Probability is a useful tool in geographical analysis, especially in situations where hard data does not exist. The application of probability can allow a geographical analyst to make reasonable predictions in these situations. Consider the lack of data regarding how people in the United States migrate and change residences. A geographical analyst can use the probabilities of moving certain distances along with the probabilities of moving certain directions to predict the average migration patterns of citizens of the United States.
In geographical analysis, analysts often want to make meaningful comparisons. However, whether the data be air pollution levels in big cities or state population growth, simply looking at the data to determine if there are differences present is poor method to make this determination. Statistics offers geographical analysts the ability to use hypotheses tests to conclude with high probability whether differences are present and in what ways the things being compared differ.
Geographical analysis relies heavily on finding data sets with which to perform analyses; yet the choice of data is a complicated procedure. To avoid collecting a biased data set, geographical analysts must employ a suitable sampling method for the situation. How to appropriately select a sample is a well-researched topic of statistics, and geographical analysts make heavy use of the well-founded statistical practice of selecting unbiased, representative samples.
Often, geographical analysts perform analysis on a small geographical area because of restrictions in funding, time or other resources. In spite of this, analysts execute their analyses with the overall goal of making inferences about larger geographical areas. The problem is that without the appropriate statistical techniques these inferences will not hold. Statistics inference allows analysts to move away from simply describing their sample and move toward using their results to make larger, more general conclusions.