Lab 6
Spatial statistics
Overview
In this assignment you will:
- Compute quadrat analysis by hand
- Evaluate how well a dataset conforms to a statistical test’s assumptions
- Use nearest neighbor analysis to determine if a dataset is clustered, dispersed, or randomly distributed over space
- Determine if a statistical result is valid given realistic geometries
- Interpret p-values and test statistics
- Compare patterns of crime to social vulnerability data
Part I: Quadrat analysis
- Observe the point pattern below. Make a prediction about whether it is clustered, dispersed, or random. (1 pt.)
Next, compute the variance by hand, and show your work. You may upload a picture of your work or you may put the cell counts and arithmetic in your word processing document (1 pts.).
What is the variance to mean ratio (1 pt.)?
Is the process clustered, random, or dispersed (1 pt.)?
Part II: Nearest neighbor analysis
Data retrieval
First, retrieve the following datasets:
-
- For these, you’ll need to create a filter, select appropriate criteria, click “Export,” and then download the modified data as a .csv.
SVI Data for the state of Illinois by census tracts for the most recent year
- First, make a prediction about the number of crimes by those three types. Which will be the most common? Which will be the least common (1 pt.)?
Data preparation
- Add all data to an ArcGIS Pro project map
- Transform data into an appropriate CRS for spatial analysis.
- Create an individual layer for each of the three crimes
Discuss the spatial patterns of each crime type. Are there visible patterns in the data? If so, where (3 pts.)?
Next, make a prediction about the state of clusteredness of each. Will each be clustered, dispersed, or random? Which will be the most clustered? Which will be the most dispersed (2 pts)?
Compute nearest neighbor analysis on all three subsets (i.e. layers) of the data simply using the minimum/maximum x,y values as the bounding box for the study area (this is the default in both ArcGIS Pro and QGIS). Create a table with the following for all three layers (3 pts.):
- Nearest neighbor index
- z-test statistic
- The conclusion (i.e. the word “dispersed”, “clustered”, or “random” based on the test results)
E.g.,
| Crime type | Nearest neighbor index | z-test statistic | Conclusion |
|---|---|---|---|
| Theft | |||
| Homicide | |||
| Narcotics |
Next, you will compute nearest neighbor analysis again for each of the three datasets, but this time you will use an area that is appropriate for the data.
What dataset are you using to determine the area? Why did you make that selection (1 pt)?
Compute nearest neighbor analysis on all three subsets (i.e. layers) of the data using an appropriate area. Re-create a table with the following for all three layers (3 pts.):
- Nearest neighbor index
- z-score
- The conclusion (i.e. the word “dispersed”, “clustered”, or “random” based on the test results)
E.g.,
| Crime type | Nearest neighbor index | z-test statistic | Conclusion |
|---|---|---|---|
| Theft | |||
| Homicide | |||
| Narcotics |
How did your results change? Did any conclusions change (1 pt.)?
Find a city in the United States that may be particularly problematic for computing nearest neighbor analysis for these types of crimes even if an accurate area is supplied for the test. Show a screenshot of the municipal boundaries, and describe how the tests could be skewed computationally (2 pts.).
Next, you will count the number of homicides in each census tract (using a spatial join or “summarize within”) and conduct an informal assessment of the relationship between homicides and SVI.
What is the relationship between SVI and number of homicides visually? Use a single variable like “Persons below 150% poverty estimate” or another similar variable (refer to the data dictionary here to find the appropriate variable code: https://svi.cdc.gov/map25/data/docs/SVI2022Documentation_ZCTA.pdf). What does this tell us about the relationship between crime and social vulnerability (1 pts.)?
Create an aesthetically pleasing map that effectively displays the number homicides in each tract and the SVI data (3 pts).
Extra credit
- Outside of ArcGIS, calculate the correlation between number of homicides and SVI What is the value of Pearson’s r? What does this tell us about the relationship between crime and social vulnerability (1 pts.)?