circular {eba}R Documentation

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

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.

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

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

[Package eba version 1.5-2 Index]