Bringing the Person Back In: Boundaries, Perceptions

Bringing the Person Back In:
Boundaries, Perceptions, and the Measurement of Racial
Context
Cara Wong⇤
Jake Bowers
Tarah Williams
Katherine Drake
March 16, 2012
Abstract
Place is sometimes vague or undefined in studies of context, and scholars use a range of
Census units to measure “context.” In this paper, we borrow from Parsons and Shils to offer
a conceptualization of context. This conceptualization, and a recognition of both Lippmann’s
pseudoenvironments and the statistical Modifiable Areal Unit Problem, lead us to a new measurement strategy. We propose a map-based measure to capture how ordinary people use information
about their environments to make decisions about politics. Respondents draw their contexts on
maps — deciding the boundaries of their relevant environments — and describe their perceptions of the demographic make-up of these contexts. The evidence is clear: “pictures in our
heads” do not resemble governmental administrative units in shape or content. By “bringing the
person back in” to the measurement of context, we are able to marry psychological theories of
information processing with sociological theories of racial threat.
Assistant Professor, Dept of Political Science, University of Illinois @ Urbana-Champaign
([email protected]). Acknowledgements: We thank Andrea Benjamin, Alana Hackshaw, and Laura
Potter for their excellent research assistance on the survey, the Interdisciplinary Institute at the University of Michigan
for funding the pilot study, and University of Illinois Center on Democracy in a Multiracial Society for a fellowship
for Wong. Thanks for excellent suggestions, critiques, and comments from colleagues at Illinois (particularly Jim
Kuklinski, Wendy Tam Cho, Jeff Mondak, and Mark Fredrickson), Michigan (particularly Spencer Piston and Jeff
Morenoff), and Harvard (particularly Dan Hopkins and Claudine Gay), participants of the 2011 Chicago Area Behavior
Workshop (particularly Dennis Chong, Jamie Druckman, and Eric Oliver), Kathy Cramer Walsh, Austin Troy, Rick
Wilson, and many anonymous reviewers for the political science, geography, and sociology panels of the National
Science Foundation.
⇤
The study of individuals interacting with their environments has a long history (Lewin, 1936;
Tingsten, 1937) and a vibrant presence today in the large literature on “context effects” or “neighborhood effects.” The results are fascinating, but practical matters may hinder continued progress.
In particular, scholars could make the following general observations about the last 75 years of
this research: (1) we use contextual measures that are readily available; (2) different measures of
context generate different results; (3) people’s perceptions of their environment do not resemble
governmental units; and (4) people define their environments differently. Taken together, these
critical observations suggest that when we use administratively drawn geographic units as “context,”
we risk confusion of multiple types.
Given these observations, why would scholars continue to use data collected at the level of an
administrative unit as measures of people’s contexts almost exclusively? There are at least two
reasons for this persistence: many scholars do not have the time and money to collect alternative data,
and more importantly, we do not know how to determine whether a unit is the “right” one. But, we
often require our students embarking on research projects to answer two questions: Are the concepts
and measures clear and meaningful? And, how does the proposed design relate to the ideal design?
The four observations made above imply that it would be difficult to answer these two fundamental
questions. To remedy this problem (and try to practice what we preach), we offer a theoretical
foundation for contextual effects, propose a data collection methodology that is commensurate with
it, and then present illustrative data as proof of concept.
Our new map-based measure of context ought to help future researchers answer both questions
of measurement — what kind of geographic units ought to be most relevant for individual attitudes
and behavior? — as well as questions of mechanism — how does place get into the heads of people
and how do people represent places in their minds? The operationalization of context needs to
capture the many different ways that the macro-social demography of a community is linked to the
political psychology of its residents. Therefore, we ask respondents to draw their contexts on maps
— wherever they see the boundaries of their communities — and then describe the content of these
contexts. With our new measure of context, we examine whether people’s “pseudoenvironments”
1
reflect the “objective” context across multiple units of analysis and discuss the distance between
common practice and our conceptualization of context. We also ask why levels of misperception
may vary at different geographies and across different attributes of an area, raising new questions
about the mechanisms by which contexts affect individuals.
Our results help deepen and extend our knowledge about how context matters in politics, showing
that governmental administrative units do not define the environments relevant to individuals, and
that people do not “see” what the Census “sees.” Census numbers may be related to political
judgments, but only by studying how these facts become beliefs can we understand more fully
the mechanisms by which place affects politics. By measuring the environment that is personally
relevant to the individual, we can also help researchers avoid a serious, intractable methodological
problem — the modifiable areal unit problem — that could explain the inconsistency of results in
research on racial threat and contact.
After a quick summary of some of the meanings of context and contextual outcomes, we explain
why a clear conceptualization will help us address some of the observations made about previous
research. We then describe why there are problems in measurement at the level of both the aggregate
contextual unit as well as the individual. Finally, we use a pilot study to illustrate the use of these
new ways to approach the study of context and compare the effects of different measures.
1 Situating Research on Context
The places where people live can affect them in a myriad of ways because context can be both
objective and subjective, and the outcomes can be physical or psychological (Sampson, Morenoff
and Gannon-Rowley, 2002; Shinn and Toohey, 2003).1 For example, in the case of pollution,
environmental allergens in the air breathed by individuals have a direct physical effect on their lungs
and health (Braun-Fahrlander, 2002). This “context effect” requires no knowledge on the part of its
residents about the environment or its contents; one does not have to see and recognize smog to be
affected by it. Similarly, living in a poor area can minimize people’s ability to engage in politics due
1
In this paper, we set aside explicit considerations of personal networks of acquaintances and focus on the perceptual
mechanisms of impersonal interactions only (Huckfeldt and Sprague, 1987). We do discuss how some measures of
impersonal interactions may, in fact, reflect interpersonal mechanisms, and focus on “geographic context” rather than
“social context” (Huckfeldt and Sprague, 1995).
2
to limited access to information sources and politicians’ attention, all without entering into these
residents’ cost-benefit calculations about whether to participate in politics; they may not realize
resources are missing, but the contexts in which they live can still influence their behavior.
People’s surroundings can also have less direct effects, particularly when the outcomes are
psychological in nature. For many important political phenomena, people must be cognizant of their
environment for it to have an impact. Living in a poor area, for example, can also lead individuals
to feel threatened. A preponderance in one’s community of high school dropouts, individuals
living below the poverty line, and broken windows can lead to fears of crime or dropping property
values, along with a greater sense of alienation and political inefficacy (Sampson, Morenoff and
Gannon-Rowley, 2002). Similarly, living in an area with many racial outgroup members can lead to
fear for one’s job, identity, or political voice (Blalock, 1967; Taylor, 1998). These perceived threats
are the main concern of political scientists focused on racial context (see, for only a few examples,
Key (1949); Glaser (1994); Oliver (2010)). However, one cannot argue that these environmental
characteristics lead to feelings of threat without someone — elites, if not also ordinary residents —
being conscious and cognizant of the context (Lazarsfeld, Berelson and Gaudet, 1968). After all,
fear is an emotional response to a perceived threat, and the brain acts as the filter for recognizing
outgroup members as “pollutants” or threats.
Just as the outcomes of context can be both physical and psychological (e.g., asthma and
ethnocentrism), context itself can be objective — defined by gates, walls, and lines — as well as
subjective. Political science measurement of racial context tends to emphasize the former. When we
conceptualize the environment as a container (of recognizable and commonly shared dimensions),
then it is sufficient to pick the size of the container, measure its contents, and test for any relationships
between said content and our outcome of interest, whether that is a propensity to develop asthma,
interact with outgroup members, or vote for a particular candidate. The researcher will still need to
justify the choice of the container size for statistical and theoretical reasons discussed later. But, if
“context” is conceptualized as an “objective” container, it is unnecessary to ask residents if they are
aware of the container and its contents.
However, while one’s environment may serve as a physical container within which individuals
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exist and interact, ”context” can also refer to the environment in which people believe they live; the
“pictures in their heads” or their “pseudoenvironments” are the reality with which people engage,
regardless of the accuracy or distortion of these perceptions (Lippmann, 1991). While it is a truism
in social science research that race is a social construct, we want to emphasize that people’s racial
contexts are also social constructions, as well as seemingly objective attributes of a physical reality.
Researchers have learned much from studies of phenomena like white flight, tipping points, and
racial discrimination in housing, insurance provision, and medical care, all of which emphasize
the importance of how individuals perceive, construct, and evaluate the race and ethnicity of those
they observe and with whom they interact (Yinger, 1997; Ayres and Siegelman, 1995). Recognition
of these multiple types of outcomes and perceptions of context is important because it highlights
the different mechanisms by which context can affect politics, just as adding frustration aggression
displacement theory to realistic group conflict theory emphasizes how “perceived” shortfalls can
matter as much as “objective” deprivations (LeVine and Campbell, 1971).
2 Conceptualization of Context
While political scientists have written about how environments matter for politics for almost a
century, geographic “context” is very rarely defined in contemporary articles, perhaps because its
ordinary language usage is shared by researchers. It seems almost superfluous to state explicitly that
“context” is the place, area, or environment in which people live. From such a definition, however,
one is unable to discern what does not count as context; these general definitions serve more to
delineate what Adcock and Collier (2001, 530) would call the “background concept” (including all
possible meanings associated with the concept) rather than the “systematized concept” (“the specific
formulation of a concept adopted by a particular researcher”). After all, according to these general
definitions, the earth and the Milky Way galaxy could count as context, even if political scientists
rarely work on that scale. This lack of specificity leaves scholars with little guidance as they move
from concept to operationalization, making the danger of operationalism very vivid (Blalock and
Blalock, 1968). For example, context simply becomes percent black or ethnic diversity in a county.
The concept of context should convey what unit of analysis might be most appropriate. Fortunately, there is no need to reinvent the wheel, nor is it necessary to develop an idiosyncratic
4
conceptualization. Instead, we use a classic social science definition that arose in the era of localized
studies by Lazarsfeld, Berelson, and their colleagues. In Toward a General Theory of Action, Parsons
and Shils (1951, 56) describe three components in the frame of reference of their theory: “actors, a
situation of action, and the orientation of the actor to that situation.” The situation of action
is that part of the external world which means something to the actor whose behavior
is being analyzed. It is only part of the whole realm of objects that might be seen.
Specifically, it is that part to which the actor is oriented and in which the actor acts (56).
The orientation of the actor to the situation is “the set of cognitions, catheses, plans, and relevant
standards which relates the actor to the situation” (56). We believe that Parsons and Shils’s “situation
of action” is the context to which scholars refer when they talk about context having an effect on
individuals’ political attitudes and actions. The “orientation of the actor” may include the varied
mechanisms by which contexts can affect individuals’ politics. Note that this concept encompasses
containers; a container is just a “part of the external world” toward which all people are assumed
uniformly oriented, both in terms of the size and boundaries of the contextual unit and its contents.
