Parametric Hotelling paired sample test for equal angular means. Can be
used as a paired-sample test for circular data. The test has 2 by N-2
degrees of freedom where N is the number of pairs in the phase
distribution.

If the individual phase values in alpha are mean values of
distributions, this concearns a second-level analysis. In that case,
the associated average vector lengths of these distributions are taken
into account.

H0: the two populations have equal mean phase angles
HA: the two populations have unequal mean phase angles

Usage:
[pval, F] = circ_htest(alpha1, alpha2)
[pval, F] = circ_htest(alpha1, alpha2, r1 ,r2)

Input:
alpha1: angles in radians or degrees
alpha2: angles in radians or degrees
r1: (optional) resultant vector lengths of alpha1, in case the values
in alpha1 consist of mean values of distributions themselves (i.e.
second-level analysis)
r2: (optional) resultant vector lengths of alpha2, in case the values
in alpha2 consist of mean values of distributions themselves (i.e.
second-level analysis)

Notes:
Inputs can be either a row or column vector. Inputs alpha1 and alpha2
need to have the same length. Optional r1 and r2 need to be the same
length as alpha, and each value in r should have the same index as
their alpha counterpart.

Output:
pval p-value of the Hotelling paired-sample test. Discard H0 if
pval is small.
F the test statistic of the Hottelling test

References:
Biostatistical Analysis, J. H. Zar (1999)