International Journal of Health Geographics Open Access the Complexities of Measuring Access to Parks and Physical Activity Sites in New York City: a Quantitative and Qualitative Approach

Background: Proximity to parks and physical activity sites has been linked to an increase in active behaviors, and positive impacts on health outcomes such as lower rates of cardiovascular disease, diabetes, and obesity. Since populations with a low socioeconomic status as well as racial and ethnic minorities tend to experience worse health outcomes in the USA, access to parks and physical activity sites may be an environmental justice issue. Geographic Information systems were used to conduct quantitative and qualitative analyses of park accessibility in New York City, which included kernel density estimation, ordinary least squares (global) regression, geographically weighted (local) regression, and longitudinal case studies, consisting of field work and archival research. Accessibility was measured by both density of park acreage and density of physical activity sites. Independent variables included percent non-Hispanic black, percent Hispanic, percent below poverty, percent of adults without high school diploma, percent with limited English-speaking ability, and population density.


Introduction
Environmental justice is the fair and equitable distribution of both the environmental "bads," such as hazardous waste sites, and the environmental "goods," such as parks, open space, and recreational opportunities. For more than a decade, Geographic Information Systems (GIS) have been used to examine the spatial realities of environmental justice [1][2][3][4][5][6][7][8][9][10][11]. GIS methods have been applied in environmental justice research primarily in the analysis of the spatial relationships between sources of pollution burdens and the characteristics of potentially affected populations. Environmental justice research has therefore focused on analyzing the disproportionate exposure of pollution on communities comprised of vulnerable groups, such as racial/ethnic minorities and socio-economically disadvantaged groups, and the concomitant effects of this pattern on health and environmental disparities [12][13][14]. GIS has been less often used to analyze the relationship between socio-demographic and environmental "goods," such as health-promoting land uses and positive aspects of the built environment.
Previous studies have documented that proximity to parks and open spaces has a positive influence on engaging in active behaviors, like walking and running for exercise [15][16][17][18][19]. Other studies have analyzed how the availability of outdoor space impacts on specific health outcomes, like community-level rates of mortality, cardiovascular disease, diabetes, and obesity [20][21][22][23][24][25][26]. The underlying hypothesis is that since individual-level risk factors for these highly prevalent diseases do not fully explain disparities in their distribution across population groups, or even disparities across population groups in health behaviors that are related to these diseases, modifiable environmental factors may help us to develop fuller models explaining health disparities in these health outcomes and related health behaviors. This research is of interest to public health and policy analysts who are developing interventions and policies that can mitigate health disparities that persist across socio-economic groups in the USA.
If environmental factors help us to understand the distribution of health outcomes in the population, then one might expect that active outdoor space would be less available to populations with overall worse health outcomes. Since low SES populations and racial/ethnic minorities experience worse health outcomes in the USA [27,28], access to parks and physical activity sites becomes an environmental justice issue. However, research findings have been contradictory, which suggests a complex relationship among socio-demographics, outdoor space, and individual-level health factors.
Many researchers have endeavored to evaluate access to parks and recreational facilities, and have used various methods and measures to do so. However, there are many pitfalls in developing a measure or index of accessibility, and even the more sophisticated analyses have some problems in matching their indices with reality. Research on this topic has grown more nuanced in recent years, but many of these analyses still present some methodological difficulties, which may call into question their findings, especially considering that many of these studies show significantly contradictory results (see table 1).
One of the most common methods used in examining access to park space is called the "container approach." This approach measures access by determining whether or not there is a park or recreational facility within a particular geographic unit of aggregation (e.g., zip code, census tract, or neighborhood), rather than using or developing an actual proximity measure such as Estabrooks, et al, 2003 [29]. In this container approach, the number of parks per areal unit is then summed and associations between this count and various population characteristics, such as SES, can be estimated for the chosen unit of aggregation.
This may be problematic in arriving at an accurate depiction of park access. For example, a person may live directly next to a park, but if the park is located in a different unit of aggregation (e.g., zip code, census tract, etc.), it will not be counted as "accessible" for that person. Additionally, populations that are distributed heterogeneously across a large areal unit may also introduce error in estimating park access. A population that is distributed heterogeneously within the areal unit may also introduce error in estimating park access, since, especially with larger areal units, the population may be concentrated in portions of the geographic unit that are not in close proximity to the park, although still within the same unit (see figure 1).
A number of previous studies have used this "container" method for evaluating whether or not a person has good access to parks [29][30][31], and have found contradictory results when correlated with neighborhood SES (lack of access to parks positively correlated with low SES versus negatively correlated with low SES). These inconsistent results may be due to the container method itself. In addition to the boundary problem discussed above, this method is problematic in that it often does not take into account the underlying population structure and density of the areal unit, or the relative size of these areal units. Thus it is not a fair comparison since areal units with larger populations require more parks than an equivalent areal unit with fewer people in order to be equitable.
Additionally, although some of these studies use actual park acres per geographic unit in their calculations, others simply count the number of parks and facilities per geo- graphic unit. However, creating a simple count of parks and basing equity analysis on that count does not consider the actual amount of park space available to residents, since one park may be substantially smaller than another and therefore should not receive an equal weight in the calculations.
Other studies have used proximity analysis based on "walkability" distances, which is a more refined measure of access, by setting certain distances to parks as a proxy for access, such as 1/4 mile (~400 m) or 1/2 mile (~800 m) as a standard walking distance [32,33]. However, access by proximity or distance often does not take into account the actual street network, merely Euclidean distance.
There have been a few studies using the street network to calculate distance to parks, for instance, Nicholls (2001) and Talen and Anselin (1998) each of whom compared straight-line distance with street network distance [34,35]. The Nicholls study found that approximately 80% of the area studied (Bryan, Texas) were not within 1/2 mile  Problems with the "container approach Figure 1 Problems with the "container approach. "In Tract A, population lives in close proximity to a park, but the container approach would report "no access," because the park is in a different enumeration unit. In Tract B, the population lives far from the park but the container approach would report "access," because the park is in the same enumeration unit.

