inst/help/circular multiple-sample tests.md

In circstat/JASP-module: CircularStatistics Module for JASP

Circular Hypothesis-Testing: Multiple-sample Tests

Circular multple-sample tests allow you to perform one-way and two-way ANOVAs on circular data. The null hypothesis is equal mean direction across all groups.

Assumptions

• Dependent circular variable with specified period
• Watson-Williams test: The data in each group comes from a von Mises distribution. All of these have the same concentration parameter which are sufficiently large (>1).
• Watson-Wheeler test: All groups contain at least 10 data points.
• Harrison-Kanji test: The data in each group comes from a von Mises distribution. All of these have the same concentration parameter between 0 and 2.

Default Options

One-way ANOVA:

• Watson-Wheeler: Non parametric one-way ANOVA for circular data

Default Output

One-way ANOVA:

• Watson-Wheeler:
• p: P-value of the test
• W: The Watson-Wheeler test statistics
• df: The degrees of freedom of the χ2-distribution to which W is compared

Additional Options

One-way ANOVA:

• Watson-Williams: Parametric one-way ANOVA for circular data

Two-way ANOVA:

• Harrison-Kanji: Two-way ANOVA for circular data (it always runs on the first two factors in the Fixed Factors list)

Additional Output

One-way ANOVA:

• Watson-Williams: Parametric one-way ANOVA for circular data
• p: P-value of the test
• F: The F statistics of the test
• df1 and df2: The degrees of freedom of the F distribution to which F is compared

Two-way ANOVA:

• Harrison-Kanji: It has one of the following outputs, depending on the estimate of the concentration parameter κ of the pooled data:

  • if κ < 2
  • p: P-value of the test
  • χ2: The associated χ2 component that is used as a test of difference

  • df: The degrees of freedom of the associated χ2 distribution

  • if κ > 2

  • p: P-value of the test
  • F: The F ratio of the associated component
  • df: The degrees of freedom of the associated component
  • Sum of Square: The sum of the squares of the associated component
  • Mean of Square: The mean of the squares of the associated component

References

• Watson-Williams:
• Zar JH (1998). Biostatistical Analysis (4th Edition). Chapter 27. Prentice Hall.
• Watson-Wheeler:
• Zar JH (1998). Biostatistical Analysis (4th Edition). Chapter 27. Prentice Hall.
• Harrison-Kanji:
• Harrison D, Kanji GK, Gadsden RJ (1986). Analysis of variance for circular data. Journal of Applied Statistics, 13(2), 123–138.
• Harrison D, Kanji GK (1988). The development of analysis of variance for circular data. Journal of Applied Statistics, 15(2), 197–223.

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