Geography Reference
In-Depth Information
have more certainty than our visual inspection, we need to first square the
differences between the observed and the expected counts:
Squared difference (low snowfall/500-1,000 m elevation)
= 41 - 34.209 = 6.791 2
= 46.118
This result, however, is dependent on the number of observations. The
final calculation of the chi-square test standardizes the calculation regardless
of the number of observations.
The sum of the cell values, 42.206, is the final chi-square statistic. We
now need to consider how the number of variables influences the null
hypothesis acceptance or rejection, something called “degrees of freedom”
in statistics. You have already seen how the number of observations could
effect the statistic and was taken account of. The number of variables can
have an effect as well. The degrees of freedom is calculated by multiplying
the number of rows—1—by the number of columns—1—in the observed or
expected tables.
Degrees of freedom (df) = (3 - 1)
×
(3-1)=4
Using a probability table showing degrees of confidence and confidence
level (alpha), we can establish the number of times out of 100 that would be
exceeded if the null hypothesis were true. In this case, with four degrees of
freedom and at a confidence level of 0.05, the probability is 9.49. The value
from the chi-square (42.206) is significantly higher. This means that the
probability of getting a chi-square value this high is much lower. In other
words, we can now pretty certainly say that we should reject the null hypothe-
sis and note that the relationship between the amount of snowfall and eleva-
tion has been statistically supported.
From this point, we could move on to other statistical tests to look at
specific relationships between snowfall and elevation. We might also want to
assess our chi-square statistic, comparing it with other data and trying to
make our statistic more robust. For example, we only used 20 observations
in high elevation areas. Could we get more observations? Should we find out
where the observations are located to determine if there are any biases?
These questions reflect concerns that need to be expressed when using this
data, as the chi-square statistic itself fails to account for general or specific
geographical relationships.
Spatial Interpolation
A problem for many applications of geostatistics is that data is available for
selected points in an area, but not for the entire area. A common example is
soil pH, which can be collected only at distinct points using testing equip-
ment. Basically, any ground, water, or air property is based on measure-
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