Tract A Tract B
(~800 m) of any park (as measured by network distance), but that the less affluent neighborhoods tended to be better served by parks than the more affluent areas. In the Talen and Anselin study, the distribution of playgrounds in Tulsa, OK, as measured by various methods including the network analysis, could be considered "unpatterned inequality." The playgrounds were not distributed evenly throughout the city, but were also not predicted by any specific socio-demographic variables.
Kernel density estimation, or kernel smoothing, is another method for measuring accessibility. "Kernel density estimation involves placing a symmetrical surface over each point, evaluating the distance from the point to a reference location based on a mathematical function, and summing the value of all the surfaces for that reference location. This procedure is repeated for all reference locations." [36] Kernel density estimation creates a statistical surface so that, for instance, there is an accessibility value as measured by park density, mapped at every point in the study area.
Kernel density estimation is typically considered a more refined spatial statistical model than the container approach. It can give an estimation of accessibility for every point in the study area, not just a binary answer of "within walking distance" or "not within walking distance," as in both the fixed-distance proximity and the network analyses. There have been very few studies of park access using the kernel density method, although this method has been used extensively in other types of analyses [37,38]. Moore, et al. (2008) used the kernel density estimation method to compare park access in three USA locations, and found that although pay-for-use recreational venues were more likely to be located in white and more affluent neighborhoods, public parks tended to be more equitably distributed, and densities of recreational facilities within parks were significantly higher in minority and low-income census tracts than in white and higher-income tracts, even after adjustment for population [39].

Methodology
This analysis uses the kernel density estimation approach to test whether access to park space is associated with neighborhood race/ethnic composition and SES in New York City. Densities of both park acreage and physical activity sites are mapped and correlated with SES measures. The two main categories of data used in this analysis were park information and socio-demographic information.