In other words, using the Parsons and Shils definition does not preclude the instances in which
objective characteristics of a fixed container affect individuals’ attitudes and actions directly.
According to this conceptualization, a context effect can encompass the effects of communication.
For example, one could imagine an individual who receives all of his information about his context,
accurate or not, from a demagogue who warns of encroaching outgroup members. (The individual
could be visually impaired or blithely unobservant of his environment.) If the demagogue mobilizes
voters using threats posed by outgroups without reference to a geographic area — possibly stressing
a violation of ideology or values — then this would not be a contextual effect. In contrast, if
information given about his surroundings then affects this individual’s attitudes and actions, we
would argue that there is both a contextual and communication effect.
3 Measurement of the Contextual Unit
Political scientists almost always justify their choice of contextual unit on theoretical grounds.
For example, because individuals rarely live and work in the same census tract — and the effects of
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racial context in one’s life overall, not just one’s neighborhood, may have political effects — county
may be the ideal contextual unit of analysis despite its extreme heterogeneity (Branton and Jones,
2005). Alternatively, because racial context may be understood as the interaction between ingroup
and outgroup members, the unit of analysis should be small — like the neighborhood — in order
to capture actual contact between individuals and significant social relationships (Gay, 2004). Or,
because the outgroup is defined at the national level (i.e. immigrants), the appropriate context is the
country (Quillian, 1995). Political elites at the national level may also prime a local context that is,
or is becoming more, diverse (Hopkins, 2010). And, scholars argue that multiple contexts — macroand micro-environments — may interact and should be considered simultaneously; this raises the
additional question of which of the many possible combinations of contexts to consider (Liu, 2001;
Key, 1949). As Oliver and Mendelberg (2000, 577) explain, “Identifying a context’s boundaries is
essential for understanding its potential effects.”
While the different theoretical arguments justifying area size are reasonable prima facie, a major
reason for why a particular unit may be chosen in studies of racial context is that of practical necessity.
As Glaser (2003, 608) describes,
...the social scientist’s choice of neighborhood, precinct, county or state is often arbitrary,
determined by what is available in a dataset, and there is no guarantee that he/she is
really capturing racial balance in a way that is salient to respondents.
Because few studies are designed explicitly to address questions of racial context, scholars are
constrained by the units available in a given dataset.2 Many studies, like the National Election
Studies and General Social Surveys for example, do not automatically identify respondents at
multiple geographic levels in order to protect the anonymity of survey respondents; one by-product
is that scholars are often limited to asserting that the contextual unit they use is ideal rather than
testing and proving it. And unfortunately, the many studies of racial context have not converged
to a consensus about the ideal contextual unit. In their article, Tam Cho and Baer (2011) provide
an excellent summary of many examples of the research on racial context; across 34 studies, the
2
Although more recent studies have tended to make more geographic identifiers available, this was a common
problem with older surveys.
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geographic units chosen vary from prison cells to countries. And, even when the same contextual
unit of analysis is chosen (like county), they show that the results can support contact theory, threat
theory, or even both simultaneously. Additionally, they point out that these disparate findings can
arise for substantive reasons or because of a statistical artifact.
In response to the cacophony of units and results, Tam Cho and Baer recommend that more
than one unit should be used in analyses, partly as a robustness check, but mostly to be aware of the
potential conflicting results that can arise from the “modifiable areal unit problem” (MAUP). The
MAUP is a phenomenon well-documented by geographers, whereby relationships between variables
at one level can change (and even flip signs) when studied at a different level of aggregation; the
areal units chosen are “modifiable” or arbitrary (Anselin, 1988; Cho and Manski, 2008; Achen and
Shively, 1995). The MAUP is actually composed of two problems concerning scale and aggregation.
Gehlke and Biehl (1934) found that correlation coefficients vary with the size of the unit under
study — with larger units leading to larger coefficients, even when the correlation at the individual
level across units is constant — showing that scale can affect statistical inference, whether one was
studying relationships between juvenile delinquency and monthly rental costs, or between farm
product values and numbers of farmers. Wong (2009, 5) explains the reason for the scale effect of
the MAUP:
...a general characteristic of the scale effect is to smooth out extreme values so that the
range of the values is narrower...If one follows the logic that more spatially aggregated
data are less variable, and this logic is extended to analyze correlation between variables,
it is not difficult to come to the conclusion that data at the higher aggregation levels will
likely have higher correlation than more spatially disaggregated data.
The aggregation effect is easily understood if one considers the problems of redistricting after a
census; even with the constraint that districts must have roughly the same number of residents, there
are multiple possible maps that can be drawn. Districts drawn by individuals with different political
leanings, for example, rarely lead to the same number of Republicans and Democrats elected.
Openshaw and Taylor (1979) showed the effects of both the scale and aggregation effects of the
MAUP using the relationship between the percentage of Republican voters and the percentage of
7
elderly voters in Iowa; they compared the correlations in the state’s 99 counties as well as in all
possible combinations of these counties into larger districts. They were able to find correlations
ranging from -.97 to +.99, with no clear pattern between the spacial characteristics of the districts
and the variation in the coefficients. In other words, results can vary depending on how units are
aggregated or zoned, even when they are the same scale or size.3
The effects of the MAUP are less severe if the aggregation of units is done in a noncontiguous
or spatially random way, or if the variable of interest is randomly distributed. However, African
Americans are not randomly distributed (Massey and Denton, 1993). And, given that tracts are
composed of contiguous block groups, counties are composed of contiguous tracts, and so on,
the aggregation effect of the MAUP may be even more severe in political science research on
racial context. Further research has shown that the MAUP affects multivariate regression, Poisson
regression, multilevel models, spatial interaction models, and spatial autocorrelation statistics, along
with simpler statistics like the mean, variance and correlation coefficient (Gotway and Young,
2002). As King (1996, 163) notes, “The conclusions of these studies are almost always extreme
pessimism that leads the authors to question the veracity of almost all empirical analyses.” Scholars
have proposed complex statistical solutions for the MAUP, but each has its own limitations, set of
assumptions, and critics (King, 1997; Wong, 2009).
Not many political scientists have looked at contextual effects at multiple levels, and almost all
explain discrepancies across levels in substantive terms, rather than noting the MAUP (Oliver and
Mendelberg, 2000; Baybeck, 2006; Mackuen and Brown, 1987). For example, an argument could
be made that racial diversity only has a threatening effect at the metropolitan level and not at the
neighborhood level because threat is only experienced at the larger aggregate levels (Oliver, 2010).
It is rare for scholars to test whether their findings are consistent across multiple levels, which Wong
(2009) argues is the minimum standard in handling the MAUP (see Hopkins (2007), for example).
An equally good explanation for differences in coefficients across scales is the MAUP. We have no
way of knowing whether these differences arise because of the explained substantive rationales or
whether the differences are statistical artifacts of the MAUP with no substantive import. And, even
3
For other illustrative examples of the MAUP, see Svancara et al. (2002); Wong (2009, 2003).
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if one takes into account the effects of nearest neighboring contextual units, there is still no way to
adjudicate between one scholar’s argument that census tract is the best unit of analysis and another’s
that city is superior if both conclusions are fairly robust to specifications that recognize the potential
influences of nearest neighbors.
Openshaw (1984) explains that the “simplest solution” to the MAUP has been to ignore it, and
that “the general absence of comparative studies may have helped to disguise the extent to which
zone-dependent regularities are being uncovered (31).” While simple statistical solutions to the
MAUP are elusive and ignoring it is problematic, we propose here a way of sidestepping the MAUP.
The choice of unit should not be limited by the constraints of a survey (e.g. geographic identifiers
gathered for respondents), and it should have geographical meaning. Census data, for example, are
reported for modifiable areal units (blocks, tracts, places, etc.), following criteria determined by
political and logistical considerations rather than because they are “natural areas” with intrinsic
geographical meaning (Hatt, 1946).4 If we think of the Parsons and Shils conceptualization of
context and the questions that motivate scholars of racial threat, the real question of interest is how
people react to their surroundings. Such a conceptualization naturally emphasizes new possibilities
for operationalizing context. After all, given this definition, what is the ideal context to be studied?
The “situation of action” should be measured at levels that individuals “see,” and it should be allowed
to vary by individuals. The “external world” that matters may also vary from policy to policy.
In the new measures we develop and test, we ask individuals to define their own relevant contexts;
rather than assume that administrative units are places with meaning to individuals, we ask our
respondents to draw their contexts on maps. Then, the level of interest does not have to be less
aggregated than the level of data available: we care about the context to which people are reacting,
and we can gather individual level data on both the context seen (i.e., its size, boundaries, and
content) and the reactions to it. With this new measure, we are also able to answer the question of
how the boundaries of people’s communities match up to administrative units used in most previous
racial context work in political science. If we think context is a “situation for action” and want to
understand the political outcomes of individual orientations to the situation, then we need to measure
4
In other fields, scholars have already shown that institutionally-defined boundaries are not the most relevant for a
wide range of outcomes of interest (Cho and Choi, 2005; Aitken and Prosser, 1990).
9
context at the level of the individual. If we do so, we also avoid the MAUP: we will know that our
statistical summaries reflect differences across individuals, not artifacts of aggregation and scale.
4 Measurement of Racial Threat as a Psychological Process
If context matters for individual-level psychological phenomena like threat and ethnocentrism,
it must matter via perceptions. That people observe and understand their contexts is assumed by
most research on this topic in political science, but the standard practice is to use Census data as the
measure of diversity, and the interpretation is that individuals observe qualities of their locales, and
such observations will affect their opinions and actions. We tend to assume that people’s perceptions
are similar both to Census numbers and to each other’s.
However, since the 1940s, scholars of public opinion have learned a great deal about why Census
numbers may not be good measures of people’s “pseudoenvironments.” The American public’s
level of political knowledge is often surprisingly low (Converse, 1964; Delli Carpini and Keeter,
1997). Ordinary citizens also make incorrect inferences based on personal experiences or recent,
salient events due to perceptual biases (Ross, 1978; Tversky and Kahneman, 1974). When it comes
to the racial/ethnic make-up of the U.S., for example, surveys have shown that Americans greatly
overestimate the numbers of minorities in the country (Highton and Wolfinger, 1991; Nadeau, Niemi
and Levine, 1993). Furthermore, individuals’ misperceptions influence policy preferences (Gilens,
2000, 2005; Hochschild, 2001), and simply giving people factual information does not “correct”
their policy opinions (Kuklinski et al., 2000; Nyhan and Reifler, 2010). Nevertheless, the issue of
misperception or misinformation has largely been missing in the political science research on racial
context (but see Chiricos, McEntire and Gertz (2001); Chiricos, Hogan and Gertz (1997); Alba,
Rumbaut and Marotz (2005)).
