rayleigh_test {tectonicr} | R Documentation |
Rayleigh Test of Circular Uniformity
Description
Performs a Rayleigh test for uniformity of circular/directional data by assessing the significance of the mean resultant length.
Usage
rayleigh_test(x, mu = NULL, axial = TRUE, quiet = FALSE)
Arguments
x |
numeric vector. Values in degrees |
mu |
(optional) The specified or known mean direction (in degrees) in alternative hypothesis |
axial |
logical. Whether the data are axial, i.e. |
quiet |
logical. Prints the test's decision. |
Details
H_0
:angles are randomly distributed around the circle.
H_1
:angles are from unimodal distribution with unknown mean direction and mean resultant length (when
mu
isNULL
. Alternatively (whenmu
is specified), angles are uniformly distributed around a specified direction.
If statistic > p.value
, the null hypothesis is rejected,
i.e. the length of the mean resultant differs significantly from zero, and
the angles are not randomly distributed.
Value
a list with the components:
R
orC
mean resultant length or the dispersion (if
mu
is specified). Small values ofR
(large values ofC
) will reject uniformity. Negative values ofC
indicate that vectors point in opposite directions (also lead to rejection).statistic
test statistic
p.value
significance level of the test statistic
Note
Although the Rayleigh test is consistent against (non-uniform)
von Mises alternatives, it is not consistent against alternatives with
p = 0
(in particular, distributions with antipodal symmetry, i.e. axial
data). Tests of non-uniformity which are consistent against all alternatives
include Kuiper's test (kuiper_test()
) and Watson's U^2
test
(watson_test()
).
References
Mardia and Jupp (2000). Directional Statistics. John Wiley and Sons.
Wilkie (1983): Rayleigh Test for Randomness of Circular Data. Appl. Statist. 32, No. 3, pp. 311-312
Jammalamadaka, S. Rao and Sengupta, A. (2001). Topics in Circular Statistics, Sections 3.3.3 and 3.4.1, World Scientific Press, Singapore.
See Also
mean_resultant_length()
, circular_mean()
, norm_chisq()
,
kuiper_test()
, watson_test()
, weighted_rayleigh()
Examples
# Example data from Mardia and Jupp (2001), pp. 93
pidgeon_homing <- c(55, 60, 65, 95, 100, 110, 260, 275, 285, 295)
rayleigh_test(pidgeon_homing, axial = FALSE)
# Example data from Davis (1986), pp. 316
finland_stria <- c(
23, 27, 53, 58, 64, 83, 85, 88, 93, 99, 100, 105, 113,
113, 114, 117, 121, 123, 125, 126, 126, 126, 127, 127, 128, 128, 129, 132,
132, 132, 134, 135, 137, 144, 145, 145, 146, 153, 155, 155, 155, 157, 163,
165, 171, 172, 179, 181, 186, 190, 212
)
rayleigh_test(finland_stria, axial = FALSE)
rayleigh_test(finland_stria, mu = 105, axial = FALSE)
# Example data from Mardia and Jupp (2001), pp. 99
atomic_weight <- c(
rep(0, 12), rep(3.6, 1), rep(36, 6), rep(72, 1),
rep(108, 2), rep(169.2, 1), rep(324, 1)
)
rayleigh_test(atomic_weight, 0, axial = FALSE)
# San Andreas Fault Data:
data(san_andreas)
rayleigh_test(san_andreas$azi)
data("nuvel1")
PoR <- subset(nuvel1, nuvel1$plate.rot == "na")
sa.por <- PoR_shmax(san_andreas, PoR, "right")
rayleigh_test(sa.por$azi.PoR, mu = 135)