Data -parks
The park extent data was created by the New York City Department of Parks and Recreation and represents all land owned by the Parks Department as polygons (see figure 2). These polygons are coded into various classes such as green streets, small parks, and large parks.
The park features data (elements within the parks) were created through a collaboration between the New York City Department of Parks and Recreation and Lehman College of the City University of New York. Researchers traveled to all of the New York City parks carrying portable GPS units and recorded the locations of many of the parks' features, including items such as drinking fountains, comfort stations (rest rooms), flag poles, stairways, historical markers, statues, beaches, courts, ball fields, and other recreational areas (see figure 2). This point data (latitude and longitude) were rectified with aerial photos and further processed into a more accurate and useable dataset.
For this study, two separate data layers were created based on the park information. The first layer was designed to represent park area and the second to represent physical activity sites. The park area layer was created by first identifying each acre of New York City as either 'park' or 'no park'. If there is any park space in any given acre, the pixel representing that acre was given a value of '1' ('park'). Otherwise, that pixel would have been given a value of '0' ('no park'). This grid was then converted into a statistical surface using the kernel density technique. This method involves a kernel function, which uses a moving window to apply differential weights to objects based on proximity. Thus objects that are close are weighted more heavily than more distant objects. Based on a sensitivity analysis, the bandwidth parameter for the kernel function was assigned a 1.6 km (1 mile) radius. This sensitivity analysis tested three different kernel sizes (1/4 mile, 1/2 mile, and 1 mile). Empirically, the one mile kernel bandwidth explained more of the variance in the model than the other bandwidths. This distance was also determined to be an appropriate kernel bandwidth for defining a feasible walking distance for park accessibility based on other research [39]. The kernel density estimation resulted in a 50 meter raster surface representing the density of park acreage for New York City (see figure 3a). This surface is used as a proxy for accessibility.
To prepare the data layer for physical activity sites, each discrete non-linear park feature that was identified as activity promoting (i.e. something that encourages caloric expenditure) was extracted from the main parks database, converted to a point (if necessary) and given a value of '1' (1 = physical activity site). The features that were coded are: basketball courts, handball courts, tennis courts, volleyball courts, multipurpose courts, soccer fields, baseball fields, football fields, swimming pools, hockey rinks, golf courses, and running tracks. Kernel density estimation was again performed, this time in order to estimate the density for physical activity sites in New York City. A 1.6 km radius was used as the bandwidth and a 50 meter resolution raster surface was created (see figure 3b).
These two density surfaces were used as proxies for access to park space (acres) and active recreation (physical activity sites), following the assumption that where there are higher densities of resources, access is greater.

Data -Socio-demographics
In order to evaluate the possibility of unequal access to these park measures based on socio-demographic characteristics of the population, information was gathered from summary file 1 (SF1) and summary file 3 (SF3) of the 2000 USA census at the block group level. The measures included in this analysis were percent non-Hispanic black, percent Hispanic, percent of adults aged 25 years and older with no high school diploma, percent below poverty, percent who do not speak English well or do not speak it at all, and population density (see figure 4).

Joining parks data with demographic data
To link the raster park data with the vector socio-demographic data, zonal statistics were used within the spatial analyst extension of ArcGIS. This process aggregates and statistically summarizes the values of the raster cells whose centroids fall within the corresponding block  group. As a result, each census block group in New York City is given an average value for the park acre density and physical activity site density of the grid cells that fall within its boundaries. This aggregates the kernel densityderived statistical surfaces (acres and physical activity sites) to the same geographic unit as the socio-demographic data.

