--3.3 rooms) were tested.

(1) -For the density index:

 

The mean

X

.08285

The standard deviation

5'...

The chi-square

Xi

.04898

5.48369

(not normal at 97.5% accuracy)

 

(2)

Actual 8 1

 

Expected 5.216 5.568

5.216

 

/

 

 

 

 

SOS80' /////

 

 

 

 

5’ 7%: Density Index
co
0
0‘
u:
Characteristics of Tracts 130 131 _135
% Rental occupied 80%. 88% 88%
% Single Family Homes 8% 4% 7%

 

 

 

 

Note that the distribution is bipolar.

Many areas

with few children and many areas with many children

but few with the average numbers.

For the density index:

 

The mean

i = .12831

The standard deviation
0’: .08921

The chi-square

1}: = 2.79956

(not non—normal)

-For the category ($150--209) and (2.7--3.8 rooms):

 

Actual 7 8 3 5

 

Expected 5.221 6.279 6.279 5.221

 

 

 

 

 

A.
I

Density Index

ZZS6I° /

ObI90'
IEBZT’

Note however the bias is toward having fewer children.

DATA FOR TRACTS 133/134

 

 

RENTAL AREAS

 

'DISTRIBUTION OF BLOCKS INTO AVERAGE RENTrSIZE CATEGORIES

 

 

 

 

 

 

 

Average Rent ($/month) ‘

Avg. # .

Rooms to 89 9o--149 150-—209 210--269 27o--329 330 up
to 2.6 o o ' o . o . o o
2.7--3.8 o 4 6 2 o o
3.9-~5.o o 2 13 17 o o
5.1—-6.2 o o o o o o
6.3--7.4 o o o o o o

 

 

 

 

 

 

 

 

The category ($210--269) and (3.9—-5.0 rooms) was tested.

For the density index:

 

The mean
E = .76878
The standard deviation

0" = .33569

The chi-square

TK: = .15597

 

 

 

 

 

 

Density Index

 

 

 

Actual 5 6 6
Expected 5.253 6.494 5.253
7 .

a. to

o. o:

C ax

\D 01

u: 4»
CHARACTERISTICS OF TRACTS 133 134.
'% Rental Occupied 62% 79%
% Single Family Homes 31.6% 12%

 

 

 

 

 

DATA FOR TRACTS 154/401/451

 

 

RENTAL AREAS

 

DISTRIBUTION OF BLOCKS INTO AVERAGE RENT-SIZE CATEGORIES

 

 

 

 

 

 

 

 

 

 

 

 

 

Avg. 4 Average Rent ($/month)
Rooms to 89 90--l49 150--209 210--269 270--329 330 up
to 2.6 0 o 0 0 0 0
2.7--3.8 0 17 11 1 0 0
3.9--5.0 0 23 13 3 0 0

. 5.1--6.2 o o 0 o o_ 0
6.3--7.4 0 '0 0 0 0 0

 

 

The categories (1)

(1)

(2)

($90--l49) and (2.7-~3.8 rooms)

and (2) ($90--149) and (3.9--5.0 rooms) were tested.

For the child density index:
The mean

i % .62809

The standard deviation

0": .42908

The chi-square

 

Xi = 18.40882 (not normal at 99% accuracy)
Actual 0 15 2
Expected 5.253 6.494 5.253

 

//\

 

 

 

\

 

SO9I9’
EIOVB'

; Density Index

Note that the distribution is too concentrated about

the mean to be normal.

For the child density index:

The mean

Q- = .48169

The standard deviation
0— = .18363

The chi-square

Ax: = 1.39000 (not non-normal)

Actual 5 4 8

 

Expected 5.082‘ 5.418 5.418

5.082

 

 

 

 

 

 

 

 

 

 

 

 

 

, , , ’Density Index
to ob Ch
m a: id
us F4 <5
l-' ox N
W \D b)
Characteristics of Tracts 154 401 451
% Rental housing 72% 73% 66%
% Single family housing 22% 20% 22%

 

 

DATA FOR TRACTS 402/426

 

 

RENTAL AREAS

 

DISTRIBUTION OF BLOCKS INTO AVERAGE RENT-SIZE CATEGORIES

 

 

 

 

 

 

 

 

 

 

 

 

 

' Average Rent ($/month)

Avg..# . .

Rooms to 89 90--149 150~-209 210--269 270—-329 330 up
to 2.6 l 0 0 0 0 0
2.6--3.8 0 13 10 0 0 0
3.9-~5.0 0 7 24 1 0 0
5.l-—6.2 O 0 0 0 o o
6.3--7.4 O 0 0 0 0 0

 

The category ($150--209) and (3.9--5.0 rooms) was tested.

 

For the density index:
The mean
; = .56567
The standard deviation

0" = .18271

The chi-square

“X: = 2.28900 (not non-normal)

Actual 8 5

 

EXpected 5.088 6.192

6.192

5.088

 

 

 

 

 

 

056T? ' \\

L9S9S°

VBTIL' /

\
/ Density Index

Note: The qualitative bias is toward not having

families with children.

 

 

 

 

Characteristics of Tract 402 426
% Rental housing 74% 64.2%
% Single family housing 20% 29.0%

 

 

 

 

B I B L I O G R A P H Y

 

Government Publications

 

San Francisco Department of City Planning

Residence, 1973 Vacancy Survey, October, 1973.

 

San Francisco 1970: Population Characteristics. April, 1973.

 

1973 Changes in San Francisco Housing Inventory, April, 1974.

 

San Francisco Unified School District

Planning Report: Demographics & Enrollment Facilities,
Inventory & Capacities
1975 Faculty Needs. January, 1973.

 

San Francisco Human Rights Commission

No Children (background material on the draft ordinance
File 601- ~73), Staff Report, January, 1974.

 

U.S. Bureau of Census

Block Statistics, San Francisco—Oakland Area
HC(3)-24, U.S. Census of Housing, 1970.

 

Block Group Statistics, San Francisco-Oakland
STPI-l.

 

Books

Hays, William L., Statistics, Holt, Rinehart and Winston,
New York 1963. ; 4

 

Hogg, Robert V. and Allen T. Craig, Introduction to Mathematical
Statistics, (3rd Ed.) MacMillan, London, 1970. '

 

 

‘Kmenta, Jan, Introduction to Econometrics, Macmillan, New York
1963.

Mendenhall, William, Introduction to Probability and Statistics
(Second Edition), Wadsworth Publishing Co., Inc., Belmont,
California, 1967.

 

rH ' " ' . ~.
Ii..\/fil:;/s(1 \._. /\:

l( ‘

A

FAST LN .' mHG, M

 

'f‘)_

.K,’!

 

HC—LAN

 

 

 

 

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