The Find Hot Spots tool will determine if there is any statistically significant clustering in the spatial pattern of your data.
- Are your points (crime incidents, trees, traffic accidents) really clustered? How can you be sure?
- Have you truly discovered a statistically significant hot spot (for spending, infant mortality, consistently high test scores) or would your map tell a different story if you changed the way it was symbolized?
Even random spatial patterns exhibit some degree of clustering. In addition, our eyes and brains naturally try to find patterns even when none exist. Consequently, it can be difficult to know if the patterns in your data are the result of real spatial processes at work or just the result of random chance. This is why researchers and analysts use statistical methods like Find Hot Spots (Getis-Ord Gi*) to quantify spatial patterns. When you do find statistically significant clustering in your data, you have valuable information. Knowing where and when clustering occurs can provide important clues about the processes promoting the patterns you're seeing. Knowing that residential burglaries, for example, are consistently higher in particular neighborhoods is vital information if you need to design effective prevention strategies, allocate scarce police resources, initiate neighborhood watch programs, authorize in-depth criminal investigations, or identify potential suspects.
1 Analyzing area features
Quite a lot of data is available for area features such as census tracts, counties, voter districts, hospital regions, parcels, park and recreation boundaries, watersheds, land cover classifications and climate zones. When your analysis layer contains area features, you will need to specify a numeric field that will be used to find clusters of high and low values. This field might represent the following:
- Counts (such as the number of households)
- Rates (such as the proportion of the population holding a college degree)
- Averages (such as the mean or median household income)
- Indices (such as a score indicating whether household spending on sporting goods is above or below the national average)
With the field you provide, the Find Hot Spots tool will create a map (the result layer) showing you areas with statistically significant clusters of high values (hot spots: red) and low values (cold spots: blue). This type of analysis can help you answer a variety of questions:
Which areas have the best or the worst access to services?
Based on the number of children and the number of pediatricians, for example, you can identify areas with good and poor accessibility to pediatrician services. This information may help direct incentive programs to recruit physicians with a pediatrician specialty to any poor accessibility areas you find. For this analysis you could create a variable reflecting the number of pediatricians per child. You would then run Find Hot Spots on these rates to locate statistically significant clustering of high rates (hot spots reflecting good accessibility) and of low rates (cold spots reflecting poor accessibility).
Where are particular types of events a larger than expected proportion of all events?
Suppose county fire fighters are concerned about a growing problem with cooking-related fires. You can help. First calculate the number of kitchen fires divided by the number of other residential fires for each neighborhood in the study area (census tracts, for example). Next run Find Hot Spots on these proportions to locate communities with higher than expected kitchen fire events (hot spots). The types of foods prepared along with their particular cooking practices may make some communities more prone to cooking fires than others. Advertisements or educational materials strategically placed in these high-risk areas may prevent future fires.
Where are affiliations strongest or weakest?
You may want to know which regions showed the strongest or weakest support for a particular political party, candidate, or ballot measure, for example. This information could be helpful in guiding campaign strategies for future elections. In the map below, red areas are statistically significant clusters where the percentage of Republican Party votes were much higher than the Democrat Party votes; the blue areas are statistically significant clusters of strong Democrat Party support. The map was created by subtracting the proportion of Democrat votes from the proportion of Republican votes and then running Find Hot spots on these differences.
2 Analyzing point features
A variety of data is available as point features. Examples of features most often represented as points include crime incidents, schools, hospitals, emergency call events, traffic accidents, water wells, trees, and boats. Sometimes you will be interested in analyzing data values (a field) associated with each point feature. In other cases, you will only be interested in evaluating the clustering of the points themselves. The decision to provide a field or not will depend on the question you are asking.
2.1 Finding clusters of high and low values associated with point features
You will want to provide an analysis field to answer questions like: Where do high and low values cluster? The field you select might represent:
- Counts (such as the number of traffic accidents at street intersections)
- Rates (such as city unemployment, where each city is represented as a point feature)
- Averages (such as the mean math test score among schools)
- Indices (such as a consumer satisfaction score for car dealerships across the county)
Knowing where the high and low values associated with point features cluster spatially can help you answer important questions. For example:
Where are resources sufficient and where are they insufficient?
For disaster management, for example, understanding trends in hospital bed availability can help you prepare and plan for emergencies. If your point features represent hospital facilities, calculating the average number of available beds per day, week, month, or season, and running Find Hot Spots on these averages, will show you hospital regions that are consistently full as well as regions that are consistently available, and may also reveal important temporal trends.
