Point Pattern Analysis: UFO Sightings in Arizona: Evidence of Clustering Across Multiple Scales

by Heather Robbins

Problem Statement:

Unidentified Flying Objects (UFO), or more recently, Unidentified Anomalous Phenomena (UAP) sightings are often treated as isolated incidents, but their spatial distribution may reveal patterns related to population density, air traffic corridors, or even psychological and cultural factors. Point pattern analysis examines the distribution any given phenomena to determine whether features or events are clustered in specific areas, randomly distributed, or dispersed. Understanding the spatial pattern of UFO/UAP sightings could offer insights into social, environmental, or observational factors that influence where sightings occur.

The null hypothesis suggests that reported sightings will exhibit complete spatial randomness.

Question: Are the historical reports of UFO/UAP sightings clustered in metro areas, dispersed throughout Arizona, or completely random?

Study Area

The phenomenon of UFO/UAP sightings is a global one, and Arizona ranks fourth in UFO reports within the United States (Sepulveda, 2024). The state’s varied landscape—from booming metro centers like Phoenix to vast desert regions—makes it an interesting case for examining patterns in a spatial analysis context. For this study, the entire state of Arizona was used as the study area.

Data

The National UFO Reporting Center (NUFORC) was established in 1974 to create a resource hub for anyone to report sightings anonymously. The organization is a non-profit and supports interested parties by providing a summarized version of the data that has been collected. The reported sightings data is available in a tabular csv file with latitude and longitude for each event.

Methods

After reviewing the table of recorded sightings, any records with null values of latitude and/or longitude are removed. The table is converted to points within ArcGIS Pro 3.4 using the Display XY Table as Points tool. Several records are found to have identical latitude and longitude coordinates, those are removed using the Delete Identical tool, leaving 326 points (UFO reported sightings) remaining.

Projection

The states shapefile and sighting points are projected to the UTM Zone 12N which allows for preserving shape and distance across the state making it an ideal choice for spatial statistics analysis. The extent of the analysis is the extent of the state of Arizona, the state is selected manually and exported to a new shapefile and the points are clipped to the new shapefile using the Clip tool.

Quadrat Count Method

The quadrat count method involves overlaying a grid of equal-sized cells (quadrats) over a defined study area to measure point density within each cell. Square grid cells are commonly used, both shape and size should be chosen based on the spatial extent of the study area. In this study, a fishnet grid of squares was created using the Create Fishnet tool in ArcGIS Pro, with 10 columns and 15 rows to reflect Arizona’s taller-than-wide geographic shape. The Summarize Within tool was used to count the points within each grid cell, and the Frequency tool provided a summarized version of the data, i.e. how many quadrats contain how many points. Then, the variance and mean of these counts are used to calculate the Variance Mean Ratio (VMR). A VMR close to 1 suggests complete spatial randomness (CSR), values greater than 1 indicate clustering, and values less than 1 suggest dispersion.

Average Nearest Neighbor Method

The Average Nearest Neighbor method measures the average distance between each point and its closest neighboring point. This observed average distance is then compared to the expected average distance in a hypothetical random distribution of the same number of points over the same area. The method is sensitive to the size and shape of the analysis area, which is typically defined as a minimum bounding rectangle around all input points. A Nearest Neighbor Index (NNI) is calculated to indicate whether points are clustered (NNI is less than 1), randomly distributed (NNI is close to or equal to 1), or dispersed (NNI is greater than 1). ArcGIS Pro also provides a z-score and p-value to assess the statistical significance of the result.

The Average Nearest Neighbor tool was used with the Arizona UFO report points as the input feature in ArcGIS Pro, and a report is generated to provide details on the results.

Ripley K Method

The Ripley K method measures spatial patterns and randomness for point data across a range of distance values. It evaluates how many other points fall within increasing distances from each point, allowing the detection of clustering or dispersion at multiple spatial scales. Because the study area is large, distance increments are used to analyze patterns from local to regional scales. Unlike single-scale methods such as Quadrat Count or Average Nearest Neighbor, Ripley’s K produces a line chart showing the observed distribution compared to what would be expected under complete spatial randomness, helping to visualize whether clustering or dispersion occurs at different distances.

Assumptions

Each method and parameters were considered in the scope of the scale of a large state.

For the Quadrat Count method, the Create Fishnet tool was used to generate a grid of equal-sized square cells across the study area. Arizona’s geography—being taller than it is wide—guided the decision to use 15 rows and 10 columns to maintain approximately square cells. Although 150 grid cells may seem like a large number, it is appropriate given the scale of the study area.