Inaccurate perception of racial demographics can be compounded by other misperceptions of
“that part of the external world which means something to the actor” (Parsons and Shils, 1951, 56).
While some scholars have equated “context” with racial/ethnic diversity, the content of a context
obviously extends beyond this one dimension. For example, research on racial threat has on occasion
also incorporated the effects of socioeconomic and partisan context along with racial context, and
the findings indicate that such attributes can interact or that socioeconomic status or partisan context
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may be even more relevant for people’s racial attitudes than the racial/ethnic diversity of where
people live, individuals’ personal income, or their own partisan identity (Gay, 2004; Branton and
Jones, 2005; Oliver and Mendelberg, 2000).
However, the same problem of possible misperceptions arises. For example, the research on the
effect of the economy on vote choice has supplied us with ample evidence that “it’s the economy,
stupid” should be changed to reflect that people’s perceptions of the economy are what, in fact, spur
votes (Hetherington, 1996; Kinder, Adams and Gronke, 1989). While broken windows are easy to
observe, other indicators of the average socioeconomic status of one’s neighbors can be less visible
than race/ethnicity; unless someone is wearing an old college sweatshirt, for example, it is difficult
to discern at a distance if one’s neighbor is a college graduate or not. Similarly, partisanship is not
something most people wear on their sleeve (or car or front yard) (however, see Baybeck and McClurg
(2005)); while individuals are often egocentrically biased to think other people think like them —
and therefore assume a high level of homogeneity in their surroundings — a Republican living in a
liberal college town could think himself under siege.5 Using our new maps-based measurement of
context, we can show the similarities and differences of misperceptions about the racial make-up,
socioeconomic well-being, and partisanship of one’s surroundings.6
We are not focused on misperceptions qua misperceptions; the extent of the misperceptions
simply provides evidence that we need a better understanding of the intervening steps linking Census
facts about an area, for example, to perceptions of the demographic characteristics of that same
area to feelings of threat and policy preferences. The objective indicators are, of course, important,
but we need to know about people’s “pseudoenvironments” as well. We want to be able to answer,
for example, the question of whether two people who live in a block group with the same percent
nonwhite — but believe the diversity varies a great deal — will feel the same level of racial threat.
5
And, it is not clear that reactions to status as a numerical minority work in similar ways for partisanship and race
(Finifter, 1974; Bledsoe et al., 1995).
6
Even if multiple contextual variables come from the same source — like percent black or percent unemployed
from the U.S. Census — that does not mean the causal mechanisms linking these different types of context to political
judgments are necessarily identical.
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5 Application of our New Measurement
To illustrate the utility of our proposed conceptualization and measurement strategy, we use
data from a pilot survey that we conducted of 62 individuals living in one Midwestern county in
2004. The in-person survey included a map-drawing measure of context and the research design
allows us to bring the individual back into the conceptualization and measurement of context. While
the particular maps drawn by our respondents are not meant to be generalizable to the nation, our
measure of context is broadly applicable, as are the questions our measure raises about standard
practices.
5.1 Survey Design
In the sample design of our pilot study, we use Census block groups as the basis of our sampling
because block groups are the smallest administrative unit for which racial data are available (and
largely unscrambled) and could be used as building blocks for ascertaining contextual effects at
more aggregated levels. After stratifying — and thereby targeting whites and blacks living as both
majorities and minorities in their block groups — and sampling based on non-rural block groups in
the county, we purchased a white pages sample of names, addresses, and phone numbers.7 The white
respondents lived in block groups that ranged from 0 to 74 percent black, and the black respondents
lived in block groups that ranged from 3 to 97 percent black. In other words, we were able to
interview respondents exposed to very diverse racial contexts.8
To create a measure of personally relevant places that operationalizes our conceptualization
of context, we developed a map-drawing addition to a traditional political science survey.9 So, in
addition to answering a number of survey questions, the respondents were also asked to refer to a
few maps. They were first shown two maps — one centered on the block group in which their house
was located and one encompassing all of the county from which the block groups were sampled
7
While we would like to have interviewed equal numbers of white and black respondents, our final sample contained
41 whites and 21 African Americans living within 25 different block groups. It should be noted that in the block groups
sampled, the racial composition is largely biracial.
8
Overall, the racial demographics of the county are quite similar to the nation’s. In 2000, the U.S. was 75 percent
white and 12 percent black; the county in which we conducted our study was 77 percent white and 12 percent black.
9
We build on the work on mental mapping pioneered by Lynch and which has continued in geography and sociology
(Matei, Ball-Rokeach and Qiu, 2001; Lynch, 1973; Coulton et al., 2001).
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— and were asked to draw on either map the area that made up their “local community.”10 The
approximate location of their house was indicated on each map, and the maps included both block
group boundaries as well as nearby labeled streets. In order to measure respondents’ perceptions of
the content of their contexts, we then asked about perceptions of the proportion of blacks and whites,
Democrats and Republicans, and unemployed living in that community.11 Later, they were shown a
map with their block group highlighted, and were again asked to describe the racial, partisan, and
economic breakdown of the block group. They were also asked about their perceptions of these
factors at the national level. Thus, we were able to gauge perceptions of multiple politically-relevant
characteristics of three geographic contexts, and because some of the contexts were shared, we could
make comparisons both within and across individuals of two different racial groups.
5.2 Does the Government Define Pseudoenvironments?
We wanted to allow individuals to define for themselves (using maps) what they mean by
“community,” rather than assume that how context affects political judgments must occur within
administrative units defined by government officials. While we were designing the map-drawing
questions, we had contradictory predictions. On the one hand, we were skeptical that people knew
the locations of the boundaries of any government-designated units in which they resided. On the
other hand, we thought that respondents might be guided by the cues provided and follow the bold
lines presented on the map, which designated block group boundaries.
Almost 2/3 of the respondents (n=36) chose to draw their community on the smaller maps
centered around their block group (see Figure 1(a) for examples), while the rest chose the larger one
10
The map-drawing task was one of the first in the survey, so the respondents were not primed to think about particular
issues or communities by other survey questions. We also provided no definition of “local community,” both to avoid
the respondents second-guessing what the researchers might want, and also to avoid cueing any particular level of
aggregation. Granted, the largest map that could be drawn was at the county level, although respondents could also
respond that they did not think of their “local community” in this way. While it would have been ideal to know how
perceptions of their communities changed depending on the issue, for a pilot study we were interested in getting a more
general sense of how people would define their local community. In future research, we plan to prime respondents
to think of different policies or geographies before the map-drawing. The terminology was chosen to emphasize a
politically and personally relevant grouping of people (a “community”) that is spatially interdependent (“local”).
11
While there are many possible measures of economic context, we chose to use percent unemployed. The average
education level of residents in an area may be a more reliable measure than unemployment (Huckfeldt 1986), but we
believe that if perceptions are driven in part by observational learning, then residents’ employment status may be more
visible to others than their diplomas. Ansolabehere, Meredith and Snowberg (2010) also find that information about
unemployment affects political outlooks.
13
(23) (see Figure 1(b) for examples).12 Regardless of the size of their “local community,” none of the
respondents’ drawings followed block group lines neatly. A couple of the maps had non-contiguous
areas marked, some marked areas as small as a single street, while others encompassed the entire
large map of the two cities within the county. No two maps were identical, even for residents living
in the same block group, and they ranged in size from smaller than a block to larger than two cities
together.13 There is no clear pattern by race, income, or education as to what size of community
was drawn. Furthermore, there is no simple relationship between size of community drawn and
ethnocentrism. While we believed initially that more ethnocentric individuals would choose a
smaller community — limiting their inclusion of outgroup members in the community — there is
no clear pattern across a range of racial attitudes that this is the case.14
Later in the survey, respondents were shown the “small” map again, this time with their block
group highlighted in yellow. They were told that the borders on the map showed the boundaries
of what the Census Bureau defines as a “block group.” Respondents were then asked whether they
thought the highlighted area captured what they thought of as their neighborhood. Sixty-one percent
agreed that their block group was a reasonable representation of their neighborhood. This percentage
may be biased upward for two reasons: suggestibility — with a credible government institution as
the source — and acquiescence bias. Even taking into account that the response could be inflated,
almost 4 out of 10 respondents did not think of their block group as a close approximation of
their neighborhood. Other research has also shown that people’s perceptions of their neighborhood
vary greatly (Sastry, Pebley and Zonta, 2002; Huckfeldt, 1979). This all serves as evidence that
12
We were concerned that respondents might find the map-drawing task overly difficult, but our worries appeared to
be unfounded. Only one respondent did not draw on the maps, explaining that she did not think of her “local community”
in these ways. Two respondents who were visually impaired were able to describe the major streets and landmarks that
defined the borders of their local communities. All other respondents were able to draw their local communities on the
maps. Of course, the ability to draw maps is not the same as a clear understanding of maps; nevertheless, respondents do
not need to be cartographers drawing navigable maps in order to communicate mental representations of their contexts.
13
Each hand-drawn map was traced into ARCGIS, where we could determine the size of the community and how it
related to Census block groups.
14
We need to keep in mind that even though the size of the communities drawn in the pilot varied widely, we believe the
range would have been even greater if there had been more than two choices of maps offered. Given social psychological
research about anchoring, it is very likely that people chose communities that would fit on one of these two maps, and
that if they were not so restricted to these particular spatial resolutions, the size of the community may have been even
larger for some respondents, extending beyond the county in which they live. Nevertheless, even given the limited scope
of the pen and paper maps, it is clear that people’s communities are (1) different from governmental administrative units
and (2) idiosyncratic and not commonly-shared visions.
14
“neighborhood” is no more a commonly shared container than is “community,” and that the variance
across maps is not because “community” is a particularly idiosyncratic term.15
5.3 Do You See What I See?
A common assumption in the research on racial context is that people’s beliefs align with the
facts about the demographic make-up of the areas in which they live. We are interested in whether
individuals are indeed accurate when it comes to describing their contexts. Our respondents were
asked to describe the percentages of blacks, whites, unemployed, Democrats, and Republicans in
their block group, their self-drawn “local community,” and the nation as a whole. Thus, we can
compare people’s perceptions across multiple levels with the Census reports for the same geographic
levels, and also across individuals for the same geographic unit. For the analyses presented here, we
use as a point of comparison for respondents’ “local community” the average of any block group that
is included in their drawing. For example, if a “community” was drawn to overlap with three different
block groups, then the “objective” point of comparison for racial context used is the Census-reported
percentages of whites and blacks for those three block groups together.16
Greater Misperception of Racial Context at Larger Aggregations
We predicted that respondents would be more accurate in their perceptions of their local community than the nation, given their personal experiences. Figure 2(a) shows two scatterplots, comparing
respondents’ perceptions of blacks and whites in their block groups with the Census percentages for
the respective groups in the same areas. As can be seen from the plot on the left, the fitted smoothed
curve is flatter than a 45-degree line, indicating that respondents’ perceptions of the percentage
of blacks living in their block group is greater than that reported by the Census. Conversely, their
estimates of the number of whites are smaller than the objective numbers. Even if the situation were
15
We expect that in areas where neighborhoods are named, isolated, or gated, agreement about the boundaries of the
neighborhood may be greater; however, the clarity of these borders varies a great deal across the nation, and one cannot
assume that knowledge in one area means knowledge in others. Furthermore, while other Census units may be more
politically meaningful than block group — like metropolitan area — there is no evidence that reality and perception
would overlap more for city than for block group. Again, there is a great deal of heterogeneity across the U.S.
