inst/help/circular one-sample tests.md

In circstat/JASP-module: CircularStatistics Module for JASP

Circular Hypothesis-Testing: One-sample Tests

Circular one-sample tests allow you to test a hypothesis on a group of circular data. It provides tests for uniformity (i.e. the data is distributed uniformly around the circle) and for a von Mises assumption (i.e. the data in the group comes from a von Mises distribution).

Assumptions

• Circular variable with specified period
• Rao's spacing test: At least four data points in each sample
• Rayleigh test: The alternative hypothesis assumes an unimodal distribution with unspecified location and unspecified circular variance
• V test: The alternativ hypothesis assumes an unimodal distribution with the location as the specified test value, but unspecified circular variance
• Von Mises assumption check: None

Default Options

Uniformity Tests:

• Rao's spacing with α = 0.01: Runs a Rao spacing test with a signifance level of 1%

Default Output

Uniformity Tests:

• Rao's spacing:
• α: Significance level that was specified in the input
• Statistic: Rao test statistics
• Critical: Critical value of the test statistic according to the specified significance level α

Additional Options

Uniformity Tests:

• Rayleigh: Runs a rayleigh test
• V: Runs a V test, i.e. a modified Rayleigh test
• Test value: The test direction of the V test

Assumption Checks:

• Von Mises: Runs a Watson's goodness-of-fit test on the data with a von Mises distribution as evaluation and with the specified significance level α

Additional Output

Uniformity Tests:

• Rayleigh:
• p: P-value of the test
• Statistic: Rayleigh test statistics (Rayleigh's R)
• V:
• p: P-value of the test
• Statistic: V test statistics (Rayleigh's R weighted with cos(θ - μ0), where θ is the mean direction of the sample and μ0 is the test direction. It therefore can be negative.)

Von Mises Assumption Check:

• α: Significance level that was specified in the input
• U2: The Watson test statistics
• Critical: Critical value of the test statistic according to the specified significance level α
• Est. κ: The maximum likelihood estimate of the concentration parameter of the von Mises distribution given by the data points

References

• Rao's spacing test:
• Rao JS (1976). Some Tests Based on Arc-Lengths for the Circle. Sankhyä: The Indian Journal of Statistics, Series B (1960-2002), 38(4), 329–338.
• Russell GS, Levitin DJ (1995). An expanded table of probability values for rao's spacing test. Communications in Statistics - Simulation and Computation, 24(4), 879–888.
• Rayleigh test:
• Fisher NI (1993). Statistical Analysis of Circular Data. Chapter 4. Cambridge University Press.
• V test:
• Zar JH (1998). Biostatistical Analysis (4th Edition). Chapter 27. Prentice Hall.
• Watson's goodness-of-fit:
• Lockhart RA, Stephens MA (1985). Tests of fit for the von Mises distribution. Biometrika, 72(3), 647–652.

circstat/JASP-module documentation built on Nov. 4, 2019, 8:53 a.m.