Statistics for GIS Professionals

One of the things I  tell my students is that our data wants to tell us a story, we just need to listen.  One of the ways we can listen to our data is by looking at descriptive statistics like the mean, standard deviation, and skill. These are always to see what jumps out at us, and it helps us make good decisions when forming a hypothesis.

Spatial data is a different animal when you consider statistical tests.   There are some very tricky conundrums we have to be aware of, and this lecture will consider how descriptive statistics are used, and how the concept of the modifiable area unit problem (MAUP) plays into the proper use of statistics and GIS.

This is another one of those topics that we are only going to spend about 20 minutes on. However, you could literally take multiple courses just in probability itself. But, this lecture is going to help you understand the role that probability plays in statistics, and specifically why statistics work. 

Everyone always talks about how people can lie with statistics. The reality is, if you choose a bad sample your statistical analysis will be junk. This lecture is going to talk about strategies for taking really good samples so that way we can have more confidence in our results. We will have confidence that the sample we’ve taken truly represents the population.  

Is it really possible to make an estimate with 90% certainty? The average person thinks that statisticians are just making up numbers. But this short video is going to demonstrate that if you have a good sample, sure enough, you can create a range that will capture the true value of a population parameter with 90 or 95% certainty. Is it really possible to make an estimate with 90% certainty? The average person thinks that statisticians are just making up numbers. But this short video is going to demonstrate that if you have a good sample, sure enough, you can create a range that will capture the true value of a population parameter with 90 or 95% certainty

Here is a short little video that illustrates the concept of what statistical significance means. We’ll use a simple example from baseball to illustrate the point and make the topic fun.

Sometimes you take a sample and want to determine if it is representative of the population. That is called a one sample test.  we are going to describe what a one sample test is and then walk through a few examples to show how it works.

Sometimes you take two sampleS and want to determine if  they come from the same population. That is called a two sample test.  We are going to describe what a two sample test is and then walk through a few examples to show how it works.

Continuing our discussion of tests among samples, we are going to expand the one and two sample test for three or more samples. These are called ANOVA tests and are used to determine if three or more samples come from the same underlying population.

Do two things relate to each other?  We all have our hunches, but correlation analysis allows us to statistically determine with two different samples come from the same underlying population.  This is so important in GIS analysis, whether it's revenue based on advertising dollars, or growth of plants based on moisture content, or even locations of drug dens and homicides.  Correlation is a powerful tool that a GIS professional can use. 

Where correlation tested whether two samples are related, it really didn’t give much consideration to the nature of form of that relationship. Regression is a more sophisticated statistical test that is widely used in the sciences to not only determine if there is a relationship among variables, but it quantifies what that relationship is.

We look at maps all the time, and make judgments as to whether the objects on the map are random, clustered or dispersed.  But, those are just our judgments.  The use of nearest neighbor analysis takes our subjective view, and allows us a way to quantitatively test whether the spatial data might in fact be clustered together.  While many GIS products have a button to perform nearest neighbor analysis, this lecture is going to show you the underlying concepts and how to properly assess whether the data  exhibits any spatial relationship.