Key concepts 2 Statistics - Spatial Data Analysis: An Introduction for GIS Users - page 42

One key problem relates to statistical inference, as discussed above. One of the assump-
tions of standard signii cance tests is independence in the observations of the samples.
In simple terms, this means that the value of one observation should not be af ected by
the value of another observation. As will be shown in Section 4.8, values of observa-
tions of spatial variables are ot en very similar to the values at neighbouring locations.
Indeed, the fact that this is so frequently the case provides the basis of many spatial
data analysis approaches. In the present context, the problem with this is that signii -
cance levels tend to be inl ated as the ef ective number of degrees of freedom is
reduced—that is, if the observations are spatially dependent then there are ef ectively
fewer independent observations. In words, use of standard signii cance tests with spa-
tial data is problematic and solutions may not be straightforward. Rogerson (2006)
provides a detailed discussion of this topic.
Summary
This chapter provides a summary of some key ideas and methods in descriptive and
inferential statistical analysis. Many methods for the analysis of spatial data have their
origins in standard aspatial statistical methods, and knowledge of some key methods
and issues in statistical analysis is essential for the developing spatial analyst, who will
need to make frequent use of standard statistical approaches in the initial exploration of
spatial data sets. Many of the themes introduced here will be revisited in later chapters,
but with adaptations refl ecting the focus of this topic on spatial data.
Further reading
The topic by Rowntree (2000) provides an excellent introduction to some important statis-
tical concepts. Various topics provide introductions to statistics for geographers and the
topic by Rogerson (2006) is a good example. The topics by Kitchin and Tate (2000) and
O'Sullivan and Unwin (2002) also include relevant introductory material. Rowntree (2000)
and Rogerson (2006) include very clear introductions to some key concepts in inferential
statistics. Brunsdon (2008) provides an introduction to some key concepts in statistical
inference and discusses some issues related to inference in a spatial context. Section 7.3.1
illustrates the chi-square ( c 2 ) test, a commonly used statistical hypothesis test.
The next chapter explores some key concepts in spatial data analysis and is the third
of the three chapters introducing key concepts that provide foundations for the rest of
the topic.