Absolute space. Space considered as a container which may or may not be filled with objects, associated with Euclidean geometry where points are related by fixed distances or metrics between them.
Activity spaces. The local areas within which people move or travel in the course of their daily activities.
Central place theory. Based on ideas of city and town spacing by Walter Christaller, the theory deals with hierarchies of goods and services, threshold populations required to market these goods and services, and ranges or territories over which the goods and services are sold. As used here, the theory applies to the distribution of health manpower or facilities within an urban area. Large hospitals or specialist physicians are higher order functions and thus require larger thresholds and ranges.
Cluster analysis. A method of grouping spatial units or variables measured over spatial units by bringing together the two 'closest' units or variables, the next closest units or variables and so on until all units or variables are in one cluster. The number of clusters finally chosen for further analysis is based on maximizing between cluster differences and minimizing within cluster differences.
Cluster dendogram. The tree-like diagram output from a cluster analysis that indicates how the spatial units or variables in the analysis are related to each other in clusters.
Coefficient of areal correspondence. This measure, defined as the ratio of the intersection of two phenomena to the union of the same two phenomena can be used to determine the degree of correspondence between disease maps and maps of possible factors related to diseases.
Connectivity. The connectivity of a point or vertex of a graph or network is the degree to which the point is linked to other points. It can be measured in several ways.
Contagious diffusion. Diffusion of an idea, innovation or disease based on person-to-person contact within a local population, depending to a great extent on the distances among people.
Correlation coefficient. A measure of the strength of the relationship between two interval data variables.
Difference maps. A method of analyzing the pattern of differences between two maps which are based on the same areal units by comparing the number of units where they are the same or different with a theoretical, random distribution.
Directed graph. A graph or network in which relations among points or vertices are either unequal and reciprocal or non-reciprocal.
Dispersion (of a graph). A measure of the total distance among nodes or vertices in a graph or network, the sum of the rows of the matrix of shortest paths among points.
Eccentricity. A measure of the shape of an ellipse, defined as the ratio of the distance between the foci and the length of the major axis. Smaller values indicate greater ellipse elongation or 'out-of-roundness.'
Ecological fallacy. Most often referred to as a logical flaw which results from making a causal inference about an individual phenomenon or process on the basis of observations on groups.
Flow analysis. The analysis of Rows (e.g. patients) among various nodes or vertices (e.g. homes and hospitals) of a network.
Fourier series. Expressions used to fit trend surfaces to spatially distributed variables if the variables are thought to behave in an oscillatory manner across space.
Free sampling. When calculating Moran's join count measures, the assumption that the probabilities of obtaining a 'black' or 'white' area are known in advance.
Graph theory. A theoretical framework for examining the relationships or links (represented by lines) that exist among places, towns, regions and so on (represented by points, nodes or vertices).
Hierarchical clustering. A method which emphasizes how adjacent spatial units with high or low disease rates might cluster by ranking the units by disease rate and then examining how probable cluster adjacencies would be compared to random conditions and marking off successive clusters wherever low probability values occur.
Hierarchical diffusion. A diffusion process in which an idea, innovation or disease spreads by moving from larger to smaller places, often with little regard to the distance between places.
Isoline. A line which connects points of equal value. For example, isotherms connect points of equal temperature and isomorbs connect points with equal disease rates.
Latency. The period between the onset of any given cause and disease detection.
Linear transect. A line drawn across an area along which samples for data analysis are chosen.
Location quotients. A method of spatial standardization which can be used by medical geographers to map or health care resources. For each spatial unit, disease incidence or prevalence or resources per population rates for that spatial unit are divided by total disease or resource per total population rates.
Lorenz curves As used in medical geography, a graphical representation of spatial inequality in health care resources which plots cumulative resources like medical manpower against cumulative populations for spatial units.
Mean center. The mean center of a set of points in space is a unique point whose x- and y-co-ordinates are the means of the x- and y-co-ordinates of the individual points
Metric properties. Those properties of a relation defined on a space that require a fixed distance among points in the space. Non-metric properties do not have this requirement.
Modifiable units. The idea that if the boundaries of the spatial units one deals with are changed, the results of spatial analysis will differ also.
Monte Carlo methods. Techniques for estimating the solution of a numerical or mathematical problem by means of an artificial sampling experiment. In the Monte Carlo simulations mentioned in this paper, a computer is employed to establish a theoretical distribution of disease events against which an observed distribution can be measured.
Multidimensional scaling. A technique that takes a matrix of dissimilarities or 'distances' (metric and non-metric) among a set of objects and creates a spatial configuration of these objects such that the distances between pairs of objects match as closely as possible the dissimilarities. In using the technique, one strives to have as few dimensions as possible in the configuration; two are the most ideal for mapping the pattern.
Nearest neighbor analysis. A technique of determining whether a set of points in space is distributed in a regular, random or clustered pattern by comparing the mean distance of points to their nearest neighbors to the mean distance expected if the pattern were random.
Nodality. The nodality of a point or vertex of a graph or network is the number of network paths or links incident at that point.
Pathogenesis. Cellular and other events and reactions and other pathologic mechanisms occurring in the development of disease.
Poisson distribution or process. A spatial point process in which each quadrat (grid cell area) in an area has an equal and independent chance of containing a point.
Population potential. The potential at any point on a population potential surface is the sum of the reciprocals of distance (or some power of distance) of every person in the population from the point. It is population density weighted by the reciprocal of distance and is analogous to magnetic or electric fields.
Power series polynomials. Polynomial expressions of linear, quadratic, cubic or higher orders that are used in the fitting of trend surfaces to spatially distributed variables.
Quadrat analysis. A method of simulating whether a pattern of points is clustered, random or regular by comparing an observed frequency distribution of points in grid cells with an expected (Poisson) frequency distribution if the distribution were random.
Random walk. A method of simulating random movements by beginning at a point and proceeding to a succession of new points by choosing angles at random and moving a standard distance in the directions indicated by these angles.
Relative risk (ratio). The ratio of the incidence of a disease among those exposed to the the incidence among those not exposed.
Relative space. Space as a relation defined on a set of objects, without the requirement of fixed distances or metrics among points in the space.
Residuals from trend surface models. The differences between observed values at points and values predicted by a trend model, an indication of over- or under-prediction at various points.
Spatial autocorrelation. The degree of relatedness of a set of spatially located data, the extent to which adjoining or neighboring spatial units influence particular variables recorded on those units.
Spatial correlogram. A graph which records the degree of spatial autocorrelation among a set of areal units at different spatial lags where the first lag involves adjoining or neighboring units, the second lag neighbors of neighbors, and so on.
Standard deviational ellipse. An ellipse whose major and minor axes are drawn to represent the magnitude of the minimum and maximum dispersion of a set of points from their mean center.
Standard distance. A measure of the dispersion of a set of points in space, analogous to the standard deviation of a set of data.
Standardized mortality ratio. The number of deaths, either total or cause-specific in a given sub-population or spatial unit expressed as a percentage of the number of deaths that would have been expected in that sub-population or unit if the age- and-sex-specific rates in the general population had obtained.
Trend surface analysis. The decomposition of each observation of a spatially distributed variable into components associated with regional and local effects. Fitting a function which relates values of points in space to the point co-oordinates to create a trend surface, and examination of the residuals.
Variance/mean ratio test. A Student's t-test which compares the ratio of the variance and mean of a histogram of quadrat (grid cell) counts of a set of points in space to the expected ratio of 1 if the points were randomly distributed.
Velocity field. A graphical representation of journey times between pairs of points in an urban area.