Quantitative analysis/results
Two discrete statistical methods were used on the data: ordinary least squares linear regression (OLS) and geographically weighted regression (GWR). The datasets used in the analyses were identical. Census block groups with fewer than 256 residents were excluded (lowest 5%) in order to stabilize the model. Block groups that had missing data from any of the variables were also excluded (0 .1%). After the data were cleaned and prepared, 5,439 block groups out of the original 5,732 remained (94.9%). Log10 transformed park acreage density (ACRE) and log10 transformed physical activity site density (PAS) were used as the dependent variables. The independent variables included: percent non-Hispanic black, percent Hispanic, percent of adults with no high school diploma, percent below poverty, percent with limited English language ability, and population density.
When analyzed globally (with OLS) it appears that PAS and ACRE behave differently with respect to the independent variables (see table 2). There are some interesting changes in directionality with the percent non-Hispanic black and the percent limited English language variables when comparing PAS and ACRE scores. Both variables are positively associated with the density of physical activity sites yet negatively associated with park acre density. Since both models explain a relatively small amount of the variance in the dependent variables (23% and 11% for PAS and ACRE, respectively), the same models were recreated using a geographically weighted regression (GWR) in an attempt to account for potential spatial non-stationarity (i.e. local variation in the relationships).
Geographically Weighted Regression (GWR) is a technique developed by Fotheringham, Brunsdon, and Charlton designed to quantify locally varying relationships among data, rather than the more common global rela-tionships (e.g., OLS regression). These local relationships may vary over space therefore accounting for any potential spatial non-stationarity. In other words, the measurement of the relationship may be partially dependent upon where the measurement is taken. Fotheringham, et al (2002) suggest several reasons for locally varying relationships, such as sampling variation, a misspecification of the model (e.g., omitted variables or those which are not measureable), or simply a relationship which intrinsically varies over space [40]. GWR is essentially a modification of traditional regression techniques, except rather than calculating global parameter estimates based on one regression, GWR performs many local regressions, each of which is influenced by the surrounding data. In this way, GWR shows local variations in the relationships and accounts for spatial non-stationarity. In this study, we used GWR to enable us to see where these relationships vary and hypothesize as to why they behave as such. By definition, the R 2 will rise and the models will technically perform better. An adaptive kernel, which attempts to minimize the Aikaike Information Criterion (AIC) by running many iterations of the model, was used to determine the optimal number of nearest neighbors for the regressions. This adaptive kernel, rather than a fixed bandwidth, was chosen in order to reduce edge effect since we do not have detailed park data for the areas outside New York City. Although this method ensures a sufficient local sample size for all regression points, it can result in unstandardized geographic sizes for individual regression points (particularly near study boundary edges) which can lead to overly smoothed results for those areas. Although this is certainly a limitation, it may not be critical in this study since we were interested in examining the potential environmental justice issues regarding New York City residents and New York City parks only, that by necessity must be confined to the boundaries of the city's jurisdiction. The adaptive kernel method resulted in the utilization of 271 nearest neighbors for the PAS model and 279 nearest neighbors for the ACRE model. Although these samples are certainly large enough for a stable model, they represent only approximately 5% of the original data, suggesting that the relationships are quite local (as the number of nearest neighbors used in the GWR approaches the total number of observations in the data, the model becomes more similar to a global OLS). The local nature The GWR analysis identified the relationships between park access measures and socio-demographic variables as behaving inconsistently across New York City. These idiosyncrasies could benefit from a qualitative evaluation of the relationship between SES characteristics with physical activity sites and park density.

Justifications for qualitative analysis
The GWR analysis revealed a tendency toward what has been termed "unpatterned inequality," meaning that while the parks and physical activity sites are not evenly distributed across the city in a geographical sense, neither are they predicted globally by race/ethnicity, income or the other variables typically investigated in environmental justice analyses. There are no discernable consistent associations between park access and socio-demographic indicators [35]. This is, of course, not to say that everyone has equal access to parks and physical activity sites, or that all neighborhoods have good access to these resources. Certainly, a quick glance of a map of New York City's parks indicates that not all parts of the city are equally wellserved by parks.
Therefore, we thought it would be beneficial to investigate case study areas on a more detailed basis, which might illuminate the spatial incongruities that exist. More explanatory power may be realized through a qualitative analysis, which includes historical background of the parks and surrounding neighborhoods, a description of the past and current socio-demographics, and an overview of the physical aspects of the study areas.
New York City has a complex relationship between its physical infrastructure and its population distribution. Many parks are quite old and were established in neighborhoods having very different socio-demographic characteristics than those of the same neighborhoods today. Parks are a special category of fixed infrastructure for that reason -most occupy large parcels of land and once they are established, it is unlikely that they will be eliminated or moved. The populations surrounding them, however, are quite changeable. This is why it is difficult to ascribe environmental justice implications to the locations of parks. It is still instructive to try to determine which populations, if any, are currently underserved by parks and recreational spaces in New York City, despite the original purpose of the parks, and who those parks were intended to serve.

Selection of study areas/delineation of study area boundaries
Our objective in the qualitative analysis was to compare two case study areas that behaved differently in the GWR analysis. The Highland Park study area on the Brooklyn-Queens border exhibits a positive relationship between percent non-Hispanic black and physical activity site density, whereas the Marine Park study area in Brooklyn exhibits a negative association between the same two variables. Both parks have similar amounts of useable area, and possess a relatively high number of physical activity sites (see table 5). What might account for the differences reported in the GWR between the two study areas?
An 800 m buffer, generally accepted as the upper end of "walking distance" [34], was drawn around the boundaries of each park to create the study areas. Census tracts that intersect this boundary were chosen for demographic analysis to represent the approximate catchment area of the park. The intersection was first performed by the GISc software, and the tracts which intersected but had a very small proportion of their area within the buffers were manually removed. For Highland Park, this area includes parts of the following neighborhoods: Highland Park and Cypress Hills, Brooklyn; and Glendale, Queens. For Marine Park, this area includes parts of the following neighborhoods: Gerritsen Beach, Sheepshead Bay, Marine Park, Flatlands, and Mill Island (all in Brooklyn).

