Spatial Stats

A statistical measure of the linear relationship between two variables. Covariance measures the degree to which two variables move together relative to their individual variabilities.
The frequency or amount at which a thing or things occur within a given domain.
A graph showing the distribution of values in a set of data. Individual values are displayed along a horizontal axis, and the frequency of their occurrence is displayed along a vertical axis.
The estimation of surface values at unsampled points based on known surface values of surrounding points. Interpolation can be used to estimate elevation, rainfall, temperature, chemical dispersion, or other spatially based phenomena.

A property of a natural process or data where spatial dependence (autocorrelation) changes only with the distance between two locations—direction is unimportant.

Anisotropy occurs where spatial dependence (autocorrelation) changes with both the distance and the direction between two locations.

The average for a set of values, computed as the sum of all values divided by the number of values in the set.
Mean Center
The location of a single x,y coordinate value that represents the average x-coordinate value and the average y-coordinate value of all features in a study area.
The middle value of a set of values when they are ordered by rank. When there are two middle values (if the set has an even number of elements), the median is the mean of these two values.
Normal Distribution
A frequency distribution of a dataset in which the distribution of values can be graphically represented as a symmetrical bell curve. Normal distributions are typically characterized by a clustering of values near the mean, with few values departing radically from the mean. There are as many values on the left side of the curve as on the right, so the mean and median values for the distribution are the same.
An unusual or extreme data value in a dataset. In data analysis, outliers can potentially have a strong effect on results and must be analyzed carefully to determine if they represent valid or erroneous data.

A mathematical function that is the sum of at least two terms and has the form:


where n is a non-negative integer and where each value {an, …, a0} is a constant.

Each component of the polynomial equation is referred to as a term. The order of the polynomial refers to the exponent, or degree, of the leading term.

QQ Plot
A scatter plot in which the quantiles of two distributions are plotted against each other. The most common type of QQ plot is the normal QQ plot.
A function of the distance separating two locations that is used to quantify dependence. It is calculated as half of the squared difference between two data values at two locations. The semivariogram generally increases with distance before becoming flat and is described by nugget, sill, and range parameters. If the data is stationary, then the semivariogram represents the spatial autocorrelation structure of the data.
Spatial Autocorrelation
A measure of the degree to which data values depend on their spatial locations.
Spatial Stats
The field of study concerning statistical methods that use space and spatial relationships (such as distance and/or other spatial characteristics of data) directly in their mathematical computations. Spatial statistics are used for a variety of different types of analyses, including point pattern analysis, surface modeling and prediction, spatial regression, and more.
Standard Deviation
A statistical measure of the spread of values from their mean, calculated as the square root of the sum of the squared deviations from the mean value, divided by the number of elements minus one. The standard deviation for a distribution is the square root of the variance.
In geostatistics, a property of a spatial process in which the covariance between the values of any two points depends only on the distance between them.
Thiessen polygon
Polygons generated from a set of sample points. Each Thiessen polygon defines an area of influence around its sample point so that any location inside the polygon is closer to that point than to any of the other sample points.
In a spatial model, non-random variation in the value of a variable that can be described by a mathematical function such as a polynomial.
Voronoi Map
A partition of space into areas, or polygons, that surround a set of geometric objects (usually points) such that all locations within a polygon are closer to the object it surrounds than to any other object in the set. The value of each polygon is determined by the values of the objects in neighboring polygons, so a Voronoi map can be used to investigate local variation. Voronoi maps are also often used to delineate areas of influence around geographic features. Voronoi maps are named for the Ukrainian mathematician Georgy Fedoseevich Voronoi (1868-1908).
Ratio Scale Data
A constant interval and true zero point
Interval Scale Data
A constant iinterval but with NO true zero point
Ordinal Scale Data
No constant interval
Nominal Scale Data
Quality rather than quantity is measured