16
We considered a couple other alternative measures, but none seemed superior. Using only block groups that were
entirely enclosed within a “community” is problematic because some communities did not include a single entire block
group. We also considered calculating the fraction of the area of a block group contained within a “community” and
including only that proportion in the demographics; however, this assumes that individuals are evenly distributed across
a block group, which is clearly incorrect.
15
a container, orientations toward the container are not uniform and are not accurate. While there
is an obvious relationship between objective indicators and subjective perceptions, Lippmann’s
pseudoenvironment is not identical to the world described by Census numbers.
Because of the sampling design, we are also able to look at the perceptions of white and black
respondents living in the same block group; while one could hypothesize that neighbors may have
shared spatial experiences and similar perceptions of the neighborhood in which they live (Stipak
and Hensler, 1983), one might also hypothesize that black and white respondents have different
experiences living in the same area (Kwan, 2000). Scholars have found, for example, that while both
whites and blacks are willing to live in integrated neighborhoods, their definitions of “integration”
are markedly different (Clark, 1991). Blacks and whites also rely on different sources of media for
news and entertainment. Comparing white and black respondents who live within the same block
group, we find that blacks’ estimate of the proportion of blacks living in their block group was, on
average, 12 percentage points lower than their white neighbors’ estimates, and their estimate of
the proportion of whites was 13 percent higher than that of their white neighbors. Within-racialgroup average differences range from 1 to 5 percent. However, whites and blacks both tend to
misperceive their racial contexts and in the same directions, overestimating the percentage of blacks
and underestimating that of whites.
Perceptions of racial context in subjectively-defined “communities” are similar to those at the
block group level, with some variation. At this geographic level (see Appendix A), the line for
percent black appears even flatter and the percent white steeper than those in Figure 2(a), indicating
that perceptions of the numbers of blacks and whites are even more distorted when people evaluate
their own “community” compared to block group perceptions. Respondents do not know their own
drawn “communities” better than their Census block group, and misperceptions are even greater at
the national level. Furthermore, while black and white neighbors have different pictures of the same
block group in which they live, black and white respondents in our survey share similar visions of
the nation; blacks’ estimates of the proportion of blacks living in the nation were only 3 percentage
points lower on average than whites’ estimates.17
17
We do not think these results are merely due to innumeracy (see Appendix B).
16
While the percentages of blacks are consistently overestimated and that of whites underestimated,
an interesting pattern emerges from comparing these different geographic units: perceptions of
racial context become more accurate at more localized levels. In other words, while respondents
tended to overestimate the percentage of blacks in the nation by 17 percentage points — thinking
the nation is 30 percent black instead of 12 percent — the overestimate at the block group level was
only 8 percentage points.18 It appears that people are more misinformed about their racial contexts
at larger geographic units compared to smaller ones. This difference in misperception perhaps could
be explained by different sources of information about each geographic level. We will come back
to this possibility after examining perceptions of economic and partisan context across these same
three levels. The story of growing levels of misperception as the “pseudoenvironment” increases in
size becomes more complicated when we look at these different types of context.
Raising New Questions About Mechanisms with Economic and Partisan Context
We start with respondents’ beliefs about the economic and partisan contexts of their block groups.
Figure 2(b) and Figure 2(c) present plots for perceptions of the percent unemployment, Democrat,
and Republican at the block group level, compared with Census figures and vote returns for 2004.
In contrast to the racial content of one’s context, the relatively flat line in Figure 2(b) shows that
respondents are even more misinformed about the level of unemployment in their block group than
the percentage of blacks and whites, with very little relationship between objective and subjective
economic contexts.19 On average, respondents overestimated the percentage of residents unemployed
in their block group by 16 percent, although the misperceptions ranged from an overestimate of 82
percent to an underestimate of 10 percent. Respondents’ perceptions of the partisan make-up of
their contexts also seem to bear only a passing resemblance to the objective measures of partisan
18
These national results are replicated almost identically in the 2000 General Social Survey. In the GSS, respondents’
estimates of the proportion of whites and blacks were 59 percent and 31 percent, respectively. In our pilot, the
corresponding numbers were 58 percent and 30 percent. This similarity lends support to the idea that these levels of
misperception in our pilot are not unique to our sample.
19
For “objective” data about unemployment rates, we use data from the 2000 Census. For the block groups in our
sample, unemployment ranged from 0 to 14 percent. In contrast, Baybeck and McClurg (2005) find that respondents
are fairly well-informed about the economic and partisan status of their neighborhoods. However, their measure of
“objective” context was the aggregated self-report of respondents in the neighborhood.
17
context.20 On average, respondents underestimated the percentage of Democrats in their block group
by 6 percentage points, and overestimated the percentage of Republicans by 6 percentage points. So,
while there is little relationship between perceptions and objective indicators of socioeconomic and
partisan contexts, respondents are, at least, more accurate, on average, in their estimates of living in
predominantly Democratic block groups than in their beliefs that about one out of every six residents
of their block group is unemployed.
Misperception of economic context of the “local community” is similar to that at the block
group level, with an average overestimate of 15 percent and very little overall relationship between
perceptions and objective measures. Perceptions of partisan context at the “local community” level
are also similar to that at the block group level: respondents underestimated the proportion of
Democrats by 6 percentage points and overestimated the proportion of Republicans by 3 percentage
points, but hand-in-hand with this greater accuracy is very little relationship between the perceived
partisan make-up of a community and objective measures of partisanship for that same area (see
Appendix A). A similar pattern of misperception appears at the national level as well. Misperceptions
about unemployment in the U.S. are, on average, an overestimate of 15 percent. So, in contrast to
perceptions about racial context, people’s visions of the economic context are distorted to the same
extent across all three levels, whether they are thinking of their block group, community, or nation.
There was also a lack of variation across levels for partisan context: at the national level, there was
again only a low level of misperception on average; respondents overestimated the proportion of
Democrats by less than 5 percent and underestimated that of Republicans by about 5 percent.
Comparing results across the three types of context — racial, partisan, and economic — across
the three levels of context — block group, “local community,” and nation, it is clear that (1) there
is little variation in average misperceptions of unemployment and partisanship from the local to
national level, and (2) perceptions of economic and racial context are more distorted than those of
partisan context on average (see Appendix C for a table summarizing these results).
20
For the “objective” basis of comparison of partisanship, we use the 2004 presidential vote. Because vote returns are
aggregated at the precinct level, we average the vote for any precincts that overlap with a block group’s boundaries to
create its “objective” partisanship. The block groups in our sample ranged from 62 to 96 percent Democrat, and the
county as a whole voted 64 percent Democrat.
18
6 Sources of Varying Misperceptions
Why does our new measurement strategy reveal differing levels of accuracy about racial context
across geographic units? People may simply have a better vision of their block group, and can more
easily envision 100 people, for example, than they can picture about 300 million Americans. Another
explanation is that people learn about their various environments in different ways. For example, in
their work contrasting sociotropic and aggregate economic studies’ effects, Ansolabehere, Meredith
and Snowberg (2010) speculate that people learn about “the economy” from a variety of sources.
In our pilot, we asked all respondents to tell us, in an open-ended format, the source(s) of
information for their perceptions at the local, block group, and national level. The responses differ
greatly between where one gathers knowledge about the nation and where one gains information
about one’s local community and block group, with the responses about the latter two blending
together (see Appendix D for details). Personal experience, families, and friends play a much
larger role in knowledge about people’s community and block group; as shown in previous research,
everyday observation was cited by at least half our sample as a source of information about their
“local community” and block group, and personal social networks provided information to about
a quarter (Gilliam, Valentino and Beckmann, 2002). In contrast, media is the primary source of
information about the nation; over two-thirds of the responses given referred to media, and few
mentioned any other source as the basis of their knowledge about the United States as a whole.
Potential biases from the availability heuristic seem more prominent in national racial perceptions
than local, which suggests the important role of the media in creating perceptions of racial context
and feelings of threat (Busselle and Crandall, 2002).
One possible explanation for perceptions of economic context is that such beliefs — regardless
of level — are also mainly based on media reports. Because few news sources would ever discuss
unemployment at levels smaller than a respondent’s city, he or she most likely is not exposed to
systematic information about unemployment at the block group level. Inferences across all levels
could be drawn from the same source of information, with an assumption of uniformity across levels.
When it comes to understanding the accuracy of perceptions of partisan context across all
three levels, on average, one possible explanation is the role of media and elections in learning.
19
Stories about election returns may highlight partisan surroundings in a dramatic way for individuals,
unmatched by any event that would highlight their racial and economic contexts as clearly, regularly,
and officially. Of course, one obvious problem with the explanation that media coverage can lead
to greater accuracy is the fact that the news media regularly presents stories about the nation’s
unemployment rate and Census results, yet respondents were much more misinformed about these
facts relative to facts about partisanship at the national level. Neighbors’ partisanship is unlikely to
change rapidly from year to year, so it may be easier for respondents to learn about their partisan
context than the more volatile unemployment rate over time — assuming residential stability — but
neighbors’ races are even less likely to fluctuate than party loyalties. There is another plausible
explanation: in contrast to economic and racial context, the partisan composition of the nation (and
likely many communities and block groups) is more evenly distributed between Democrats and
Republicans. Therefore, if a respondent took a guess around 50 percent, he or she is more likely to
appear “accurate” about partisan context at the national level, but grossly incorrect about economic
and racial contexts. Research also shows that people are more likely to misperceive rare events than
common ones. However, if one looks more closely at the contexts in our sample, this explanation is
also problematic: the county from which we drew our sample leans Democratic, and the means and
medians of the distributions in both block groups and the local communities drawn ranged between
75 and 80 percent Democratic. Obviously, future research is needed to gain a better understanding
of how people develop their perceptions of different types and sizes of context.
