Comparing Populations in Data Involving Spatial Information

Observations corresponding to spatial units are commonly studied. If we want to see whether a continuous variable has the same distribution in a group of populations, different methods can be used according to the characteristics of the data. It could occur that observations in geographical data are related because they correspond to the same spatial unit, in which case we can use a repeated measures model. Whether or not repeated measures are involved, parametric and non-parametric methods are available. We analyze how repeated measures can be seen as a linear model and their relationship. We illustrate all these methods using data concerning economical activity in five sectors in specific regions in Mexico, where we want to see if all sectors are equally relevant. We also show through simulated data how by not selecting an adequate model we can obtain wrong inferences. In data involving spatial units, the independence assumption associated with a one-factor ANOVA could be violated when a variable changes spatially so that there are similar values between neighbors. Then, an equivalent linear model involving that spatial information could be used. We use a geographically weighted regression and illustrate the method through data concerning income in Mexico. We also show how the lack of independence is solved through the spatial model and perform a post hoc analysis