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Determining the Probability that Data Distribution is Not Random
Problems:
The Fort Worth Fire Department is planning safety training for its personnel. One of the key goals is to help first responders to recognize real emergencies and avoid false alarms. To conduct this training, the department needs to determine if false alarms are exhibiting any clustering, the distance at which they cluster and if high priority calls are falling into clusters.
The Oleander Library is trying to determine if there is residence clustering of their patrons by neighborhood.
Analysis Procedures
The Fort Worth Fire Department supplied data of monthly call reports for January and February of 2015 in the Battalion 2 service area. This database provides the location of the call and the type of emergency. To solve the problems described above required several methods of analysis in ArcGIS Pro to determine the existence of clustering, the distance of occurrence and to what extent any clustering is based on the severity of the emergency. To determine the existence of clustering, I first ran the “Nearest Neighbor” tool and found at a 90% confidence level that there was some clustering going on in the data. Knowing that there was a strong likelihood of clustering, I ran the “General G” tool several times to determine the clustering distance of high priority calls. The results of the “General G” tool was confirmed when I ran the “Ripley’s K” function on this data.
For the Oleander Library data, “Moran’s I” function was used to autocorrelate the addresses of patrons to a spatially joined 300 ft. grid.
After examining the attributes of the Feb 2015 Incident data and noting the size of the area being analyzed in the Battalion 2 layer, I set a definition query on the data to only include incident types coded between 700 and 745. I then ran the “Nearest Neighbor” tool setting the area for the random data generation to the same size area as the Battalion 2 layer. This produced an observed mean distance of 995.29 ft. which equated to a Z-score of -1.698 or a 90% confidence level that some amount of clustering was occurring.
To refine this portion of the analysis further I used the “Getis-Ord General G” statistic to locate clustering of high priority calls. Before running this tool, I used the “Calculate Distance Band from Neighbor Count” tool to determine that the average distance between features and their 7 nearest neighbors was approximately 1,074 ft. Using this number as a guide to determine a range, the General G statistic was calculated six times starting with a fixed distance band of 700 ft. Each time the statistic was calculated, the fixed distance band was increased by 100 ft. while the input field remained set the attribute value for call priority. This yielded six different Z-scores that all fell within the 99% confidence level with the highest Z-score at 9.401 at a distance of 900 ft.
To verify the results that clustering of high priority calls was occurring at around 900 ft., I used “Ripley’s K”. This multi-distance statistic tool was set to a starting distance of 200 ft. with an increase of 100 ft. for each of 10 iterations. I also took advantage of another feature of this tool by having it compute a confidence envelope with 99 permutations. To find the distance of maximum clustering I then added a field to the resulting data table and a field calculation subtracting the high end of the confidence envelope from the observed “K” value which was then graphed. The resulting graph (as shown in Fig. 3 below) showed the point of highest clustering at 900 ft.
Spatial autocorrelation was completed on the Oleander Public Library Patron location data using the “Moran’s I” tool. I aggregated this data to a 300 ft. grid through a spatial join and then created a definition query to remove any grid squares with a value lower than one from the spatial autocorrelation. In the “Spatial Autocorrelation” tool I set the input field to “Count” and using the zone of indifference parameter started with a distance band of 2,800 ft. Z-scores were recorded and the process was repeated increasing the distance band by 200 ft. with each iteration until reaching the 3,800 ft. distance band. The results showed the most significant clustering at 3,400 ft with 99% confidence.
Results
Click images for a larger version
Fig. 1 - The analysis shows that there is a minimal amount of clustering of false alarms.
Fig. 2 - The clustering found of high priority calls with the Getis-Ord General G statistic.
Fig. 3 - Use of Ripley's-K statistic to confirm the findings of the Getis-Ord General G statistic.
Fig. 4 - Addresses of patrons aggregated to a 300 ft. grid for Spatial Autocorrelation showing large clusters of 3400 ft.
Application and Reflection
Problem description:
Venus flytraps are a carnivorous plant familiar to many people. Most people don't realize that they only grow in wetlands of southeastern North Carolina and extend into a small area across the border in South Carolina. The plant is listed as vulnerable to extinction because of it's limited range and poaching of the protected plant. Conservation not only include protection but also research to identify optimal growing conditions to support the natural population and identify areas where undiscovered clusters may exist or could be introduced.
Data needed:
Biologists with The North Carolina Natural Heritage program along with volunteer citizen scientists have collected extensive data on the species including location and soil conditions. This data is available from the program. These results along with wetland and soil data collected by the USGS would be used to visualize the data.
Analysis procedures:
Moran’s I spatial autocorrelation works best when the input field dataset has a variety of values. I would use Moran’s I function to examine an aggregated data set of flytrap population and ideally the nitrogen, phosphorus and potassium content of the soil they grow in to gain a better understanding of the natural conditions that increase their numbers. I would not use the Zone of Indifference conceptualization because we would be examining scattered isolated populations and the zone of indifference conceptualization treats every feature to be a neighbor of every other feature. In the Venus flytrap population data, there are variables that interfere with nutrient transport through soil (such as slope, roads, drainage, etc.) so not every specimen group is a neighbor of every other group. For this method, I would use the inverse distance conceptualization after calculating a distance band using the “Calculate Distance Band from Neighbor Count tool”. I would also be interested to use the Ripley’s K function on this data set to see how the values of soil nutrient level associated with the features are clustered after being compared to 999 random data sets. This would also serve as a method for checking the results from the Moran’s I function.
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