Department of Urban Studies and Planning
Massachusetts Institute of Technology
11.220 Quantitative Reasoning and Statistical Methods for Planning I
Spring 1999
Homework Set #3
Due: I have made this homework set shorter than normal, including only material that we will
cover before spring break. Also, I am not asking for it to be handed in until one week after the
draft Census Paper. Hopefully, this will afford more of you the opportunity to write draft Census
Papers. Therefore, this homework set is due in class, Monday, April 5. (Note that this also
means that Homework Set #4 will cover quite a bit of material. We will not be able to change
the due date (April 14) because of the necessity to grade it and give you feedback before the
midterm exam.)
[Total = 78 points]
Sampling, Surveys, Opinion Polling, Probability
Question 1
This question is based on a journal article: Faranak Miraftab, “Revisiting Informal-Sector
Home Ownership: The Relevance of Household Composition for Housing Options of the
Poor,” International Journal of Urban and Regional Research, Vol. 21, No. 2, 1997.
Part of Professor Miraftab’s analysis was based on a survey. Quoting from the research
methodology section of the paper:
“The study presented in this paper was carried out in 1992-93 in the
Metropolitan Area of Guadalajara, the second largest city of Mexico with
over 2.8 million inhabitants (1990 census). Complying with the national
trend, the majority of the city’s housing units are owner-occupied (67.13%
owner-occupied versus 24.4% rental units, according to the 1990 Censos
de poblacion y vivienda). Based on preliminary research, I chose three
areas that embraced a range of housing alternatives commonly adopted by
the poor in Guadalajara. These included renting, owning or sharing a
residence, and choosing to live in central or peripheral locations. The first
research area was in the city center, and included renters of the multitenant vecindades, which are characterized by a series of rooms
surrounding a common courtyard. In vecindades each household rents
their own room, but they share the courtyard as well as the sanitary
services and washing areas located in the courtyard. The second research
area was a newly developing irregular settlement located on the northern
edge of the Metropolitan Zone. This area predominantly constituted
owner-occupied units constructed through self-help strategies. However,
11.220: Quantitative Reasoning and Statistical Methods for Planning
Homework Set #3
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it lacked basic urban services such as sewerage, pavements, water, and
electricity, and had only limited transportation connecting it to the rest of
the city. The third research area was a colonia in which I had previously
lived and worked on a different research topic. It is located between the
other two areas, less than ten kilometers from the city center, and is fairly
accessible to other parts of the city. It is an older working class
neighborhood, with a mix of renters and owners. Initially formed in the
1950s as an irregular settlement, it had obtained basic urban services over
the past four decades.
The field research included two phases and employed quantitative and
qualitative approaches. In the first phase of research, 90 random surveys
were conducted with adult female members of households (30 households
in each neighborhood) to explore possible relationships between housing
and household variables. For example, the relation between the gender of
the household head and the location of the housing (peripheral vs. central),
the housing tenure (renting vs. owning), and the residential spatial
arrangement (shared vs. single residency) were examined through the
survey data….”
[6]
(a)
What type of probability sampling did the author use in this study? Why did she
choose this form of sampling instead of one of the other forms?
[4]
(b)
Given this description of the sampling technique used, can you think of any
problems that might have crept into the sampling and biased the resulting
estimates. (Please concern yourself with bias rather than a lack of precision here.)
In a section of the paper entitled, “Research results: links between household composition
and housing decisions,” Professor Miraftab reports the following results, making
reference to Table 1:
“The results of the random survey showed a clear correlation between the
housing options adopted by low-income families and the composition of
their household based on the gender of the household head. In my sample,
households who identified their head as a woman (32.6% of all
households) commonly adopted different residential alternatives than
those who identified their head as a man. This differential pattern
concerned locations within urban space, tenure status and living
arrangement. In general, female-headed households were concentrated
among renters in the inner-city area and in shared residencies; by contrast
male-headed households had a lower concentration in the inner city, were
more likely to be home owners and were equally distributed in shared or
single-residencies (see Table 1).
Of all the female householders in my sample group, 42.9% were
residents of the multi-tenant units of the inner city, with 32.1% living in
11.220: Quantitative Reasoning and Statistical Methods for Planning
Homework Set #3
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the peripheral settlement and 25% in the consolidated colonia. This was,
however, the reverse for male-headed households, whose concentration
was less in the inner-city vecindades (26.7%) than in the two other areas
(36.2% in each). Considering the sample group in each area, the survey
shows that close to half of all residents (sic) of the inner-city vecindades
(42.9%) were headed by women alone. In the peripheral settlement,
however, less than a third (32.1%) and in the consolidated colonia only a
quarter of all the households (25%) were headed by women.
