Applied Statistics Using SPSS, STATISTICA, MATLAB and R

10.5 Tests on von Mises Distributions 395
A: Figure 10.10 shows the respective plots obtained with MATLAB functions
colatplot and longplot. Both plots suggest an important departure from von
Misesness. The colatplot and longplot results also indicate the rejection of
the null hypothesis for the co-latitude (h = 1) and the non-rejection for the
longitude (h = 0).
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Figure 10.10. Co-latitude plot (a) and longitude plot (b) for the gradient
measurement set M1 of the soil pollution dataset.
10.5 Tests on von Mises Distributions
10.5.1 One-Sample Mean Test
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The most usual one-sample test is the mean direction test, which uses the same
approach followed in the determination of confidence intervals for the mean
direction, described in section 10.3.
Example 10.15
Q: Consider the Joints’ dataset, containing directions of granite joints measured
from a city street in Porto, Portugal. The mean direction of the data was studied in
Example 10.5; the 95% confidence interval for the mean was studied in Example
10.7. Assume that a geotectonic theory predicts a 90º pitch for the granites in
Porto. Does the Joints’ sample reject this theory at a 95% confidence level?
A: The mean direction of the sample has a co-latitude θ = 178.8º (see Example
10.5). The 95% confidence interval of the mean direction corresponds to a
deviation of 4.1º (see Example 10.7). Therefore, the Joints’
dataset does not
reject the theory at 5% significance level, since the 90º pitch corresponds to a colatitude
of 180º which falls inside the [178.8º − 4.1º, 178.8º + 4.1º] interval.