7 Old versus New Measures of Context
While this paper has focused on measurement, we realize that some may ask whether it is worth
the extra effort to measure perceptions of context rather than use administrative numbers. The first
answer is that we cannot know for sure whether results that differ using administrative numbers
across multiple levels of aggregation arise as statistical artifacts from the MAUP unless we measure
“context” at the level of the individual. A second answer is that measuring perceptions gives us the
potential to better understand the mechanisms by which context affects politics; for example, we can
observe if racial context affects people like particulates in the air (i.e. affecting outcomes, regardless
of subjects’ awareness of their environment) or if it works via Lippmann’s pseudoenvironments.
20
Some might suggest that we could use Census numbers to approximate the psychological
measures that we might prefer. Or, put more critically, might difficult, novel, and messy psychological
measures merely proxy for clean and easy Census numbers? In this section we engage with these
questions using an example focused on the relationship between “racial context” and racial attitudes
among white respondents; our pilot study offers the opportunity to compare the effects of (1) Census
numbers in a Census geography, (2) Census numbers in a perceived geography, (3) perceived
numbers in a Census geography, and (4) perceived numbers in a perceived geography.
We start with the simple relationship between percent black in a Census block group and
responses to a racial resentment scale (Kinder and Sanders, 1996).21 On average, do whites living
among more blacks report higher racial resentment? Our dataset replicates what has become the
standard in larger and more representative surveys: the leftmost line in Figure 3 shows that, in our
data, whites who live with many blacks in their block group tend to be more resentful than whites
who live near relatively few blacks. In our particular data, we see that the 66 percent interval for
a difference of 10 percentage points in percent black in a block group ranges from about 0.03 to
about 0.07 points of difference in the resentment scale: the scale runs from 0 to 1, sd of .2. In the
absence of other measures of context, we cannot know whether this relationship is masking some
aggregation and/or zoning artifact (i.e. the MAUP), nor do we know whether this relationship has
the psychological content that many theories of context would use this analysis to assess.
What if we were interested in the differences between people based not on what the Census
reports about a Census unit, but about what the Census reports for a personally relevant unit? The
second line from the left in Figure 3 shows that Census numbers for percent black in subjective
maps relate to racial resentment more or less as strongly and in the expected direction as using
Census numbers and boundaries, even if the diversity of maps increases the width of the interval:
the center of the interval is in the .04 to .10 range. Because we were able to produce an individual
level, non-modifiable measure of content, we could thus reassure ourselves that the analysis using
Census boundaries was not misleading.22
21
See Appendix E for information about the scale and details of the analyses that follow.
In these analyses we do not adjust the estimates for any covariates. Here, the goal is not to disentangle the effects of
context from the many and complex possible sources of it (such as selection effects), but rather to compare context based
differences in racial resentment across measures of context (each of which may have its own interesting relationship
22
21
While the map-drawing measure helps us avoid the MAUP, it does not tell us if Census numbers
are good proxies for perceptions, or more generally, much about the mechanism by which environments affect people’s political decisionmaking. We therefore turn to what we believe is the next step
in the mechanism that can lead to threat: perceptions. We compare the effects of subjective measures
— measures where we asked white respondents to report on the proportions of blacks living either in
the boundaries of a context drawn by the Census or the boundaries drawn by the respondent. Would
such subjective reports have explanatory power beyond that provided by objective context? We
matched respondents to one another, creating pairs on the basis of objective context (using either
Census numbers in the block group or in their hand drawn community).23
If the subjective reports have little to add beyond objective numbers, then within pairs matched
nearly exactly on objective numbers, we should see little difference in subjective reports and, more
importantly, differences in subjective reports should not relate to substantively relevant outcomes
(and should mainly be seen as noise). The rightmost lines in Figure 3 suggest that this is not the
case: subjective context is nearly as strongly related to racial resentment as is objective context
even holding objective context almost exactly constant. Specifically, the point estimates and centers
of the posteriors arising from the multilevel models estimated conditional on the matching, show
that differences in subjective perceptions of percent black in a block group are associated with
differences of about .05 on the racial resentment scale.24 A similar result is evident when it comes
to perceptions of the subjective boundaries (the line labeled “subjective community”) in Figure 3.
Even within pairs in which both respondents’ maps contained almost the same percent black, the
white respondent who perceived more blacks tended to report more racially resentful attitudes than
with background covariates such as education and socialization).
23
This matching is not the usual form used in political science in which members of a treatment group are matched to
members of a control group (also called “bipartite” matching to indicate that the matching is in two parts). We used
non-bipartite matching, in which every unit is a potential pair with every other unit. The algorithm then assigns units to
pairs so as to minimize the total differences on the matching scale (here, percent black in the block group). For more on
non-bipartite matching, see Lu et al. (2001, 2011); Rosenbaum (2010). See Appendix E for more explanation about how
to use and assess non-bipartite matching.
24
The uncertainty around this estimate (shown as the vertical lines in the “subjective block group” line on the figure) is
wider than the corresponding objective block group analysis: a priori we did not know whether to expect that the loss of
degrees of freedom from conditioning on pairs would decrease our precision or whether the increased variation arising
from the subjective block group reports would increase our precision or whether the conditioning itself would increase
precision by adding explanatory power (given the preceding analysis in which the objective block group numbers did
predict the outcome).
22
the person who perceived fewer black people in their “local community.”25
So, what we have shown here suggests that (1) our pilot is consistent with past research, such that
objective context predicts racial attitudes; (2) that any of the three methods to side-step the MAUP
shows a relationship with racial attitudes (and, in our particular case, helps confirm that the sign on
the relationship between objective block group percent black and racial resentment in our pilot study
is not likely a statistical artifact); and (3) that even within pairs of white respondents more or less
identical on objective Census numbers, the person perceiving more blacks tended to be the person
with higher racial resentment. That is, in terms of the mechanism by which the environment affects
political beliefs, we learnt that perceptions of the context matter for attitudes, above and beyond
objective characteristics. Parsons and Shils’s “situation of action” matters, and objective numbers
should not simply be used as proxies for people’s perceptions, even if they may matter in other ways.
8 Discussion
One question raised by the finding that misperception of racial context is greater at larger units
is how best to interpret previous findings that context is politically, economically, and culturally
threatening at larger units but not at smaller ones. For example, most of the research that finds
support for the racial threat hypothesis measures context at the level of county, metropolitan area,
state, region, or country; in contrast, the research that has found support for the contact theory
tends to measure context at smaller units, like census tract or zip code. In the past, this difference
was interpreted as evidence that contact at the smaller units would diminish ethnocentrism, while
diversity at the larger aggregate levels made such intergroup contact more likely. Diversity without
contact, in contrast, would lead to feelings of threat (Stein, Post and Rinden, 2000).26 Another
25
Notice that we did not control for education or other covariates in these analyses. When we did this in analyses
not reported here (using matching on mahalanobis distances created from rank transformed education, income, gender,
and length of residence in a community, and/or using said distances to penalize the matchings on objective context
and/or adding those covariates into the linear models as controls), we noticed weaker effects albeit a similar pattern.
This suppports the points made here: if subjective context is a real entity, then it ought to relate strongly to education
and other personal attributes that would make different people perceive their contexts differently. And, objective context
effects ought to depend on such characteristics too, both (a) indirectly as they matter for perceptions and (b) directly as
such characteristics are proxies for the processes driving residential segregation.
26
We find in our pilot study that contact with outgroup members has no noticeable effect on people’s perceptions of
their contexts; for example, whites who have contact with blacks at work, at their place of worship, or in their circle of
friends are not more or less accurate in their perceptions of how many blacks live in their block group or community,
compared to whites whose daily lives are more segregated. In other words, in our pilot, actual interactions with outgroup
members do not lead to either greater accuracy or misinformation. So, while contact may diminish ethnocentrism
23
interpretation, however, is that these differences in outcomes across levels are simply the result of
the MAUP, and we should draw no substantive conclusions about differing perceptions of threat
across levels. A third interpretation, given our findings, is that overestimates of the size of outgroups
at larger contextual units relative to misperceptions at smaller units is what leads to a greater sense
of threat in the more aggregated levels. In other words, if individuals had a more accurate picture of
their surroundings, they might not feel a sense of racial threat at the metropolitan or county level,
for example. This does not preclude the idea that personal interactions with outgroup members
diminish ethnocentrism, but it does raise more questions as to why racial context rarely poses a
“threat” at the more localized level in previous research.
We also raise the question of how one should interpret perceptions by different racial or ethnic
groups. While the bulk of research on racial threat has focused on the attitudes and actions of
white Americans, recent research has expanded to include the effects of context on the political
judgments of racial/ethnic minorities (Gay, 2004; Barreto, Segura and Woods, 2004; Glaser, 2003).
The theoretical arguments advanced for all groups are similar — predominantly group conflict or
contact theory — although the specifics are left a bit vague as to why groups of such disparate sizes
should behave in similar ways. It does seem peculiar to argue that white respondents who compose
a majority in a county are as “threatened” by blacks as black respondents in that same county are by
whites. After all, if one considers the Black Belt studied by Key, the threat of lynching for blacks
was much more real and vivid than the threat of losing political power was for whites. Another
complication is added by the fact that previous research has shown that Americans of all races
overestimate the numbers of minorities in the United States and underestimate the number of whites
in the country. What has not been mentioned is that the motivations attributed to these inaccuracies
cannot be the same across groups: if whites, for example, exaggerate the numbers of blacks due to a
sense of threat, then why do blacks also exaggerate the numbers of blacks? Threat cannot explain
why an individual overestimates the numbers of both her outgroup and ingroup.
These misperceptions also have policy effects. The literature on white flight discusses the fact
that whites are unhappy and flee when blacks move into their neighborhoods. However, Harris
(Allport, 1979), it does not seem to do so via greater awareness of one’s surroundings.
24
(2001) has found that blacks are also threatened by other blacks moving into their neighborhoods,
a threat that cannot be motivated by fear of a racial outgroup. It is possible that economic threat
motivates both groups’ responses, or they may have different impetuses; teasing out the meaning
depends on understanding how different groups perceive and interpret the same environments. When
scholars study one group at a time, it is easier to find plausible theoretical explanations for the
empirical findings; it is only by comparing groups that one is confronted by the more complicated
picture of how perceptions of context can affect political judgments.
The housing literature is also relevant for another reason to the analyses presented here. According
to Schelling’s argument about tipping points, small preferences at the individual level can become
magnified at the aggregate level, such that slight preferences for a homogeneous neighborhood
lead to the dramatic levels of residential racial segregation that exists in this country (Schelling,
2006; Massey and Denton, 1993). Furthermore, as Bruch and Mare (2006) show in their analysis
of Schelling’s model, the existence of a threshold is key to explaining how slight differences in
preferences could lead, in a theoretical model, to an “apartheid America.” While the strikingly low
threshold observed in real life may reflect the “objective” status of the neighborhood’s make-up, it is
also possible that the neighborhood is perceived as more diverse than it is in reality, and that the
threshold for white flight in people’s minds is higher than the one observed. In other words, someone
might be willing to live in a neighborhood that is one third black, but because he overestimates
the percentage of blacks living in his neighborhood, he ends up moving away well before his real
threshold has been reached. While the practical implications may be the same in terms of policy
interventions to prevent flight and hypersegregation, there may be a role for public education about
the demographics of one’s surroundings that could at least slow down white flight.