Another example might analyze where school teachers are most needed. If your point features are schools and each point is associated with an average student-to-teacher ratio, Find Hot Spots applied to these ratios will show the school districts deficient in teachers and/or classroom facilities.
Which areas get the best and worst exposure?
If, for example, retail establishments in a shopping mall are represented as point features with an analysis field reflecting shopper traffic, Find Hot Spots allows you to confidently determine which areas of the mall get the most and the least exposure to shoppers.
2.2 Finding clusters of high and low point counts
For some point data, typically when each point represents an event, incident, or indication of presence/absence, there won't be an obvious analysis field to use. In these cases, you just want to know where clustering is unusually (statistically significant) intense or sparse. For this analysis, area features (a fishnet grid that the tool creates for you, or an area layer that you provide) are placed over the points and the number of points that fall within each area is counted. The tool then finds clusters of high and low point counts associated with each area feature. Knowing where statistically significant clusters of point counts are located can help you answer a number of questions such as:
Where are additional resources needed?
If each point feature represents a crime in your city, running the Find Hot Spots tool on these points can show you the highest and lowest crime areas. This information can help guide the allocation of crime prevention resources.
Where are the priority areas?
With point data reflecting the mature trees in a forest, Find Hot Spots can reveal areas with the highest and lowest tree densities which could be valuable information for forest managers.
Similarly, if each point represents a tree with a disease or pest infestation, using Find Hot Spots to identify areas where these problems are most intense (hot spots) can help determine priority areas for treatment. Identifying areas with low incidence of disease or pests (cold spots) may provide clues about the factors promoting resistance. Knowing that the clustering of either high or low disease/pest incidence is statistically significant provides strong evidence that underlying factors are at work to either promote or discourage these problems.
A hot spot map of traffic accidents involving one or more fatalities can help prioritize safety improvement projects.
Running Find Hot Spots on home foreclosures can help determine where assistance programs are most needed. Finding cold spots where the number of foreclosures is unexpectedly low provides clues about homeowner resilience.
For this type of analysis (unless you provide aggregation areas for counting incident points) the Find Hot Spots tool will construct a fishnet grid and place it over the points in the analysis layer. The number of points falling within each fishnet square will then be counted and analyzed. Only fishnet squares with at least one point will be analyzed unless you define where points are possible.
Any statistically significant hot spots (red) in the results layer reflect spatial clusters of fishnet squares with high count values. Similarly, statistically significant cold spots (blue) reflect spatial clusters of fishnet squares with very low count values. Note: The results layer is not a density surface, but rather it indicates locations where high or low point counts are too clustered to be the result of random processes. It may be that there are no statistically significant clusters in the point data you are analyzing.
2.2.1 Defining where points are possible
Specify an area layer, or draw areas defining a study area where you want analysis to be performed in all locations where the incident point features could possibly occur. For this option, the Find Hot Spots tool will overlay your defined study area with a fishnet grid and count the points falling within each fishnet square. When you do not indicate where incident points are possible by using this option, the Find Hot Spots tool will only analyze fishnet squares that contain at least one point count. When you make use of this option to define where points are possible, however, the analysis will be done for all fishnet squares that fall within the bounding areas you define. Here are some examples of when specifying the boundaries for your analysis would be especially helpful:
Where are the trouble areas within the boundaries provided?
If your point data represent ship requests for harbor assistance, you might provide bounding areas reflecting the harbor waterways where ships travel. Any hot spots detected would reflect locations with unexpectedly high assistance requests. Knowing that these locations exist may prompt investigation and lead to implementation of prevention measures.
Other scenarios:
- Retail fraud would only occur where retail establishments operate. Finding locations with unusually high fraud incidents might suggest potential suspects.
- Home foreclosures would only occur where there are homes. Finding hot spots of foreclosures may identify neighborhoods needing priority assistance.
- Forest fires would only occur in forested areas and wouldn't occur within large bodies of water. Any statistically significant hot spots or cold spots from this analysis could inform forest management policies and practices.
2.2.2 Counting points within your own aggregation areas
In some cases, area features such as census tracts, police beats, or parcels will make more sense for your analysis than the default fishnet grid. Here are some examples of when it makes sense to provide an area layer for aggregation purposes:
Which administrative reporting areas reflect statistically significant clustering of high or low point counts?
To find the sections of a city where asbestos abatement programs are most needed, you could provide an area layer of the census tracts in the city to overlay point locations where asbestos in homes has been identified.
To better understand how the flu virus is spreading within a country, you might provide postal code boundaries and point features representing flu incidents. By analyzing new incidents each week, you learn where the hot spots are and if they are growing, shrinking, or moving.
