Department of Urban Studies and Planning
Massachusetts Institute of Technology
11.220 Quantitative Reasoning and Statistical Methods for Planning I
Spring 1999
[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, 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.

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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….”
(a) What type of probability sampling did the author use in this study? Why did she [6] choose this form of sampling instead of one of the other forms?
Ms. Miraftab used stratified random sampling in her survey. She was interested in examining the housing options facing poor households in Guadalajara, Mexico (her target population). In particular she was interested in the relationship between gender and location tenure and spatial configuration. She chose her strata, which are the three locations, in order to embrace these housing options. She also chose elected to conduct her sample among females within the three geographic locations, and thereby eliminates poor male headed households with no female present from her sample.
A number of people assumed that because the samples were based in geographic areas she was using cluster sampling. However, cluster sampling involves the following three steps:
1.
Divide the population into groups (clusters)
2.
Obtain a simple random sample of clusters
3.
Use all the members in the clusters as the sample
Although the author did divide the population into geographic groups (Step #1), she did not follow steps 2 or 3 above. Therefore, in the strict sense of the definition this is not cluster sampling.
The author chose this form of sampling because of her interest in examining the housing options facing the poor, and her belief that these three areas encompassed those options. However, it also appears that she chose her particular sample based on time and resource constraints, and her familiarity with at least one of the areas.
Since the author was interested in a particular segment of the population in Guadalajara (poor), a simple random sample would be to broad. However, once she had defined her strata she could use either simple random or systematic sampling. Here she chose to take a simple random sample of 30 females within each of the three geographic areas.
[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.)

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The author's sampling technique could lead to non-random sampling error as well as nonsampling error. One main problem source of non-random sampling error could be that her sample was not representative of the population of interest. The author chose to take a sample of
30 from each of the three locations. Not only are these small samples when trying to generalize to a very large poor population, but these locations most likely differ in size, as well as tenure.
In order to present accurate results she could have varied the sample size in each area to reflect the area’s overall share of the poor population, or, more easily, weighted the results in order to reflect differences in the relative size of the areas.
A second source of non-random sampling error could result because she had lived in the
Colonia, one of the three areas included in the sample. Her familiarity with the area, and with the residents of the area, could have resulted in more candid responses from female household members in the Colonia than in the other two areas. Also, personal experience bias, or lack of complete objectivity could have resulted due to her familiarity with the Colonia.
Another problem with the sampling technique used by the author is with her decision to interview female household members only. The poor in third world countries such as Mexico have strictly imposed gender roles that may lead to non-sampling errors, or problems with the responses. In addition, as mentioned above, by failing to interview males she eliminates male households with no females present from her parent population although these households are included in the target ‘poor’ population.
[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.
The author uses the word correlation to indicate an association between gender of household head and choice of housing among the poor, in other words, they are not independent. She is claiming that there is a recognizable difference in choice of location and type of housing based on gender. Female household head tended to choose inner-city locations and multi-tenant settlements, while male headed households were less concentrated in the inner city.
The author is actually using joint probability here not correlation in the strict mathematical sense of the term. In other words, she is looking at the joint probability of inner-city versus peripheral location based on gender of household head; the joint probability of tenure (rent versus own) based on gender of the household head; and the joint probability of shared versus single family residence based on gender of the household head.
[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?

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Perhaps the author was unable to interview some of the sample female household members, or for some other reason they did not respond. If this were the case the author would lose these observations. This may be of concern if the households that were unable to be interviewed were more likely to have a common characteristic, such as being headed by females. In the Periphery we see a larger share of male-headed households. If the females in these locations don't need to work, and thus are more likely to be at home for an interview, then we may be losing something by not including female headed households who are working in the Inner-city or Colonia.
Another possibility is that there are some households made up of unrelated individuals. If this were the case then there would be no single household head. The author may have chosen to eliminate these households from the sample.
Minimally, the author should have explained the reason for the missing sample data. This would help inform the reader, and prevent the reader from misinterpreting, or trying to fabricate a reason for the missing observations.
[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?
The author accounted for 5 of the missing respondents by explaining that they were neither renters nor owners, but were 'casa prestades'. If we assume that the four observations missing from the location columns, and apparently missing from the spatial configuration columns are also missing here, then we are left with 3 unexplained missing observations in the tenure area.
Here the error is of concern because when coupled with the other missing households, there are a large number of total households missing. The most likely reason for these additional three missing observations is that these households fit under some form of tenure other than renting or owning. If this is the case, then the sample question did not include all foreseeable tenure categories and another column should be added to explain these missing observations.
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).

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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 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
Househol d
Type 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)
Inner city Periphera
27.6%
(16)
Location l
36.2%
(21)
Colonia
Inbetween
36.2%
(21)
Own
Tenure*
52.8%
(28)
47.2%
(25)
Spatial Configuration
Rent Shared &
Semishared
50%
(29)
Singlefamily residence
50%
(29)
Male- headed
(58)
Femaleheaded
(28)
42.9%
(12)
32.1%
(9)
25%
(7)
44%
(11)
56%
(14)
71.5%
(20)
28.6%
(8)

