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Confidence Interval around the Mean Direction of Circular Data after Batschelet (1971)

Source: R/statistics.R
confidence.Rd

Probabilistic limit on the location of the true or population mean direction, assuming that the estimation errors are normally distributed.

Usage

confidence_angle(x, conf.level = 0.95, w = NULL, axial = TRUE, na.rm = TRUE)

confidence_interval(x, conf.level = 0.95, w = NULL, axial = TRUE, na.rm = TRUE)

Arguments

x

numeric vector. Values in degrees.

conf.level

Level of confidence: \((1 - \alpha \%)/100\). (0.95 by default).

w

(optional) Weights. A vector of positive numbers and of the same length as x.

axial

logical. Whether the data are axial, i.e. pi-periodical (TRUE, the default) or directional, i.e. \(2 \pi\)-periodical (FALSE).

na.rm

logical value indicating whether NA values in x should be stripped before the computation proceeds.

Value

Angle in degrees

Details

The confidence angle gives the interval, i.e. plus and minus the confidence angle, around the mean direction of a particular sample, that contains the true mean direction under a given level of confidence.

References

  • Batschelet, E. (1971). Recent statistical methods for orientation data. "Animal Orientation, Symposium 1970 on Wallops Island". Amer. Inst. Biol. Sciences, Washington.

  • Mardia, K.V. (1972). Statistics of Directional Data: Probability and Mathematical Statistics. London: Academic Press. (p. 146)

  • Davis (1986) Statistics and data analysis in geology. 2nd ed., John Wiley & Sons.

  • 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_sd_error()

Examples

# 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
)
confidence_angle(finland_stria, axial = FALSE)
#> [1] 10.43928
confidence_interval(finland_stria, axial = FALSE)
#> $mu
#> [1] 129.1903
#> 
#> $conf.angle
#> [1] 10.43928
#> 
#> $conf.interval
#> [1] 118.7510 139.6296
#> 

data(san_andreas)
data("nuvel1")
PoR <- subset(nuvel1, nuvel1$plate.rot == "na")
sa.por <- PoR_shmax(san_andreas, PoR, "right")
confidence_angle(sa.por$azi.PoR, w = 1 / san_andreas$unc)
#> [1] 5.135345
confidence_interval(sa.por$azi.PoR, w = 1 / san_andreas$unc)
#> $mu
#> [1] 138.9025
#> 
#> $conf.angle
#> [1] 5.135345
#> 
#> $conf.interval
#> [1] 133.7671 144.0378
#>