So, what’s the “point” to all of this?….

Lecture 5

> Lecture 1: Introduction > Lecture 2: Geographical Data & Measurement  Lecture 3: Introduction to Spatial Analysis  Lecture 4: Spatial Data Our Next Lecture and Topic is: Lecture 5: Point Pattern Analysis Lectures and Topics covered to this point

With the beginning of Lecture 5, we will look into the various application tools used in Spatial Analysis: Point Pattern Analysis Surface Analysis Grid Analysis Network Analysis Decision Making: Locational Analysis

With the beginning of Lecture 5, we will look into the various application tools used in Spatial Analysis: Point Pattern Analysis Surface Analysis Grid Analysis Network Analysis Decision Making: Locational Analysis

Spatial Analysis Tool: Point Pattern Analysis Introduction What is Point Pattern Analysis?

Spatial Analysis Application: Point Pattern Analysis Introduction A point pattern is defined as the spatial pattern of the distribution of a set of point features. In point pattern analysis, spatial properties of the entire body of points are studied rather than the individual entities. Because points are zero-dimensional features, the only valid measures of point distributions are the number of occurrences in the pattern and respective geographic locations.

Spatial Analysis Application: Point Pattern Analysis Descriptive Statistics of Point Features The distribution of point features can be described by frequency: density, geometric center, spatial dispersion and spatial arrangement. With the exception of spatial arrangement, evaluation of the spatial properties of point features can be based on basic descriptive statistics. Descriptive Statistics of Point Features

Spatial Analysis Application: Point Pattern Analysis Descriptive Statistics of Point Features Frequency is the number of point features occurring on a map. It is always the first measurement of a point distribution whenever two distributions of point features are compared, or when the same distribution of a point pattern is evaluated at different times in order to study the pattern’s developmental process.

Spatial Analysis Application: Point Pattern Analysis Descriptive Statistics of Point Features The next page illustrates four point patterns that differ in dispersion characteristics

Spatial Analysis Application: Point Pattern Analysis Descriptive Statistics of Point Features y x

y x

y x

y x This pattern depicts a large standard deviation along the x axis and a lower level of dispersion along the y axis

Spatial Analysis Application: Point Pattern Analysis Descriptive Statistics of Point Features y x This pattern depicts a large standard deviation along the x axis and a lower level of dispersion along the y axis Consequently, the distribution is elongated horizontally

Spatial Analysis Application: Point Pattern Analysis Descriptive Statistics of Point Features y x

y x

y x

y x When the dispersion is small along the x axis and large along the y axis, the distribution becomes elongated vertically.

Spatial Analysis Application: Point Pattern Analysis Descriptive Statistics of Point Features y x

y x The trend line is “positive” and “significant”

Spatial Analysis Application: Point Pattern Analysis Descriptive Statistics of Point Features y x When both x and y show a similar level of variance, the correlation between x coordinates and y coordinates can be examined to determine the pattern

Spatial Analysis Application: Point Pattern Analysis Descriptive Statistics of Point Features y x When both x and y show a similar level of variance, the correlation between x coordinates and y coordinates can be examined to determine the pattern In this example the correlation is positive and significant, then the point features are distributed in an elongated, sloping pattern.

Spatial Analysis Application: Point Pattern Analysis Descriptive Statistics of Point Features y x When both x and y show a similar level of variance, the correlation between x coordinates and y coordinates can be examined to determine the pattern In this example the correlation is positive and significant, then the point features are distributed in an elongated, sloping pattern.

Spatial Analysis Application: Point Pattern Analysis Descriptive Statistics of Point Features y x

y x Any discernible pattern to these points?

Spatial Analysis Application: Point Pattern Analysis Descriptive Statistics of Point Features y x This example illustrates a random pattern where the correlation is insignificant

Spatial Analysis Application: Point Pattern Analysis Descriptive Statistics of Point Features y x This example illustrates a random pattern where the correlation is insignificant No significant differences in the standard deviation

Spatial Analysis Application: Point Pattern Analysis Spatial Arrangement of Point Features The spatial arrangement of point features is an important characteristic of a spatial pattern, because the location of point features and the relationships among them have a significant effect on the underlying process generating a distribution. The three basic types of point patterns are: clustered, scattered and random.

Spatial Analysis Application: Point Pattern Analysis Spatial Arrangement of Point Features Clustered : Point features are concentrated on one or a few relatively small areas and form groups.

Spatial Analysis Application: Point Pattern Analysis Spatial Arrangement of Point Features Scattered/Uniform : Point features are characterized by a regularly spaced distribution with a relatively large inter-point distance.

Spatial Analysis Application: Point Pattern Analysis Spatial Arrangement of Point Features Random : Neither the clustered nor the scattered pattern is in evidence.

Spatial Analysis Application: Point Pattern Analysis Point Features Analysis: Nearest Neighbor Nearest Neighbor Analysis The nearest neighbor analysis is a common procedure for determining the spatial arrangement of a pattern of points within a study area. The distance of each point to its nearest neighbor is measured and the average nearest neighbor distance for all points is determined. The spacing within a point pattern can be analyzed by comparing the observed average distance to some expected average distance, such as that for a random or Poisson distribution.

Spatial Analysis Application: Point Pattern Analysis Point Features Analysis: Nearest Neighbor Nearest Neighbor Analysis The nearest neighbor technique was originally developed by biologists who were interested in studying the the spacing of plant species within a region. They measured the distance separating each plant from its nearest neighbor of the same species and determined whether this arrangement was organized in some manner or was the result of a random process. Geographers have applied this technique in numerous research problems, including the study locational problems such as settlements in central place theory and economic functions within a urban region.

Spatial Analysis Application: Point Pattern Analysis Point Features Analysis: Quadrat Quadrat Analysis An alternate methodology for studying the spatial arrangement of point locations is quadrat analysis. Basically, quadrat analysis requires overlaying a grid onto a map of point features in order to examine the distribution based on frequency of occurrence rather than the separation of distance.

Spatial Analysis Application: Point Pattern Analysis Point Features Analysis: Quadrat Random Points

Spatial Analysis Application: Point Pattern Analysis Point Features Analysis: Quadrat Grid: Each cell of the grid is called a quadrat

Spatial Analysis Application: Point Pattern Analysis Point Features Analysis: Quadrat Overlaying a grid over the random points

Spatial Analysis Application: Point Pattern Analysis Point Features Analysis: Quadrat Frequency of points within the boundaries of each quadrat is counted

Spatial Analysis Application: Point Pattern Analysis Point Features Analysis: Quadrat Frequency of points within the boundaries of each quadrat is counted

Spatial Analysis Application: Point Pattern Analysis Point Features Analysis: Quadrat Frequency of points within the boundaries of each quadrat is counted 1

Spatial Analysis Application: Point Pattern Analysis Point Features Analysis: Quadrat However, there is a simple rule to our game: each quadrat must contain at least 5 point features for it to have any significance. 1

Spatial Analysis Application: Point Pattern Analysis Point Features Analysis: Quadrat And as seen in our grid system, we do not have anything close to having 5 points to a grid. 1

Spatial Analysis Application: Point Pattern Analysis Point Features Analysis: Quadrat And as seen in our grid system, we do not have anything close to having 5 points to a grid. 1 What do we do, now?

Spatial Analysis Application: Point Pattern Analysis Point Features Analysis: Quadrat The answer is that we create new classes to ensure that there are at least 5 points to each quadrat

Spatial Analysis Application: Point Pattern Analysis Point Features Analysis: Quadrat The answer is that we create new classes to ensure that there are at least 5 points to each quadrat