Highland Park
In 1891 Brooklyn purchased the land surrounding the Ridgewood Reservoir (built in 1856) to be used as a park.
In 1905, the park was extended south, and by 1908 the park was extended west and set the boundaries that remain today. By 1908 the park already included football fields, baseball fields, tennis courts, several gardens, footpaths, and park structures. Situated among a chain of seventeen mid-19 th century cemeteries that straddle the In 1974, 1024 acres were transferred to the Gateway National Recreation Area. [42] According to the New York City Department of Parks and Recreation, the park contains nearly 800 acres, although some of that acreage includes land that is under water. The park is adjacent to Rockaway Inlet and consists largely of salt marshes. The majority of the park's space is a protected "Forever Wild Preserve" (see figure 8a). Because the Geographically Weighted Regression of Physical Activity Sites Figure 5 Geographically Weighted Regression of Physical Activity Sites. Spatial distribution of local t-values from PAS GWR linear regression. Purple areas suggest positive association between physical activity site density and the independent variable, white areas suggest no statistically significant relationship, and gold areas suggest negative associations. Geographically Weighted Regression of Park Acreage Density Figure 6 Geographically Weighted Regression of Park Acreage Density. Spatial distribution of local t-values from park acre density GWR linear regression. Purple areas suggest positive association between park acre density and the independent variable, white areas suggest no statistically significant relationship, and gold areas suggest negative associations. Gerritson and Mill Creeks run north into the park, functionally separating the east and west sides from each other save for a sliver of greenery that connects the two sides in the north. Access to the park from the east is nearly impossible since a waterway (Mill Basin) borders the park here (see figure 8b). Access from the south is not possible either except for those who kayak in from Jamaica Bay via the Rockaway Inlet. Park access, then, is limited to the northern and western areas of the park, and not surprisingly, all physical activity sites, except for the golf course, are located in these areas. [42] Description of physical aspects of study areas Based on a GIS analysis of New York City land use data by property tax lot and ground-truthed by a visual inspection of the areas, both study areas were determined to be fairly similar in their land use makeup, with the vast majority of property lots containing residential buildings. However, the Highland Park study area consists of higher proportions of multi-family buildings, mixed commercial/residential, and industrial/manufacturing land uses whereas the Marine Park study area has a much higher proportion of one-and two-family buildings (see figure 9).

GWR Results: Local t-Values Park Acre Density Model
Both of the neighborhoods surrounding both Highland Park and Marine Park are heterogeneous in terms of levels  of maintenance, upkeep, and cleanliness and there is a dramatic range of housing types, from mansions to lowincome public housing complexes, found within the 800 m buffer of the parks, albeit not necessarily adjacent to one another (see figures 7h, 8f and 8g). There are also various types of business and commercial strips in both study areas (see figure 7g and 8e).
For both parks, it is difficult to qualitatively assess the association between the apparent socio-economic status of the neighborhood and accessibility to the park. For instance, the north side of Highland Park in Queens has much less access to the park than the comparatively less affluent neighborhood to the south of the park in Brooklyn. The Queens neighborhood is isolated from the park by obstacles such as cemeteries and a major highway (see figure 7b and 7c), and is by far the furthest neighborhood from the park's physical activity sites. One anomaly is that the mansions and larger homes located to the west of Highland Park appear to have excellent park access. It is interesting to note that when observing the Brooklyn side of the park alone, housing conditions do seem to deteriorate the further one travels away from the park.
For the Marine Park study area, park access appears more evenly distributed, regardless of SES. While the higher value housing around Marine Park is located near the main physical activity sites (see figure 8h), there is also high access to other physical activity sites from lowincome housing complexes. There are some neighbor-a-h: Highland Park Study Area   hoods within the 800 m buffer of Marine Park that also have physical obstacles to access. The park itself contains natural areas of salt marsh and streams which are not easily traversable. There are also two neighborhoods in close proximity but separated from the park by water bodies (see figure 8b). One of these neighborhoods is a relatively higher income area and the other is lower-income.

