Geography Reference
In-Depth Information
16
Mean: 37.00
Median: 37.00
Mode: 37.00
SD: 4.140
Skew: 0
14
12
10
8
6
4
2
0
26.1-28.0
30.1-32.0
34.1-36.0
38.1-40.0
42.1-44.0 46.1- 8.0
44.1-46.0
28.1-30.0
32.1-34.0
36.1-38.0
40.1-42.0
A
Value
22
20
Mean: 35.19
Median: 34.00
Mode: 32.00
SD: 3.865
Skew: 0.924
Mean: 39.16
Median: 40.00
Mode: 42.00
SD: 3.965
Skew: -0.826
20
18
18
16
16
14
14
12
12
10
10
8
8
6
6
4
4
2
2
0
0
27.1-29.0
35.1-37.0
39.1-41.0
43.1-45.0
45.1-47.
27.1-29.0
31.1-33.0
35.1-37.0
39.1-41.0
43.1-45.0
45.1-47.0
31.1-33.0
29.1-31.0
33.1-35.0
37.1-39.0
41.1-43.0
29.1-31.0
33.1-35.0
37.1-39.0
41.1-43.0
B
Value
C
Value
Figure 3.2
Histograms: (A) normal distribution, (B) positive skew, (C) negative skew.
Values are precipitation amounts in millimetres. SD is the standard deviation
and Skew is the skewness coeffi cient.
then be conducted using the transformed variables and these can be back-transformed
(i.e. converted back to the original values) at er the analysis. h e logarithmic transfor-
mation is used widely to account for distributions with long tails of positive values (i.e.
a small proportion of large values); in such cases, the distribution of the log- transformed
data should be approximately normal and the transformed data can then be analysed
in the usual way. A logarithm of a number is that particular number expressed as a
power of another number. Natural logarithms are numbers expressed as powers of
e
(ot en given by exp), which is the exponential constant (approximately equal to (this
term is indicated by ยช) 2.718281829; see Appendix B for more details) while common
logarithms are expressed as powers of 10 (Shennan, 1997). For example, 42 to the
natural base (log
e
) is 3.738, which can be given by
e
3.738
, and 42 to the base 10 (log
10
) is
1.623, which can be given by 10
1.623
. Logarithms can be calculated using standard
spreadsheet and GIS packages. Introductions to transformations are provided by
Gregory (1968) and Shennan (1997).
h e next section is concerned with analysing two or more variables simultaneously.
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