Cartography and Spatial Statistics

Good day all,

     Here we have a post about how Spatial Statistics interrelate into cartography. This specifically applies to the analyses of data on a map. The integration of these two items is seen through this weeks learning objectives below:

• Define key spatial statistics terms
• Know what questions to ask about your data before choosing an analysis tool.
• Examine the spatial distribution of a data set to identify clusters and spatial relationships in the data.
• Interpret a histogram to determine the frequency distribution data set.
• Find outliers in your data using a semivariogram cloud, Voronoi map, histogram, and normal QQ plot.
• Use a trend analysis graph to identify patterns in your data.
• Assess which analysis tools are appropriate given the spatial distribution and values of your data. 

The majority of the above were exercised through Esri.com specific user training "Exploring Spatial Patterns in Your Data Using ArcGIS." The examples used in this weeks assignments covered map data for the depth of wells across an area, weather station & temperature readings, and murder rates across various cities. You can see that that data requiring statistical/spatial analyses can vary to just about any topic you can imagine. Below we will look at some of these particular tools that I delved into using ArcGIS this week. 

Lets start with some of the basics. The Mean, Median Center, and general distribution of data. 

Recall;

Mean = The average of all of your data points

Median Center= The middle value of all of your data

Distribution= how your data is graphically oriented in reference against a particular standard, Ie Normal distribution is judged against a bell curve.

The above data was provided by ESRI, with the map being created by myself exclusively in ArcGIS. I first took the data and had ArcGIS compute the Mean center, and Median center, which show there is only a slight difference in location between the two. This difference lends you to see how the more densely packed areas in the north and south, south-east drive the mean and median locations slightly apart. Also you can see an overall directional distribution computed to 1 standard deviation (meaning approximately 68% of the overall data falls in this area). We can see with this overlay that the station locations have a roughly east-west distribution. Overall this portion of the lab essentially tells us where and how the data is located.

The next thing I did with this data was to determine if it was normally distributed. This was done in two ways, showing a histogram and QQ Plot of the data. You can see these computations and graphics below, as generated in ArcGIS.

Luckily for me, ArcGIS does all of the heavy computations. The statistics side would make my brain hurt. Above we have a Histogram with potential outlier on the right side. But in general you can see that this does lend itself to a mostly normal distribution with only slight positive skew due in part to that potential outlier. 

Again, the beauty of ArcGIS is that it does the calculations and has these amazing displays to save the aspiring Cartographer / GIS Professional from having to do such things by hand, like the wonderful scientists coming before. Here we have the QQ Plot, whose data should predominately fall upon that central line to show if the data favors normal distribution or not. thankfully with few exceptions, this data is normally distributed. 

The scope of the this weeks lesson did go beyond the examples above. But those items are beyond the scope of this post for today. Spatial statistics are a huge portion of the mapping world which i have only scratched the surface. Thanks for viewing this little bit.