9 Conclusion: Attitudes are not Asthma
Medical researchers who study the effects of pollutants on the development of asthma measure airborne particulates in a geographic region and the presence of asthma and other respiratory
symptoms for the population living in that area. When political scientists study the effects of racial
context on ethnocentrism and policy opinions, their studies mimic the pollution studies: outgroup
members are the threatening allergens and attitudes are the asthma. However, in general, perceptions
25
of context do not surreptitiously affect one’s attitudes and actions like smog can invisibly penetrate
one’s lungs, even if perceptions can lead to fear (which in turn can lead to a panoply of unconscious
reactions). Parsons and Shils include this perceptual stage — Lippmann’s “pseudoenvironments”
— in their conceptualization of context, and our map-based measure of context is valid for this
conceptualization. Our operationalization of context allows us to ask questions about respondents’
self-drawn communities as compared to places that group people by administrative fiat, thus sidestepping the MAUP. We also do not need to presume that ordinary citizens are fully informed consumers
of government statistics, nor do we need to assume that people are exchangeable agents who see
and react to their contexts in the same ways. When we find contextual effects using convenient,
institutionally-drawn boundaries, it is impossible to determine if these effects are overly conservative
or liberal, or whether they are statistical artifacts, since they most likely vary a great deal across
individuals, across subgroups, and across geographic units.
Our first attempt at following our guiding research principles from concept to questionnaire
measure and design suggests a need to “bring the person back in.” Furthermore, by examining
different aspects of people’s contexts in our pilot study, we are able to contrast the varied ways
that facts about the environments in which people live are converted into beliefs. We find that the
mechanisms by which racial, socioeconomic, and partisan contexts are perceived and affect political
attitudes and actions do not appear to be the same. And, while we are building on an interdisciplinary
tradition of research in mental mapping, our specific use of these maps is novel in political science.
If pictures fixed in people’s heads do not match Census pictures, the practical implications extend
beyond the confines of citizens’ minds or the voting booth. The “fear of crime” literature in sociology
has explained that personal and altruistic fear—regardless of accuracy—leads to purchases (e.g.,
guns and personal safety devices), behavioral changes (e.g. not going out at night ), and abandonment
of locations (e.g., parks and industrial areas) (Warr and Ellison, 2000). Political scientists need
to understand whether perceptions of community heterogeneity and interracial competition have
equally serious consequences for political actions and outcomes.
26
(a) “Local Communities” drawn on “small” maps.
(b) “Local Communities” drawn on “big” maps.
Figure 1: Examples of Map-Based Measures of Context: “Local Communities” Drawn on Block Group and
County Maps.
27
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Census %White in Block Group
0.2
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Census %Black in Block Group
0.2
0.4
0.6
0.8
● ●
0.0
0.2
0.4
0.6
0.8
1.0
% White Perceived in Block Group
(a) Relationship between Objective Racial Context and Perceptions at the Block
Group Level.
Census %Unemployed in Block Group
0.0
0.2
0.4
0.6
0.8
1.0
Total
!!
!!
!
!
!!
!
!!
!!
!
!
!
!
!
!
!
!
! ! ! !
!
! !
! ! !
!
!
! !
!
!
!
!
!
!
0.0
0.2
0.4
0.6
0.8
1.0
% Unemployed Perceived in Block Group
(b) Relationship between Objective Economic Context and Perceptions.
!
!
0.0
0.2
0.4
!
0.0
0.2
0.4
0.6
0.8
1.0
% Democrat Perceived
in Block Group
!
!! !
!
!
!
!
!
!!
! !
!
!
!!
!! ! !
1.0
0.8
Blacks
0.6
0.6
!
!
!
! !
!!
! !
!!
! ! !
!
! !
!!
!
!
! !
!
!
!
!
!
0.4
! !
!
! !
!
Whites
!
! !
All Respondents
! !
!
!
!
!
!
!
!
!
! !
! !
! !
!
!! ! ! !
! ! !
!
!
!
! ! ! ! !
!
! !
!
! !
!
0.2
!
!
0.0
Census %Unemployed in Block Group
0.0
0.2
0.6 04 Presidential
0.8
1.0
%0.4
Republican
Vote in BG
!
0.8
Census %Unemployed in Block Group
% Democrat 04 Presidential Vote in BG
0.0
0.2
0.4
0.6
0.8
1.0
1.0
All Respondents
!
!
0.0
0.2
0.4
0.6
0.8
1.0
% Republican Perceived in Block Group
!
! !
! !
!
!
!
!
!
!
!
!and !
!
!
! !
(c) Relationship
between Objective
Partisan!! Context
Perceptions.
!
0.0
0.2
0.4
0.6
0.8
1.0
0.0
0.2
0.4
0.6
0.8
!
1.0
Figure 2: “Objective”
versus Perceived
Racial,
Economic, and
Partisan Context
theGroup
Block Group Level
% Unemployed
Perceived in
Block Group
% Unemployed
Perceived inAt
Block
28
0.15
subjective
community
subjective
block group
objective
block group
●
●
●
●
0.00
Point ± 66% and 95% HPD CI
0.05
0.10
objective
community
Matched on
Objective Context
Figure 3: Racial resentment scale responses as predicted by different measures of racial context (“objective”
percent black in the block group or in the hand drawn “community” and “subjective” percent black in the
Census block group and hand drawn “community”). Points are empirical Bayes point estimates. Line segments
represent highest posterior density intervals (HPD intervals) to summarize model-based uncertainty in the
estimates (based on 10,000 samples from the posteriors implied by the Normal-Normal multilevel model with
random intercepts and slopes). Estimates of the effects of objective context are not adjusted for any other
covariates. Estimates of subjective context are conditional on pairs in which members have almost exactly
the same objective context measurements. Creation of the pairs involved non-bipartite matching (Lu et al.,
2001, 2011; Rosenbaum, 2010) on absolute distance of objective context (“community” for the subjective
community number, and block-group for the subjective block group analysis).
29
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Appendix A
Census %White in Community
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Census %Black in Community
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1.0
% Black Perceived in Community
0.0
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1.0
% White Perceived in Community
Census %Unemployed in Community
0.0
0.2
0.4
0.6
0.8
1.0
(a) Relationship between Objective Racial Context and Perceptions.
All Respondents
!
! !
! !
!
!
! ! !
! !
!!
!!!
!
! !
!
!
! ! !
!!
!
!
!
!
!
!
!
!
0.0
0.2
0.4
0.6
0.8
1.0
% Unemployed Perceived in Community
All Respondents
!
!
0.0
0.2
! !
!
! Democrat
!
! !
!!
!!!
!
!%
!
!
!!!
!
Whites
!
!
! !
!
!
! !
! !
!
! ! !
! !!
!
!
!
!
! !
!
! ! !
!
!
!
! ! ! ! ! !
!
!
0.4
0.6
0.8
1.0
!
!
Perceived
in Community
(c) Relationship
between
Objective
0.0
0.2
0.4
0.6
0.8
1.0
% Unemployed Perceived in Community
Census %Unemployed
in Community
Objective %Republican
in Community
0.0
0.2
0.4
0.6
0.8
1.0
0.0
0.2
0.4
0.6
0.8
1.0
Census %Unemployed in Community
Objective %Democrat in Community
0.0
0.2
0.4
0.6
0.8
1.0
0.0
0.2
0.4
0.6
0.8
1.0
(b) Relationship between Objective Economic Context and Perceptions.
All Respondents
Blacks
!
!
!
!
!
! ! !
!
!! !
!
! !
! ! ! !
! !
! !
!
! ! ! ! ! !! !
!
! !
!
!
!
!
0.0
0.2 ! 0.4
0.6 ! 0.8 ! 1.0
!
!
!
!
!
!
!
!
! !
Perceived
in Community
! !
! Republican
!
!%
Partisan
0.0 Context
0.2 and
0.4Perceptions.
0.6
0.8
1.0
% Unemployed Perceived in Community
Whites
1
!
!
!
!
! ! !
!
!
!
! ! !
!! ! !
!
!
! ! !
!
an in Community
0.6
0.8
1.0
rat in Community
0.6
0.8
1.0
Figure Appendix A1: “Objective” versus Perceived Racial, Economic, and Partisan Context At the “Local
Community” Level
Whites
Appendix B
It is possible that ordinary citizens do not have a sophisticated understanding of percentages, providing answers that sum to more than 100. The gap between objective and subjective context, in that
case, could result from a simple lack of mathematical understanding. In order to determine whether
this is the case (and test the reliability of our map-based measure of context), we included in our
survey multiple measures of respondents’ perceptions of their self-defined communities. In addition
to being asked what percentage of blacks, for example, lived in their “local community,” they were
asked (later in the survey) to look again at the map they drew and say whether their community
was “mostly white,” “mostly black,” “half and half,” or “a mixture.” While Americans may not
always give percentages that add up to 100 percent, our respondents do display an understanding of
percentages generally: for example, for those who described their community as “mostly white,” the
estimates for percent black in their community ranged from 1 to 50 percent, and averaged 64 percent
white and 25 percent black. For those who thought their areas were “mostly black,” they perceived
their communities to be anywhere from 60 to 95 percent black, with an average of 75 percent black
and 19 percent white. In other words, the percentages were not just random guesses; they seem to
map reasonably onto common sense understandings of quantity and proportion.
2
Appendix C
Whites Subjective %
Whites Objective %
Whites Average Difference
Blacks Subjective %
Blacks Objective %
Blacks Average Difference
Unemployed Subjective %
Unemployed Objective %
Unemployed Average Difference
Democrats Subjective %
Democrats Objective %
Democrats Average Difference
Republicans Subjective %
Republicans Objective %
Republicans Average Difference
National
59
75
-16
30
12
17
21
6
15
52
48
4
46
51
-5
Local Community
50
63
-13
41
26
15
21
5
15
68
75
-6
27
24
3
Block Group
49
53
-5
42
35
8
21
5
16
71
77
-6
27
21
6
!
Table
3: Average across
Subjective
andGeographic
Objective Levels.
Percentages
of differences,
the Nationnegative
Table A1:
Misperceptions
TypesPerceptions
of Context and
For the
numbers represent underestimates and positive numbers represent overestimates.
