Some basic elements of statistics

Abstract

In statistics we are primarily concerned with a quantitative analysis of data. This introductory chapter gives a short summary of some basic statistical tools. In particular those procedures have been included that apply to spatially varying pixels and hence are of use for remote sensing data. Variability (Oxford: the fact of quality of being variable in some respect) in space is defined as the phenomenon that a property changes in space. If at a location a variable is observed, this variable may be observed to deviate from the previous observation at a small distance from this location. The deviations may increase when distances increase. Description of variability (how large are the deviations if the distance increases) may be important for a process based interpretation. Relatively large variation within small distances indicate that the variable is subject to local influences. On the other hand, gradual changes indicate an influence at a more global scale, e.g. extending over the size of many pixels. The study of variability is in principle independent of any discipline, and even from earth sciences. In remote sensing and earth sciences, however, a quantitative approach using GIS and geostatistics has now for a large part been developed. Statistical (and geostatistical) procedures may be helpful in a number of stages of interpreting and evaluating data showing spatial variation. In many studies they have proven to be indispensable, especially when the number of available data increases as is the case for remote sensing images. Without having the intention to being complete, one may think of the following aspects: 1.