For the Ripley’s K method (Multi-Distance Spatial Clustering Analysis), parameters were selected based on the extent of Arizona. A maximum distance of 200,000 meters was used, with increments of 20,000 meters and 10 distance bands to capture patterns across multiple scales. The number of permutations was set to 999 to produce a 99.9% confidence envelope. A user-defined study area (the projected Arizona boundary) was provided to ensure accurate spatial extent.

Results

Quadrat Method

With 150 quadrats and 326 points in the study area, Complete Spatial Randomness (CSR) would result in approximately 2.17 points per cell. The observed variance is 15.499, yielding a Variance Mean Ratio (VMR) of 7.13. Since the VMR is significantly greater than 1—the expected value under randomness—this indicates strong clustering in the distribution of sightings. A visual inspection of the heat map supports this, showing prominent clusters around the Phoenix and Tucson metropolitan areas.

UFOQuadratTable

Average Nearest Neighbor

The summary report provided by the Average Nearest Neighbor tool presents a Nearest Neighbor Ratio (NNR) of 0.631 and suggest statistically significant clustering. The calculated observed average distance between points is about 10,096 meters, while 16,006 meters is the expected mean distance to reflect spatial randomness. With a p-value of 0.00 and z-score -12.75, the ANN method reinforces that UFO sightings in Arizona are clustered rather than randomly or evenly dispersed.

Ripley K

The Ripley’s K analysis was conducted using 10,000 and 20,000 meter increments to explore clustering at different spatial scales. In both cases, the observed K values consistently exceeded the upper confidence envelope, indicating statistically significant clustering across all distance bands. The similarity between the results at different increments suggests that the pattern of clustering is stable and occurs at both local and regional scales across Arizona.

Conclusion

Three point pattern analysis methods were used to test the spatial distribution of 326 UFO sightings across Arizona, and all indicated statistically significant clustering. Visual patterns emerged around major cities like Phoenix and Tucson, as well as along major highways. Although each method measures spatial concentration differently, they consistently supported the same conclusion.

The Quadrat Count quantifies density using a uniform grid; Average Nearest Neighbor compares observed distances to those expected under randomness; and Ripley’s K evaluates clustering at multiple spatial scales. Together, they provide strong, complementary evidence that UFO sightings are clustered rather than randomly or evenly dispersed. This allows for confidently rejecting the null hypothesis of complete spatial randomness.

However, the Quadrat Count method is sensitive to the shape and size of grid cells—the size and shape selection may have influenced the high VMR, and future studies could explore the effect of alternative grid configurations. Another limitation lies in the dataset itself: it's unclear whether the coordinates represent the actual sighting location or where it was reported. Additionally, several sightings shared identical coordinates, suggesting either duplicated reports or highly localized clusters.

Future research could expand this analysis using kernel density estimation, regression models with variables such as population density or light pollution, or pair correlation functions to better understand clustering dynamics across spatial scales.

Average Nearest Neighbor (Spatial Statistics)—ArCGIS Pro | Documentation. (n.d.). https://pro.arcgis.com/en/pro-app/latest/tool-reference/spatial-statistics/average-nearest-neighbor.htm

Gimond, M. (n.d.). Chapter 11 Point Pattern Analysis | Intro to GIS and Spatial Analysis. https://mgimond.github.io/Spatial/chp11_0.html

Multi-Distance Spatial Cluster Analysis (Ripley’s K Function) (Spatial Statistics)—ArCGIS Pro | Documentation. (n.d.). https://pro.arcgis.com/en/pro-app/latest/tool-reference/spatial-statistics/multi-distance-spatial-cluster-analysis.htm

National UFO Reporting Center (NUFORC), & Axel, S. A. (2014). UFO sightings [Dataset; CSV]. https://github.com/planetsig/ufo-reports

O’Sullivan, D., & Unwin, D. J. (2010). Geographic Information Analysis. https://doi.org/10.1002/9780470549094

Sepulveda, L. D. (2024, February 22). Arizona has 4th most UFO sightings in the US. See the rankings. The Arizona Republic. https://www.azcentral.com/story/news/local/arizona/2024/02/17/arizona-ufo-sightings/72612486007/

U.S. Census Bureau. (2018). Cartographic boundary files [Dataset; Shapefile]. In Census geographies. https://www.census.gov/geographies/mapping-files/time-series/geo/carto-boundary-file.html

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