3
Appendix D
Media
Social Network
Institutions
Everyday Observation
Guess and DK
Other
Block Group
4
22
6
61
6
2
Local Community
8
27
5
50
8
2
United States
67
0
5
5
16
7
Table
4: How did
you learn
about
the composition
of thiswere
area?
Table A2: Sources
of Perceptions
of Context
across
Geographic
Levels. Respondents
allowed to mention
as many or few sources as they liked in the open-ended question format. Their responses were then coded
into these categories.
4
4
Appendix E: “Bringing the Person Back In”
This document provides additional information about the items and analyses presented in the paper and also
shows exactly how the results were produced. Since this is the first, to our knowledge, use of nonbipartite
matching in political science, and also because we have invented some new graphical methods for assessing
the success of a given matching procedure, we are privileging the use of this document for teaching (and thus
showing more computer code and computer output) over the use of this document to present well formatted
tables.
E1 Data and Description
E1.1 Missing Data
We delete one observation before proceeding. Person 416 does not have a valid outcome. Since this analysis
is exploratory and we have only one such person, we elect to drop this person rather than worry about how
this person might have changed the results that follow [i.e. if including this one person with some value for
the outcome dramatically changed then we would worry about him as an outlier exerting more than his fair
share of influence on the results.]
1
2
dat.w dat.w [ dat.w $ Resp ! = 416 ,]
dat.w $ incomef factor ( dat.w $ incomef ) # # Drop empty categories
E1.2 Context
Our measures of context have as objects either the Census map of the respondents’ block group (.bg) or the
self-drawn map of a ‘local community’ (.com). They are either ‘objective’, in that they are based on Census
numbers or ‘subjective’ in that they are based on self-reports.
obj . bg
Min .
:0.0000
1 st Qu .:0.0662
Median :0.2001
Mean
:0.2573
3 rd Qu .:0.3581
Max .
:0.7408
suj . bg
Min .
:0.000
1 st Qu .:0.100
Median :0.250
Mean
:0.313
3 rd Qu .:0.475
Max .
:0.850
NA ' s
:3.000
misper . bg
Min .
: -0.4408
1 st Qu .: -0.0476
Median : 0.0241
Mean
: 0.0610
3 rd Qu .: 0.2264
Max .
: 0.3940
NA ' s
: 3.0000
obj . com
Min .
:0.0533
1 st Qu .:0.0958
Median :0.1771
Mean
:0.1942
3 rd Qu .:0.2597
Max .
:0.4624
suj . com
Min .
:0.000
1 st Qu .:0.175
Median :0.300
Mean
:0.327
3 rd Qu .:0.400
Max .
:0.850
NA ' s
:3.000
misper . com
Min .
: -0.2883
1 st Qu .: 0.0342
Median : 0.1150
Mean
: 0.1364
3 rd Qu .: 0.2442
Max .
: 0.6135
NA ' s
: 3.0000
E1.3 Outcomes
The Racial Resentment scale was created from the following 6 agree/disagree items: (1) Irish, Italian, Jewish
and many other minorities overcame prejudice and worked their way up. Blacks should do the same without
any special favors. (2) Generations of slavery and discrimination have created conditions that make it difficult
for blacks to work their way out of the lower class. (3) It’s really a matter of some people not trying hard
enough; if blacks would only try harder they could be just as well off as whites. (4) Over the past few years,
blacks have gotten less than they deserve. (5) Most blacks who receive money from welfare programs could
get along without it if they tried. (6) Government officials usually pay less attention to a request or complaint
from a black person than from a white person.
Min . 1 st Qu .
0.140
0.300
Median
0.500
Mean 3 rd Qu .
0.492
0.600
Max .
1.000
E1.4 Covariates
Although covariates are not a central part of our analysis, we present information about them here to provide
a sense of the characteristics of our sample.
1
1
summary ( dat.w $ hometen ) # # Number of years lived in current home
Min . 1 st Qu .
0.0
3.2
1
Mean 3 rd Qu .
10.9
12.8
Max .
44.0
table ( dat.w $ educationf , useNA = " ifany " )
B.A.
8
1
Median
7.0
M . A . AdvDeg
9
3
A.A.
2
HS
16
table ( dat.w $ female , useNA = " ifany " )
0 1
26 12
1
as.matrix ( table ( dat.w $ incomef , useNA = " ifany " ) )
under $10000
$10000 -19999
$20000 -29999
$30000 -39999
$40000 -59999
$60000 -74999
$75000 -109999
$110000 or over
[ ,1]
4
4
6
4
6
7
3
4
E2 Matching
Although we will look at unadjusted relationships for objective block group percent black and objective
local community percent black, when we assess the relationships between perceptions and outcomes, we
want to condition on objective context: we want to know whether subjective measures add anything to our
understanding of the outcome even when objective measures are held constant.
The most intuitive and rigorous way to “hold constant” is just that: to run an analysis within subsets of cases
which are all the same on objective context, within subsets, the values of objective context are effectively
constant.
The methodological problem arising here is that when you have few units and a continous variable, exact
subsetting leaves many units alone. Luckily modern algorithmns for subsetting or matching exist. We make
use of one such algorithmn that does not require us to match one type of unit to another type of unit (such as
the relatively more common bipartite matching which matches “treated” to “control” units). Non-bipartite
matching merely creates sets (pairs in our case) which are matched as closely as possible in terms of a distance
(here, absolute difference in percent black in the block group or ‘local community’).1
We created two different matched designs: (1) matching on objective block group percent black and (2)
matching on objective local community percent black. Here are the steps we took.
E2.1 Make Distance Matrices
Produce distance matrices. First, we need a function to produce matrices of absolute distances.
1
2
3
4
scalar.dist function ( var ) {
# # Utility function to make n x n abs dist matrices
outer ( var , var , FUN = function (x , y ) { abs ( x-y ) })
}
1 See
Lu et al. (2011) for a nice article introducing non-bipartite matching.
2
Objective community distance:
1
2
o b j . c o m . d i s t . m a t scalar.dist ( dat.w $ obj.com ) * 100 # # the matching software wants integers
dimnames ( o b j . c o m . d i s t . m a t ) list ( row.names ( dat.w ) , row.names ( dat.w ) )
Objective block group distance:
1
2
o bj . bg .d i st .m a t scalar.dist ( dat.w $ obj.bg ) * 100
dimnames ( o b j. bg . di s t. ma t ) list ( row.names ( dat.w ) , row.names ( dat.w ) )
E2.2 Specify number of units to exclude from the matching.
We do not try to give the matching procedure an opportunity to delete bad matches. If we had trouble with
balance assessments, we might come back to this step.
E2.3 Do the matching
Now convert the distance matrices into the format desired by nonbimatch (including making them integers):
1
2
obj.com.dist.mat.dm
obj.bg.dist.mat.dm
dis tancem atrix ( o b j . c o m . d i s t . m a t 3 * 100)
dist ancema trix ( o b j . b g . d i s t . m a t 3 * 100)
Now, do the matching.
E2.4 Evaluate the Success of the Matching
We matched on “objective” context. If we succeeded, we should see (1) that people in matched pairs are
more similar to each other on objective context than they would be if they were randomly paired; and (2)
that differences within pairs are small in an absolute sense. We cannot use standard techniques for assessing
balance on the matching variable itself so we rely on descriptive techniques here.
0.8
0.8
obj.com
0.4
0.6
obj.bg
0.4
0.6
1.0
Matching on Objective ‘Local Community'
1.0
Figure 1 show us the success of the matching in a fine grained manner and also show the diversity of subjective
perceptions within matched set. Horizontal lines show matches in which the two units in the pair are quite
similar. Lines that are angled toward the vertical show matches that are less than exactly the same.
●
●
●
●
●
●
●
●
●
●
●
●
●
● ●
●
0.0
●
0.0
Matching on Objective Block Group
0.2
●
0.2
2
nbm.obj.com nonbimatch ( o b j . c o m . d i s t . m a t . d m )
nbm.obj.bg nonbimatch ( o b j . b g . d i s t . m a t . d m )
0.0
1
0.2
0.4
suj.com
0.6
0.8
● ●
0.0
0.2
0.4
suj.bg
0.6
0.8
Figure 1: Objective context by subjective context (either referring to the Census map of a block group (bg) or referring
to a respondent’s own map of a ‘local community’ (com). Units paired after non-bipartite matching are connected with
line segments.
3
We can see that the matching was quite successfull: most of the lines are nearly exactly horizontal. We also
see that the matching did not erase heterogeneity in subjective perceptions of context: such variation will be
important as we ask the question about whether subjective context appears to predict outcomes above and
beyond the effects of objective context.
Matching on Objective Block Group Now, in an absolute sense, how close were the pairs? First, let us look
at the unmatched situation:
1
summary ( ob j. b g. di s t. m at [ lower.tri ( o bj .b g .d i st .m a t ) ]) # # Before Matching
Min . 1 st Qu .
0.0
8.8
Median
18.2
Mean 3 rd Qu .
24.4
36.9
Max .
74.1
So, without matching, people differed from one another by as much as 74 percentage points of percent black.
This is sensible given our design: we sampled block-groups stratified by percent black in an effort to ensure
that we had wide variation on the explanatory variable of interest.
Now, after matching, we see that pairs hardly differ in percent black in the block group. What we see below is
that about 2/3 of the sets were matched exactly. In 6 of the sets where the difference was greater than zero,
most differed by less than 5 percentage points. We did have two sets which were not so tightly matched —
they differed by about 6 and 9 percentage points of black population. In the subsequant analysis, however, we
see no evidence that the results are overly sensitive to the imbalance in these two sets.
1
2
s et d if fs . ob j. b g with ( dat.w , tapply ( obj.bg * 100 , nbm.obj.bg.sets , function ( x ) { abs ( diff ( x ) ) }) )
summary ( se td i ff s. o bj . bg ) # # Summary of paired differences
Min . 1 st Qu .
0.00
0.00
1
Median
0.00
Mean 3 rd Qu .
1.19
1.44
Max .
8.90
quantile ( setdiffs.obj.bg , seq (0 ,1 , .1 ) )
0%
10%
20%
30%
40%
50%
60%
70%
80%
90% 100%
0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.682 2.031 3.412 8.899
1
mean ( s e t d i f f s . o b j . b g < 1 ) # # Avg diff among the tightly matched pairs
[1] 0.684
1
table ( se td i ff s. o bj . bg [ se td i ff s. o bj . bg ! = 0]) # # If not identical , then how big differences ?
1.13693 1.73516 2.47391 2.87526 5.56134 8.89921
1
1
1
1
1
1
Matching on Objective ‘Local Community’ The story for the matching on objective ‘local community’
percent black is more or less the same. Before matching, we see that most people differ from each other in
their perceptions.
