GeoWorld

GeoWorld May 2011

Issue link: http://read.dmtmag.com/i/33025

Contents of this Issue

Navigation

Page 9 of 31

Correlate Maps with a Numerical Mindset BEYONDMAPPING L ast month’s “Beyond Mapping” column discussed a technique for comparing maps, even if they were “apples and oranges.” The approach normalized two sets of mapped data using the standard normal-variable equation to translate the radically different maps into a common “mixed-fruit” scale for com- parison (see “You Really Can Compare Apples and Oranges,” April 2011). Continuing with this statistical-com- BY JOSEPH BERRY parison theme (maps as numbers—bah, humbug), a measure of linear correlation between two continuous quantitative map surfaces can be considered. A general dictionary definition of the term correlation is “mutual relation of two or more things” that’s expanded to its statistical meaning as “the extent of correspondence between the ordering of two variables; the degree to which two or more measurements on the same group of elements show a tendency to vary together.” So what does that have to with mapping? Maps are just colorful images that tell us what is where, right? No, today’s maps actually are organized sets of numbers first, pictures later. And numbers (lots of numbers) are right down statistic’s alley. So although we’re severely chal- lenged to “visually assess” the correlation among maps, spatial statistics, like a tireless puppy, eagerly awaits the opportunity. Joseph Berry is a principal in Berry & Associates, consultants in GIS technology. He can be reached via e-mail at jkberry@du.edu. 10 Statistics Primer Recall from basic statistics that the correlation coefficient (r) assesses the linear relationship between two variables, such that its value falls between -1 ≤ r ≤ +1. Its sign indicates the direction of the relationship, and its magni- tude indicates the strength. If two variables have a strong positive correlation, r is close to +1, meaning that as values for x increase, values for y increase proportionally. If a strong GEO W ORLD / M AY 2O11 Figure 1. Correlation between two maps can be evaluated for an overall metric (left) or a continuous set of spatially localized metrics (right). This “numerical mindset of maps” is catapulting GIS beyond conventional mapping and traditional statistics, ahead of long-established spatially aggregated metrics. negative correlation exits, r is close to -1 and, as x increases, the values for y decrease. A perfect correlation of +1 or -1 only occurs when all the data points lie on a straight line. If there’s no linear correlation or a weak correlation, r is close to 0, meaning there’s a random or non-linear relation- ship between the variables. A correlation greater than 0.8 is generally described as strong, whereas a correlation of less than 0.5 is described as weak. The coefficient of determination (r2 ) is a related statistic that summarizes the ratio of explained to total variation. It represents the percent of the data

Articles in this issue

Links on this page

Archives of this issue

view archives of GeoWorld - GeoWorld May 2011