Socio-demographic characteristics of study areas
Since   A comparison of socio-demographic characteristics between the two study areas based on the more nuanced categories available in the 2000 census shows some differences (see figure 12). The Highland Park area is characterized by a high percentage of Hispanic population, a significant proportion of adult residents without a high school diploma, and a high poverty rate, whereas the Marine Park area is characterized by a predominantly non-Hispanic white population, lower poverty rates and a lower percentage of adults with no high school diploma. Furthermore, residents around Highland Park have a higher proportion of residents with limited ability to speak English than living near Marine Park. Both areas show a relatively high percentage of housing units with vehicles, however this percentage is higher in the Marine Park area than in the Highland Park area.

Results of quantitative and qualitative analyses
Even though the OLS statistics suggest a trend toward racial/ethnic minorities and lower SES populations having higher access to parks and physical activity sites, the GWR points towards "unpatterned inequity," meaning that disparities in park access exist, but the inequity is inconsistently correlated with specific socio-demographic variables. This is further supported by the qualitative analysis, which implies that a global (city-wide) analysis of accessibility may not be the appropriate analytic method for this data. A limitation of the qualitative analysis is that only two case study park areas were examined, which is Land-use Characteristics of the Two Study Areas, 2000 Figure 9 Land-use Characteristics of the Two Study Areas, 2000. Data Source: LotInfo, SpaceTrack, Inc. The variability of the quantitative and the qualitative results suggests a number of potential limitations and shortcomings of our analyses. These limitations are discussed in detail below.

Limitations/future steps
As noted earlier in this paper, there are many pitfalls and problems in developing a meaningful park accessibility measure, and our analyses have reinforced the need for a more comprehensive approach. A number of additional variables might be included when measuring park access, in order to potentially establish more definitive results. In addition, our analysis focused on park access in New York City, which may or may not conform to the realities of other geographies.

Proximity analysis based on "Walkability" distances
Access based on proximity or distance often does not take into account the actual street network, as noted earlier, and there may be a major highway or other barrier between the residents and the park. This was shown in our qualitative analysis of Highland Park, which is essentially cut off from the residential neighborhood on the northern side by large stretches of cemeteries and highways. Utilizing a network analysis may prove to be more realistic than the kernel estimation that we used, that quantified park access as a function of density of park acres and/or physical activities sites.

New York City
Actual points of entry to the parks A measure of access also needs to consider actual points of entry to the park. For some parks, there are entry points that may be at a far remove from the residential neighborhoods, even though the park may border the neighborhood. This can also be addressed using network analysis provided that the entry points are known and mapped.

Perceptual access
Most accessibility measures do not take into account perceptual access. For example, racial/ethnic minority residents might not feel welcome in a park or recreational facility used predominantly by non-Hispanic white individuals. Similarly, female park users might not feel welcome in male-dominated physical activity sites such as basketball courts.
Perceptual access can also be based on park cleanliness or perceived or actual crime within or near the park. A park may be in close proximity but unused due to the bad conditions within the park. These "incivilities," such as graffiti, broken glass, liter, or evidence of drug or alcohol use, or the presence of violent crime could be important factors in making the park unattractive for use. While it is difficult to include perceptual access into a measure or index, if data on park maintenance and crime rates are available, they could be included in an analysis. Additionally, other more qualitative methods, such as interviews and surveys of local residents, as well as cognitive (mental) mapping and participatory GIS, can be used to discern attitudes and perceptions about access to parks and physical activity sites.

Park characteristics
Most measures of accessibility do not consider park characteristics, either, such as types and quantities of activities available, or park size. A tiny vest-pocket park will not have as much to offer in the way of physical activity potential as a large park. Although our study did incorporate park acres and number of activity sites, it could be improved by looking at variation of the types of physical activity sites, (e.g., does the park contain only basketball courts, or are there tennis, basketball, and a variety of other types of sites within a given park?). Presumably, a park having a greater variety of types of physical activity sites would make the park more of a draw to residents of different ages, genders, and physical fitness status, and therefore that park would merit a higher rating.
Another park characteristic that may be taken into account is the requirement of permits in some physical activity sites. For instance, permits are required to use the tennis courts in all parks. Since these permits have fees, access is limited based on financial ability.