1
summary ( o b j . c o m . d i s t . m a t [ lower.tri ( o b j . c o m . d i s t . m a t ) ]) # # Before Matching
Min . 1 st Qu .
0.0
4.8
Median
10.6
Mean 3 rd Qu .
12.3
17.8
Max .
40.9
After matching, we see that the differences within pair become an order of magnitude smaller. Since this
measure is now particular to an individual’s drawing, no two people are exactly the same but most people
are within 1 percentage point of the other person in their pair. We have one pair with a difference of about 4
percentage points, but, again, we see no evidence that this relatively loosely matched set is driving our results
as presented below.
4
1
2
s e t d i f f s . o b j . c o m with ( dat.w , tapply ( obj.com * 100 , nbm.obj.com.sets , function ( x ) { abs ( diff ( x ) ) }) )
summary ( s e t d i f f s . o b j . c o m ) # # Summary of paired differences
Min . 1 st Qu .
0.08
0.18
1
Median
0.37
Mean 3 rd Qu .
0.76
0.94
Max .
4.28
quantile ( setdiffs.obj.com , seq (0 ,1 , .1 ) )
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
0.0787 0.1369 0.1541 0.2200 0.2745 0.3673 0.6122 0.7333 1.2009 1.4697 4.2833
1
mean ( s e t d i f f s . o b j . c o m < 1 ) # # Avg diff among the tightly matched pairs
[1] 0.737
1
table ( s e t d i f f s . o b j . c o m [ s e t d i f f s . o b j . c o m
1]) # # If not less than 1 pct pt , then how big differences ?
1.11107719289295 1.33567626720755 1.44349481284163 1.57466868340358 4.28326348931586
1
1
1
1
1
E2.5 Covariate Balance
Our matching was not designed to create balance on covariates, so this is not really an assessment of the
success of the matching itself. Rather, it is just a summary of the extent to which people differ within pairs
on the covariates. We are comfortable if people differ within pairs on covariates for these analyses: after
all, if “perceptions” is to have construct validity it ought to relate to education and other factors that matter
for perceptions. Here we look at the mean difference on background covariates across levels of the variable
matched on following Hansen and Bowers (2008).
Compared to a paired-randomized experiment, most of these covariates were relatively balanced in the first
place. Matching improved balance somewhat.
Pre.Matching
Objective.Community.Matching
chisquare
15.95
14.15
df
13.00
13.00
p.value
0.25
0.36
Table 1: Omnibus tests for differences tests in means before and after non-bipartite matching on objective ‘local
community’.
5
Strata:
educationfB.A.
educationfM.A.
educationfAdvDeg
educationfA.A.
educationfHS
incomefunder $10000
incomef$10000-19999
incomef$20000-29999
incomef$30000-39999
incomef$40000-59999
incomef$60000-74999
incomef$75000-109999
incomef$110000 or over
hometen
female
Pre.Matching
p
0.98
0.03
0.53
0.57
0.21
0.52
0.33
0.09
0.47
0.92
0.60
0.67
0.04
0.09
0.66
Objective.Community.Matching
p
0.15
0.34
0.89
0.31
0.26
0.17
0.35
0.21
0.20
0.64
0.11
0.69
0.29
0.85
0.49
Table 2: One-by-one differences in means tests before and after non-bipartite matching on objective ‘local community’.
Categorical variables like education and income are broken into binary categories for assessing balance here.
Pre.Matching
Objective.Block.Group.Matching
chisquare
17.49
6.00
df
13.00
6.00
p.value
0.18
0.42
Table 3: Omnibus differences in means tests before and after non-bipartite matching on objective block-group.
Strata:
educationfB.A.
educationfM.A.
educationfAdvDeg
educationfA.A.
educationfHS
incomefunder $10000
incomef$10000-19999
incomef$20000-29999
incomef$30000-39999
incomef$40000-59999
incomef$60000-74999
incomef$75000-109999
incomef$110000 or over
hometen
female
Pre.Matching
p
0.60
0.01
0.78
0.15
0.20
0.84
0.17
0.13
0.33
0.52
0.86
0.68
0.07
0.55
0.56
Objective.Block.Group.Matching
p
0.32
0.44
0.32
0.32
0.11
0.32
0.32
0.34
0.32
0.32
0.32
1.00
0.24
0.60
0.19
Table 4: One-by-one differences in means tests before and after non-bipartite matching on objective block-group.
Categorical variables like education and income are broken into binary categories for assessing balance here.
6
E3 Outcomes Analysis
E3.1 Simple Bivariate Relationships
Matching on Objective Community
●
0.8
1.0
Matching on Objective Block Group
0.8
1.0
We rescaled the context measures so that a 1 unit difference is more substantively meaningful — i.e. it is
a change in 10 percentage points rather than 1 percentage point. Figure 2 shows that the person in the pair
perceiving higher proportions of blacks (in his/her block-group or self-defined community) tends also to be
the person with the higher score on racial resentment: this is a simple version of what we will show later
using a multilevel model.
●
●
●
●
●
●
● ●
●
●
symrac01
0.4
0.6
symrac01
0.4
0.6
●
●
● ●
●
0.2
0.2
●
●
0.0
0.0
●
0
2
4
suj.bg.10
6
8
0
2
4
suj.com.10
6
8
Figure 2: Within pairs nearly identical on objective context, subjective context relates to symbolic racism.
The data support what our eyes suggest: on average, the person with the higher subjective perceptions of
percent black tends to be the person with the higher racial resentment score. We also see one pair in which both
people perceive the same proportion black in their block-group/‘local community’. The averages presented
here are with respect to the pair-specific mean, so, a negative number means that the person has the lower of
the two racial resentment scores in the pair.
1
with ( dat.w , tapply ( symrac01.md.obj.bg , suj.bg.rank.obj.bg , mean ) )
1
-0.0318
1
2
18
with ( dat.w , tapply ( symrac01.md.obj.com , suj.com.rank.obj.com , mean ) )
1
-0.0613
1
2
0.0318
with ( dat.w , tapply ( symrac01.md.obj.bg , suj.bg.rank.obj.bg , length ) )
1 1.5
18
2
1
1.5
0.0000
1.5
0.0000
2
0.0612
with ( dat.w , tapply ( symrac01.md.obj.com , suj.com.rank.obj.com , length ) )
1 1.5
18
2
2
18
7
E3.2 Multilevel Models
We have more information available than merely ranking pair members. If subjective context matters for racial
resentment, then we would expect pairs differing greatly in subjective context to display greater differences in
racial resentment than pairs that differ a little. A linear model is a nice tool to use in summarizing this kind of
relationship. We use multilevel models to represent the idea that we sampled people within block-group and
that we expect some unmodelled dependencies within block-group.
Effect of objective context on racial resentment with random intercepts and slopes following the sample
design (which sampled at the block-group level as well as at the individual level), with no adjustment (i.e. no
matching).
1
2
lmer3.sr.bg
lmer3.sr.com
lmer ( symrac01 ⇠ 1+ obj.bg.10 +(1| bg ) +(0+ obj.bg.10 | bg ) , data = dat.w )
lmer ( symrac01 ⇠ 1+ obj.com.10 +(1| bg ) +(0+ obj.com.10 | bg ) , data = dat.w )
Next, the effect of subjective context on racial resentment with random intercepts and slopes and removing
a fixed effect for objective context via the matched designs [we use the pair-mean-deviated formulation of
this adjustment, the indicator/dummy variable version would produce identical results for our variable of
interest but would produce messier tables and use degrees of freedom to estimate effects that we hold fixed
(i.e. pair-specific intercepts do not need to be estimated in this model)].
1
2
lmer 2.sr.b g.md lmer ( s y m r a c 0 1 . m d . o b j . b g ⇠ -1 + s u j . b g . m d . o b j . b g +(0+ s u j . b g . m d . o b j . b g | bg ) , data = dat.w )
l me r 2. sr . co m. m d lmer ( s y m r a c 0 1 . m d . o b j . c o m ⇠ -1 + s u j . c o m . m d . o b j . c o m +(0+ s u j . c o m . m d . o b j . c o m | bg ) , data = dat.w )
Now, sample from the posterior implied by the chosen likelihood (Normal) and priors (univariate Normal —
not multivariate here). We’ll use these samples for interval creation. The reason that we don’t use a single
p-value here is because we don’t really have a clear way to calculate a degrees of freedom from a multilevel
model of this type, but the posterior distribution is well defined. So, we can get reasonable statistical inferences
from that distribution even if we might not know exactly how to calculate the df for a t-distribution.
The results of the multilevel models (point estimates and 66% and 95% highest posterior density (HPD)
intervals:
subjective block group
subjective community
objective block group
objective community
point
0.049
0.076
0.050
0.071
lower66
0.009
0.051
0.033
0.045
upper66
0.061
0.090
0.064
0.109
lower95
-0.021
0.029
0.015
0.008
upper95
0.089
0.112
0.082
0.145
Table 5: The relationship between the different measures of context and racial resentment. The rows using subjective
measures arise from models conditioning on objective context matched sets. Upper and lower boundaries of intervals
refer to highest posterior density regions based on 10,000 samples from the posteriors implied by the multilevel models.
8
0.15
subjective
community
subjective
block group
objective
block group
●
●
●
●
0.00
Point ± 66% and 95% HPD CI
0.05
0.10
objective
community
Matched on
Objective Context
Figure 3: Racial resentment scale responses as predicted by different measures of racial context (“objective” percent
black in the block group or in the hand drawn “community” and “subjective” percent black in the Census block group
and hand drawn “community”). Points are empirical Bayes point estimates. Line segments represent highest posterior
density intervals (HPD intervals) to summarize model-based uncertainty in the estimates (based on 10,000 samples
from the posteriors implied by the Normal-Normal multilevel model with random intercepts and slopes). Estimates of
the effects of objective context are not adjusted for any other covariates. Estimates of subjective context are conditional
on pairs in which members have almost exactly the same objective context measurements. Creation of the pairs involved
non-bipartite matching (Lu et al. 2001, 2011; Rosenbaum 2010) on absolute distance of objective context (“community”
for the subjective community number, and block-group for the subjective block group analysis).
9
References
Hansen, Ben B. and Jake Bowers. 2008. “Covariate balance in simple, stratified and clustered comparative
studies.” Statistical Science 23(2):219–236.
Lu, B., E. Zanutto, R. Hornik and P.R. Rosenbaum. 2001. “Matching with doses in an observational study of a
media campaign against drug abuse.” Journal of the American Statistical Association 96(456):1245–1253.
Lu, B., R. Greevy, X. Xu and C. Beck. 2011. “Optimal nonbipartite matching and its statistical applications.”
The American Statistician 65(1):21–30.
Rosenbaum, P.R. 2010. Design of observational studies. Springer Verlag.
10