G 424/524 GIS for the Natural Sciences
D. Percy
e-mail: percyd@pdx.edu

Quadrat Analysis

A first cut at analyzing the distribution of points

You are going to compare the distribution of points with a theoretical Poisson distribution (random) and use a Chi-Squared statistical test to see if there is a significant difference.

These are the step-by-step instructions:

  1. Start with the earthquakes that occurred in Oregon. Add the Oregon outline shapefile. Alternatively use a different point data set.
  2. Open the Fishnet tool from the ToolBox.
  3. Use the shapefile for Oregon as your template, set cell size width and height to 0, make 20 rows and 20 columns to start with, set geometry type to Polygon, turn off Label Points. Be aware of your output location, and name your shapefile appropriately (like grid20x20, for example)
  4. Use the Selection-> Select by Location function to do a spatial query of all grids that intersect the state. Your screen might look like this. Save this selection as a new theme. We won't worry about the boundary problem.
  5. Choose (Rt-Click and choose Joins and Relates) the intersected grids theme from the previous step and do a spatial join (based on location) to the oregon_earthquakes theme. This gives you a shapefile of how many earthquakes occurred in each grid cell. You can use the Count_ field to color the cells and create a choropleth map.
  6. Open the table (Join_Output?), right-click on the field Count_ and choose Summarize. Accept the defaults in the dialog box. This gives you a table of how many grid cells had specific "quanta" of earthquakes.
  7. Export the summarized table to DBF so that you can import it to Excel. (actually, you can just open it directly in Excel without exporting, just keep track of the filename, like Sum_output2.DBF). In Excel, change your filetype to Dbase in the Open Files dialog box.
  8. The number of cells that had zero earthquakes is equal to the total cells minus cells that had quakes.
  9. Download my Poisson example spreadsheet. For a quadrat analysis you need to have at least 5 events in a category. You will probably combine all of the categories above a certain value. For my 50 x 50 example I combined everything greater than 5. Remember that the sum of all probabilities in the Poisson distribution is 1. The sum of the Expected and Observed should both be the total number of quadrats that intersected Oregon.
  10. Alter the spreadsheet to accommodate the grid size that you used. Your Chi Square value should be VERY large, if you are using the earthquake data, since this is obviously a clustered data set!