2.2.3 Choosing to divide by
There are two common approaches to identify hot and cold spots:
- By count—When you analyze a particular dataset, you often want to find hot and cold spots of the number of features in each aggregation area across your study area. For instance, you might want to find hot spots where the highest numbers of crimes have happened and cold spots where the lowest numbers of crimes have occurred in order to allocate resources.
- By intensity—On the other hand, analyzing and understanding patterns that take into account underlying distributions that influence a particular phenomenon can also be meaningful. This concept is often referred to as normalization, or the process of dividing one numeric attribute value by another to minimize differences in values based on the size of areas or the number of features in each area. For instance, with crime, you might want to understand where there are clusters of high and low numbers of crimes that take into account the underlying population. In that case, you would count the number of crimes in each area (whether that area is a fishnet grid or a different area dataset) and divide that total number of crimes by the total population in that area. This would give you a crime rate, or the number of crimes per capita. Finding hot and cold spots of crime per capita answers a different question that can also help guide decision-making.
Choosing an appropriate attribute to divide by is very important. You need to make sure that the divide by attribute is an attribute that does, in fact, influence the distribution of the particular phenomenon you are analyzing.
Appropriate normalization examples:
- Number of foreclosures divided by the total number of households
- Number of elk observed divided by the total area
- Total sales divided by the number of customers in each district
- Number of unemployed people divided by the population over the age of 16
When you choose to Divide byEsri Population, the population data from the Esri Demographics Global Coverage is used. Be sure to look at the resolution of the data available for the area that you are interested in to make sure that it is compatible with the size of the areas that are being enriched (either aggregation areas you provide or fishnet squares being created). Visit Esri Demographics Global Coverage for details regarding the available geography levels for each country and vintage of the population data that is being used in your analysis.
3 Interpreting results
The output from the Find Hot Spots tool is a map. For the points or the areas in this result layer map, the darker the red or blue colors appear, the more confident you can be that clustering is not the result of random chance. Points or areas displayed using beige, on the other hand, are not part of any statistically significant cluster; the spatial pattern associated with these features could very likely be the result of random chance. Sometimes the results of your analysis will indicate that there aren't any statistically significant clusters at all. This is important information to have. When a spatial pattern is random, we have no clues about underlying causes. In these cases, all of the features in the results layer will be beige. When we do find statistically significant clustering, however, the locations where clustering occurs are important clues about what might be creating the clustering. Finding statistically significant spatial clustering of cancer associated with certain environmental toxins, for example, can lead to policies and actions designed to protect people. Similarly, finding cold spots of childhood obesity associated with schools promoting after-school sports programs can provide strong justification for encouraging these types of programs more broadly.
4 Troubleshooting
The statistical method used by the Find Hot Spots tool is based on probability theory and, consequently, needs a minimum number of features to operate effectively. This statistical method also requires a variety of counts or analysis field values. If you are analyzing crime incidents by census tract, for example, and amazingly end up with exactly the same number of crimes in each tract, the tool cannot solve. Below is an explanation of the messages you may encounter when you use the Find Hot Spots tool:
| Message | Problem | Solution |
|---|---|---|
The analysis options you selected require a minimum of 60 points to compute hot and cold spots. | There aren't enough point features in your point analysis layer to compute reliable results. | The obvious solution is to add more points to your analysis layer. Alternatively, you can try defining bounding analysis areas, and thereby add information about where points could have occurred but didn't. With this method you will need a minimum of 30 points. You can also try providing aggregation areas that overlay your points. You will need a minimum of 30 polygon areas and 30 points within those areas for this analysis. If you have at least 30 points you may want to specify an analysis field. This changes the question from where are there many or few points to where do high and low analysis field values cluster spatially. |
The analysis options you selected require a minimum of 30 points with valid data in the analysis field in order to compute hot and cold spots. | There aren't enough points, or enough points associated with non-NULL analysis field values, in your analysis layer to compute reliable results. | Unfortunately, if you have fewer than 30 points, this analysis method is not appropriate for your data. If you have more than 30 points and you are seeing this message, the analysis field you specified may have NULL values. Points with NULL analysis field values will be skipped. Another possibility is that you have an active Filter reducing the number of points available for analysis. |
The analysis options you selected require a minimum of 30 polygons with valid data in the analysis field in order to compute hot and cold spots. | There aren't enough polygon areas, or enough area features associated with non-NULL analysis field values, in your analysis layer to compute reliable results. | Unfortunately, if you have fewer than 30 polygon areas, this analysis method is not appropriate for your data. If you have more than 30 areas and you are seeing this message, the analysis field you specified may have NULL values. Polygon areas with NULL analysis field values will be skipped. Another possibility is that you have an active Filter reducing the number of polygon areas available for analysis. |
