Geoscience Reference
In-Depth Information
ans =
1.0000 0.7981
0.7981 1.0000
and reaches a value close to
r
=1 if the outlier has a value of
(x,y)=(20,20)
.
x(31,1) = 20; y(31,1) = 20;
plot(x,y,'o'), axis([-1 20 -1 20]);
corrcoef(x,y)
ans =
1.0000 0.9403
0.9403 1.0000
We can compare the sensitivity of Pearson's correlation coei cient with that
of Spearman's correlation coei cient and Kendall's correlation coei cient
using the function
corr
. In contrast to
corrcoef
, this function does not
calculate correlation matrices that we can later use (e.g., in Chapter 9) for
calculating correlations within multivariate data sets. We type
r_pearson = corr(x,y,'Type','Pearson')
r_spearman = corr(x,y,'Type','Spearman')
r_kendall = corr(x,y,'Type','Kendall')
which yields
r_pearson =
0.9403
r_spearman =
0.1343
r_kendall =
0.0753
and observe that the alternative measures of correlation result in reasonable
values, in contrast to the absurd value for Pearson's correlation coei cient
that mistakenly suggests a strong interdependency between the variables.
Although outliers are easy to identify in a bivariate scatter, erroneous values
can easily be overlooked in large multivariate data sets (Chapter 9).
Various methods exist to calculate the signii cance of Pearson's correlation
coei cient. h e function
corrcoef
also includes the possibility of evaluating
the quality of the result. h e
p
-value is the probability of obtaining a
correlation as large as the observed value by random chance, when the true
correlation is zero. If the
p
-value is small, then the correlation coei cient
r
is signii cant.