Other variables to be considered
Resources available in parks and physical activity sites tend to be team sports-related, making it is less likely that older adults make use of these facilities. Therefore, the results of using physical activity sites as an important metric of accessibility may be misleading and skewed toward younger populations.
Socio-demographic Characteristics of the Two Study Areas, 2000  Additionally, people living in suburban-like areas within the city may have access to private open space, like backyards, usually available in single-family home neighborhoods, but not in higher-density, inner-city communities. Therefore proximity to public parks may be less important in those suburban-type areas, making any direct comparison of park and physical activity site accessibility between various types of neighborhoods and populations inaccurate. Public parks may serve a more critical function and there may be a higher need for public open space in less affluent neighborhoods, so statistical measures of equity regarding park access may not tell the whole story.
A valuable data source that was not explored in our qualitative analysis was comprehensive interviews with residents of the study areas to better understand actual and perceptual park accessibility. This could potentially provide important information necessary to address many of the limitations mentioned above.

Census data
A major limitation of population studies such as this one is the necessarily heavy reliance on data from the census. While census data is the most complete and current dataset we have at any given time, we need to acknowledge several underlying problems with its accuracy. One of the most serious sources of inaccuracy is the potential for undercounting populations in poor and immigrant communities. This has been an on-going drawback throughout the United States, but is even more pronounced in 21 st century New York City, where a very high proportion of the population is foreign-born, and less likely to be counted in the census, especially in the case of illegal immigrants who may be mistrustful of government and wish to remain unknown to them. The temporarily or permanently homeless also comprise a significant population that is traditionally undercounted, as well as populations who may rotate their domicile and are therefore often overlooked in the official count because they are not thought of as being a permanent part of the respondent's household.
Additionally, each decennial census defines racial and ethnic categories differently, making cross-census comparisons difficult for longitudinal studies. The guidelines and standards for racial and ethnic classification were revised by the Office of Management and Budget in 1999, and the 2000 census uses a markedly different classification system from the previous censuses, making the findings of longitudinal studies somewhat unreliable.

Policy implications
It is generally acknowledged that access to parks and physical activity sites has beneficial health ramifications, so a better understanding of which populations have good access to these areas will assist in identifying and targeting those areas that do not, and the potential for more fully explaining disparities in health outcomes. It is important to recognize the environmental justice implications of park and physical activity site location and spatial distribution, since ethnic and racial minorities and poor people tend to suffer disproportionately from diseases which are often preventable by proper exercise.
While we did not find an overall environmental justice impact for New York City as a whole with regard to park access and socio-demographic indicators, we know that there are many sections of the city with poor access to parks, and therefore this needs to be examined on a very local level rather than globally.
The level of need also has to be taken into account because even if parks were distributed evenly throughout the city, some neighborhoods warrant having additional resources. This may be due to the fact that these neighborhoods are more densely settled than other more suburban-like parts of the city, and their populations do not likely have additional open space resources such as backyards or options to leave the city for recreational opportunities. These are the very populations for whom parks assume an even more critical function than typically provided, and the parks and recreational facilities in these areas perhaps deserve extra resources and funding commitments in order to provide the equivalent level of support.
Physical, cultural, and perceptual barriers should be taken into account also when measuring access to parks. Even though distances may appear short, true access cannot be gauged through Euclidean measures, and much more research has to be done on what constitutes true access and equity of resources.

Conclusion
The combination of quantitative and the qualitative analyses revealed trends that may not have been otherwise detectable. While the OLS (global) regression showed a weak relationship between SES characteristics and park accessibility, the geographically weighted regression (local) found "unpatterned inequality." The qualitative analysis did not reveal anything that would refute the statistical findings of the GWR analysis, as both neighborhoods were confirmed to be different from one another in terms of SES characteristics, although the park conditions and useable park area were comparable. The qualitative analysis did, however, suggest that an approach which considers physical barriers and some of the other variables listed in the limitation section would improve the model and better reflect reality. The qualitative analysis also showed that although the demographics around the study areas were similar at the times of the parks' construction, they have changed considerably since then, allowing for the possibility of environmental justice impacts. These environmental justice impacts may introduce disparities by influencing health outcomes and behaviors.
The complexity of the issues around racial and ethnic disparities in park access has been demonstrated further by this study. Looking at one factor at a time is likely to result in misleading findings. Therefore, a more complex model that accounts for as many different types of variables as possible (park size, access points, barriers, network distance, perception of safety, crime rates, park maintenance, availability and variation of physical activity sites) will be needed to develop a more accurate measurement of park accessibility, particularly as to how it might mediate environmental justice and mitigate negative health outcomes.
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