eba (version 1.5-2)

circular: Circular triads (intransitive cycles)

Description

Number of circular triads and indices of inconsistency.

Usage

circular(mat)

Arguments

mat

a square matrix or a data frame consisting of (individual) binary choice data; row stimuli are chosen over column stimuli

Value

• T
  number of circular triads
• T.max
  maximum possible number of circular triads
• zeta
  Kendall's coefficient of consistency
• chi2
  the chi-square statistic for a test that the consistency is by chance
• df
  the degrees of freedom
• pval
  the p-value of the test

Details

Kendall's coefficient of consistency, $$zeta = 1 - T/T_{max},$$ lies between one (perfect consistency) and zero, where T is the observed number of circular triads, and the maximum possible number of circular triads is $T_{max} = n*(n^2 - 4)/24$, if $n$ is even, and $T_{max} = n*(n^2 - 1)/24$ else, and $n$ is the number of stimuli or objects judged.

The null hypothesis in the chi-square test is that the inconsistencies in the paired-comparison judgments are by chance. The chi-square approximation might be incorrect if $n < 8$.

References

David, H. (1988). The method of paired comparisons. London: Griffin.

See Also

eba, strans, kendall.u.

Examples

## A dog's preferences for six samples of food
mat <- matrix(c(0, 1, 1, 0, 1, 1,
                0, 0, 0, 1, 1, 0,
                0, 1, 0, 1, 1, 1,
                1, 0, 0, 0, 0, 0,
                0, 0, 0, 1, 0, 1,
                0, 1, 0, 1, 0, 0), 6, 6, byrow=TRUE)
circular(mat)  # moderate consistency