The sample from the three studied areas also indicated that sharing a
place of residence was much more common among female- than maleheaded households. Independent of their tenure status as renters or
owners, female-headed households were far less likely than male-headed
households to live in single-family residencies. Only 28.6% of households
with a female head were living in a single-residency setting, whereas half
of all male-headed households in my sample lived in such a setting.”
Residential tenure was another differential pattern observed in the
survey information. Female householders were mostly renters (56%), but
male-headed households were mainly home owners (52.8%). The data on
ownership status of female householders, however, should be interpreted
with caution. For a considerable number of female householders who
owned a home, the home ownership had occurred prior to their becoming
the head of household. If only those who achieved home ownership as
single mothers were accounted for, the percentage of female home owners
would be reduced from the recorded 44%, indicating an even greater gap
in the ownership status of the two household categories.”
Table 1 Distribution of male- and female-headed household by type of housing (numbers in ( )
represent number of respondents)
Household
Type
Location
Inner city
Peripheral
Tenure*
Colonia
In-between
Own
Spatial Configuration
Rent
Maleheaded (58)
27.6%
(16)
36.2%
(21)
36.2%
(21)
52.8%
(28)
47.2%
(25)
Shared &
Semishared
50%
(29)
Femaleheaded (28)
42.9%
(12)
32.1%
(9)
25%
(7)
44%
(11)
56%
(14)
71.5%
(20)
Singlefamily
residence
50%
(29)
28.6%
(8)
* Calcuation of tenure percentages excludes 5 respondents in my sample who lived for free in accommodation lent to
them by a relative or acquaintance who themselves did not live in the unit. Those living in lent houses or ‘casas
prestadas’ are neither renters nor owners.
11.220: Quantitative Reasoning and Statistical Methods for Planning
Homework Set #3
Page 4
[4]
(c)
The first sentence of this summary uses the word “correlation,” but no correlation
coefficient has been calculated here. How is the author using the word
“correlation” in this context? Use the concepts of probability in your answer.
[4]
(d)
The description of the methodology for this project stipulates that 90 households
were sampled, 30 in each neighborhood. Yet, this table tabulates fewer than 90
households. In the portion of the table that summarizes location by household
type, only 86 households are tabulated. What do you imaging happened to the
other four? Should this be of concern to the overall study?
[4]
(e)
In the portion of the table that summarizes tenure by household type only 78
households are tabulated? What has happened here? Is this of concern to the
overall study?
[8]
(f)
Create a probability tree that represents all of the probability information
contained in the portion of the table that summarizes location by household type.
Clearly mark and label all of the nodes and branches, associate the appropriate
probabilities with each branch, and calculate the correct joint probabilities for
each outcome.
[4]
(g)
From the probability tree, show how one would calculated the probability that an
inner-city household randomly selected from these combined samples would be
male-headed.
(h)
At the end of the second paragraph describing the research results are the
following sentences (copied from above):
“Considering the sample group in each area, the survey shows that close to half of
all residents (sic) of the inner-city vecindades (42.9%) were headed by women
alone. In the peripheral settlement, however, less than a third (32.1%) and in the
consolidated colonia only a quarter of all the households (25%) were headed by
women.”
[4]
[8]
What mistake has the author made in both of these sentences? (Note: I am not
referring to the incorrect usage of the word “residents” in the first sentence.)
(i)
So far, the questions that I have asked have focused on relatively minor, technical
issues associated with this study. However, in conducting the analysis in Table 1,
the author has made one tremendous conceptual error that calls all of her
conclusions into jeopardy. What is it? Explain as clearly as possible.
11.220: Quantitative Reasoning and Statistical Methods for Planning
Homework Set #3
Page 5
Question 2
Attached is a “National Survey” that was sent to me by the American Farmland Trust.
[10]
(a)
Write a paragraph discussing this survey as an instrument for gathering
information about people’s views on these agricultural issues. Be sure to discuss
the wording of specific questions as well as the order of the questions.
Question 3
Also attached is a survey put together by the Burlington, Vermont Community and
Economic Development Office.
[6]
(a)
Comment on the cover page (“Citizens’ Attitudes Toward Burlington’s Future”).
Why is all of this information being given to possible respondents? In your view,
is it effective?
[8]
(b)
What is the point of conducting what seem to be two different surveys—a
Random Sample Survey and an Individual Citizen Response survey? Why can’t
the results of the two surveys simply be tabulated together? Be as explicit as
possible in your answer.
[8]
(c)
While this is a reasonably designed survey it is possible to criticize some of its
elements. What criticisms would you make of the design of this survey
instrument to gather information on citizen attitudes toward development in
Burlington?