The analysis option you selected requires a minimum of 30 points to be inside the bounding polygon areas. | Only points that fall within the bounding analysis areas you draw or provide will be analyzed. In order to provide reliable results, at least 30 points should be inside the bounding analysis areas. | Unfortunately, if you do not have at least 30 points, this method is not appropriate for your data. With a minimum of 30 features, however, the solution here will often be to provide different, perhaps larger, bounding analysis areas. Another option would be to provide an area layer with a minimum of 30 aggregation polygons that overlay at least 30 of your points. When you provide aggregation areas, analysis is performed on the point counts within each area. |
The analysis option you selected requires a minimum of 30 points to be inside the aggregation polygons. | Only the points that fall inside the aggregation polygons will be included in the analysis. In order to provide reliable results, at least 30 points should be inside the polygon areas you provide. | Unfortunately, if you do not have at least 30 points, this method is not appropriate for your data; otherwise, you should draw or provide bounding analysis areas that overlay at least 30 of your points. The bounding areas should reflect all the locations where points could possibly occur. |
The analysis option you selected requires a minimum of 30 aggregation areas. | The option you selected will overlay the aggregation areas on top of your points and then count the number of points falling withing each area. A minimum of 30 counts (30 areas) are needed to provide reliable results. | Reliable results can be computed if you provide a minimum of 30 points that fall within a minimum of 30 aggregation areas. If you don't have 30 aggregation areas, you can try drawing or providing bounding analysis areas that overlay at least 30 of your points. These bounding areas should reflect all the locations where points could possibly occur. |
Hot and cold spots cannot be computed when the number of points in every polygon area is identical. Try different polygon areas or different analysis options. | When the Find Hot Spots tool counted the number of points within each aggregation area, it found that the counts were all identical. In order to compute results, this tool requires at least some variation in the count values obtained. | You can provide alternative aggregation areas that will not result in all areas having the exact same number of points. Rather than aggregation areas, you might also try drawing or providing bounding analysis areas. Alternatively, you can specify an analysis field. However, this changes the question from where are there many or few points to where do high and low analysis field values cluster spatially. |
There is not enough variation in point locations to compute hot and cold spots. Coincident points, for example, reduce spatial variation. You can try providing a bounding area, aggregation areas (a minimum of 30), or an Analysis Field. | Based on the number of points and how spread out they are, the tool creates a fishnet grid to overlay your points. After counting the number of points that fall within each fishnet square and removing squares with zero counts, there were fewer than 30 squares left. This tool requires a minimum of 30 counts (30 squares) to provide reliable results. | If your points occupy very few unique locations (if there are many coincident points), a good solution is to either provide aggregation areas that overlay your points, or draw and provide bounding analysis areas, indicating where points are and are not possible. Another option is to specify an analysis field. However, this changes the question from where are there many or few points to where do high and low analysis field values cluster spatially. |
There is not enough variation among the points within the bounding polygon areas. You can try providing larger boundaries. | Based on point locations and number of points, the tool creates a fishnet grid to overlay your points. After counting the number of points that fall within each fishnet square and removing squares that are outside your bounding analysis areas, fewer than 30 fishnet squares were left. This tool requires a minimum of 30 counts (30 squares) to provide reliable results. | If your points are located at a variety of locations inside the bounding analysis areas, you may just need to make or provide larger boundaries. If your points occupy very few unique locations (if there are many coincident points), a good solution is to provide aggregation areas that overlay your points. Another option is to specify an analysis field. However, this changes the question from where are there many or few points to where do high and low analysis field values cluster spatially. |
All of the values for your analysis field are likely the same. Hot and cold spots cannot be computed when there is no variation in the field being analyzed. | Most likely you specified an analysis field that has the same value for all of your points or area features in the analysis layer. The statistic used by this tool cannot solve unless there is a variety of values to work with. | You can specify a different analysis field or, for point features, analyze point densities rather than point values. |
We were not able to compute hot and cold spots for the data provided. If appropriate, try specifying an Analysis Field. | While quite unlikely, when the tool created a fishnet grid and counted the number of points within each square, the counts for all squares were identical. | The solution would be to provide your own aggregation areas, draw or provide bounding analysis areas, or specify an analysis field. |
Additional information about the algorithms employed by the Find Hot Spots tool can be found in How Optimized Hot Spot Analysis works.
5 Additional resources
ArcGIS Spatial Statistics Resources