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* Calculation 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.
[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
M-Male
F- Female
IC – Inner City
P-Peripheral each outcome.
C-Colonia
Poor HH in
P(IC|M)=.276
P(P|M)=.362
P(M)=.674
Male
P(C|M)=.362
Guadalajara,
Mexico
Female
P(F)=.326 P(IC|F)=.429
P(P|F)=.321
P(C|F)=.25
P(Male and Inner City) =
.674*.276 = .186
P(Male and Peripheral)=
.674*.362 = .242
P(Male and Colonia)
.674*.362 = .242
P(Female and Inner City)=
.326*.429 = .1395
P(Female and Peripheral)=
.326*.321 = .105
[4]
P(Female and Colonia) =
.326*.25 = .081
(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.
P(Male|Inner City) P(Male & Inner City) P(Male & Inner City)
= = =.186/(.186+.1395)= .5714
P(Inner City) P(Male & Inner City) + P(Female & Inner City
The probability that an Inner-City household randomly selected would be male headed is 57.1%.
(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

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[4] 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.)
The author is showing the percentage of all surveyed female headed households located in each of the 3 geographic areas [e.g.-P(IC|F)], NOT the percentage of the households in the geographic area headed by females [e.g.-P(F|IC)]. Because the percentage P(IC|F) = P(F|IC) the calculation is only clear when looking at the Periphery, or when looking at the comparative percentages for male headed households.
The author states that less than a third (32.1%) of the residents of the Periphery are headed by females. This is based on a denominator of 28, or the total number of female headed households, rather than a denominator of 30, or the total number of households surveyed in the Periphery.
If she were looking at percentage by gender given a geographic area, we would expect the percentages in each of the columns in the LOCATION columns of the table to sum to 100. Thus if ‘ half of all residents (sic) of the inner-city vecindades (42.9%) were headed by women alone’, then by definition 57.1% of the inner-city households must be must be headed by males.
However, we are given a value of 27.6% which actually reflects the percentage of all male headed households located in the inner-city [P(IC|M)], not the percentage of all households in the inner-city headed by males [P(M|IC)].
[8] (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.
The author has taken independent samples from the 3 locations and then combined them as if they represent the poor in the city of Guadalajara. The problem with her analysis arises when she attempts to combine and compare data across rows. Because she has not weighted each location by its relative size (the total number of poor households in each location), she is not making accurate comparisons. As long as she is looking within a column she does not have a problem because the sample is from a single area, and thus doesn't need to be weighted.
However, when she begins to compare across rows, such as comparing the share of female household heads in an area (i.e. Colonia) to the total number of female household heads in all three areas, she is not providing accurate percentages because of the difference in relative size of the areas.
Question 2
Attached is a “National Survey” that was sent to me by the American Farmland Trust.

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[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.
The American Farmland Trust “National Survey” is more a fund raising ploy than a survey instrument.
The questionnaire begins by asking whether the respondent is aware of the problem of disappearing farmland. It then points to examples of problems facing farmers and possible ways of protecting them. Finally, the ‘survey’ asks for donations to help preserve America’s farmland and protect America’s farmers. Essentially, the ‘survey’ is aimed at those sympathetic with the farming industry, and thus the results of the survey will be biased in favor of the farming industry, as non-respondents (non donators) will be less concerned with preserving America’s farmland, and thus more likely to disregard the survey.
The survey is intended to elicit personal support of the Farmland Trust, and thus the questions are leading and the words and phrases used are strongly biased in favor of the cause. Some examples of these biased phrases are: vanishing farmlands, mounting problems, encroaching development, growing burden, etc.
Another example of bias is the scare tactics that the Farmland Trust uses in order to elicit a emotional response. This is particularly evident in question #9 where they suggest that a food shortage will be eminent unless something is done immediately. Finally, nearly all of the questions are looking for simple Yes/No answers. None of the questions provide room for qualified answers, or different levels of agreement. All of these tactics used by the Farmland
Trust combine to make this survey subjective, and strongly biased.
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?
The City of Burlington's use of a clearly laid out cover page is intended to up the response rate for the survey. It provides all of the information on the cover page in order to portray itself as genuinely concerned with eliciting public participation. It outlines the various ways in which citizens may help in the formulation and development of community and economic development policies, and outlines the multistage tact that the city is taking to garner this input. In general the tactics used by the City should be effective. However, the level of its effectiveness depends upon the manor in which it is distributed. If the survey is mailed to all citizens, and widely publicized in other ways (local newspaper, billboards, etc.), and followed up on then it will be more effective.

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[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.
The City is using a dual survey approach in order to both get a high level of response from the simple random survey, and a high level of detail about issues from the from the Individual
Citizen Response survey. The random sample survey is being used to gauge the opinions of the entire population of Burlington. By making this survey relatively simple they hope to get responses from most of the survey recipients. This will give a general view of the population.
The individual response surveys are used to gather a wider variety of responses, and perhaps to gauge the depth of feelings within the town. A ‘self-selected’ group of citizens with strong concerns about the issues at hand will choose to complete the more detailed survey. The results of these surveys cannot simply be tabulated together because they are drawn from different parent populations, and therefore do not talk about the same target population.
[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?
 One problem with the survey is that in an attempt to be comprehensive, the survey gets to be too long and a bit repetitive. This may lead to careless responses by respondents.
 Another problem is that the survey does not appear to be postage paid. If the City is really interested in garnering feedback from all possible respondents it should have made it easy to fold up and return the survey without having to pay postage.
 Another problem is that the survey uses boxes that vary in size according to the strength in feeling of response. The boxes for ‘strongly agree’, ‘agree’, ‘disagree’, and ‘strongly disagree’ should all be the same size. Furthermore, a separate box should be added for no opinion.
 There are no instructions provided for questions 21-25.
 The answer boxes for each question should be next to the question to avoid error by the respondents and those transcribing the responses.
 Overall, the survey should have provided for a consistent method of response. Either check, fill in the circle, etc. By changing the way in which the respondent is to respond to different questions the survey becomes unduly complicated.