Geography Reference
In-Depth Information
the calculation of cuts and fills in construction projects, or the determination
of elevations.
Three-dimensional terrain analysis (3-D) is most commonly performed
with TIN-based terrain analysis or, less frequently, with 3-D rasters, called
“voxels.” TIN is used in analysis of surficial processes—for example, deter-
mining erosion or assessing watershed run-off. TIN-based terrain analysis
often uses a digital elevation model (DEM) and water body or road network
data. The geostatistics involved in this are commonly linear equations, but
they can involve principle component analysis, fractals, and shortest path
analysis. Voxels are used in specialized applications to analyze relationships
in the atmosphere or in the ground, including the diffusion of aerosols from
factories and the pollution of groundwater.
Chi-Square Analysis
Chi-square analysis is a straightforward statistical technique that can be used
to evaluate the validity of a hypothesis. It is used to examine the relationship
between two variables in a cause-and-effect relationship. Because it is reason-
ably straightforward, it is widely used for exploring a number of questions.
For example, does higher soil pH lead to less healthy plants? Does proximity
to bus stops lead to an increase of people using public transit? How strong is
the relationship between crop types and water resources? It may need to be
followed up by more exacting geostatistical study, but chi-square analysis
often serves as a key starting point for testing and validating questions. Chi-
square analysis compares an idealized random distribution with existing or
projected distributions. The random distribution of variables for chi-square
analysis that measure characteristics of things or events is called the “normal
distribution,” or what one would expect if there is no relationship between
the variables. The existing distribution is called the “expected distribution.”
We can go through an example, step-by-step, to get a better ideal of how chi-
square analysis works.
1. Create an Observed Frequency Table and Examine
Relationships
The first step is to organize the data into a contingency table where the rows
indicate one variable of the independent variable (considered the “causal”
factor of the relationship) and the dependent variable (the “effect” from the
independent variable). For this example, we will consider how elevation
effects snowfall. Our hypothesis is that more snow falls at higher elevations.
We have the data from 133 observations at elevations between 500 and 4,500
m and the yearly average amount of snow, which ranges from 0 to 534 cm. In
Table 14.1, the observed frequencies table, the rows indicate elevations, clas-
sified into three groups, and the columns indicate the snowfall averages,
classified into three ordinal categories. The individual cells give the number
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