Key concepts 2 Statistics - Spatial Data Analysis: An Introduction for GIS Users - page 41

multiple categories, analysis of variance (ANOVA) represents the standard frame-
work. h e ANOVA test can be used to compare variation within data columns to
variation between data columns. In words, given a null hypothesis that a set of popula-
tion means are equal, we would reject the null hypothesis if the variation between the
means of each group is signii cantly greater than the variation within the data columns
(Rogerson, 2006).
Section 3.3 discussed correlation and regression. If it is assumed that the distribu-
tions of the variables are normal and the observations of each variable are indepen-
dent of one another, then a test of the signii cance for the correlation coei cient, r , may
be conduced using the t- statistic (Rogerson, 2006):

rn - 2

t = (3.12)

2

1 - r

Given the small example in Section 3.3, where r was 0.856 and n was 9, this gives:

0.856 9 - 2 0.856 9 - 2 2.265

t = = = = 4.381

0.517

2 2

1 - 0.856 1 - 0.856

Before assessing this result, a little explanatory text is required. Hypotheses can be
one-sided or two-sided. In the former case, a test is conducted to assess if the true
value is above or below (but not both) a given value. In the latter case, the test consid-
ers if the true value is either side of a given value. h is example relates to a two-sided
(or two-tailed) test.
Given these values, examining a t- table (a table allowing identii cation of the sig-
nii cance level associated with a t value given a particular number of degrees of free-
dom (see, for example, Shennan, 1997; Ebdon, 1985)) indicates that, for a two-tailed
test with a = 0.05 (i.e. the 5% signii cance level, commonly used as a benchmark sig-
nii cance level) and with seven degrees of freedom (there are nine observations and
n - 2 = 9 - 2 = 7) the critical value of t is 2.365. Since 4.381 is greater than that value,
the correlation coei cient can be said to be not equal to zero and the null hypothesis
is rejected. An alternative is to use one of the many web-based t- test calculators. Of
course, standard sot ware packages will do the calculations for you in any case. It is
important to take into account the sample size when assessing the correlation coei -
cient (or other coei cient) as, while the correlation coei cient may suggest a strong
relationship between variables, there may in fact be little coni dence in the results if
the sample size is small.

Statistics and spatial data

3.5

h e focus of this topic is the analysis of spatial data. Spatial data cannot be blindly
treated in the same way as data that are not located spatially (i.e. aspatial data).