Statistical Analysis

This section covers statistical functions for analyzing spatial patterns and distributions in geographic datasets. These functions help determine point clustering, calculate representative centers, and visualize distribution characteristics.

For geometric operations like buffers and intersections, see Geometric Operations. For clustering algorithms, see Clustering.

Overview

Turf.js provides several statistical analysis functions that examine the spatial characteristics of point datasets:

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Statistical Analysis Module Architecture

Center Calculations

The centerMedian() function calculates the geometric median - the point that minimizes the sum of distances to all other points in the dataset.

Function	Input	Output	Purpose
`centerMedian`	`FeatureCollection<any>`	`Feature<Point>`	Finds point requiring least total travel

Center Median Implementation

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Center Median Algorithm Flow

The function uses the Weiszfeld algorithm to iteratively find the spatial median:

Extracts centroids from input features using @turf/centroid
Calculates distances using @turf/distance
Supports weighted calculations via feature properties
Iterates until tolerance threshold is met (default: 0.001)

Spatial Distribution Analysis

The nearestNeighborAnalysis() function determines whether points are clustered, dispersed, or randomly distributed by analyzing distances between nearest neighbors.

Function Interface

nearestNeighborAnalysis(
  dataset: FeatureCollection<any>,
  options?: {
    studyArea?: Feature<Polygon>;
    units?: Units & AreaUnits;
    properties?: GeoJsonProperties;
  }
): NearestNeighborStudyArea

Analysis Process

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Nearest Neighbor Analysis Process

The analysis follows these steps:

Uses @turf/centroid to extract centroids from input features
Finds nearest neighbors using @turf/nearest-point
Calculates observed mean distance using @turf/distance
Determines population density from study area using @turf/area
Computes expected distance and z-score for statistical inference

Directional Distribution Analysis

The standardDeviationalEllipse() function creates an elliptical polygon showing the directional distribution of points, containing approximately one standard deviation (70%) of the dataset.

Function Signature and Dependencies

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Standard Deviational Ellipse Dependencies

Ellipse Properties

The returned ellipse contains statistical metadata in its properties:

meanCenterCoordinates: Centroid of the distribution
semiMajorAxis: Length of major axis (standard deviation)
semiMinorAxis: Length of minor axis (standard deviation)
angle: Rotation angle in degrees
numberOfFeatures: Count of input points
percentageWithinEllipse: Actual percentage contained

Implementation Flow

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Standard Deviational Ellipse Algorithm