# Agreement Matrices

December 2, 2020

The problem of comparing the match of the dies has an extensive history in the behavioural sciences. Applications include analysis of recognition and confusion data, similarity judgments and relationships with social networks. The mantle index is the best known index of agreement because of its relationship to the correlation. However, as Hubert (1978, 1987) and Brusco (2004) have found, the mantle index can be strongly influenced by a small number of elements in the dies. Other agreements based on sampling elements within lines or columns can also be used to examine matrix chords. A second point concerns the significance tests under the matrix agreement and the availability of software for the completion of these tests (Glerean et al., 2016). In some cases, it is possible to calculate an exact p value by creating the total distribution of all possible index values that can be achieved. This is achieved by maintaining one of the two fixed dies and the value of the index for all n! Swaps of lines and columns for the second matrix. Calculating an exact p value is ideal if computable.

It is difficult to determine a precise limit of the n value for which an exact p value is achievable, as it depends on the hardware platform, software and the time the analyst is willing to wait for the p value. As a general guideline, the calculation load of listing all permutations, once the value of n is about 12 or more, reduces the probability of searching for an exact value of p. Therefore, in addition to a full enumeration program, it is useful to have a program capable of bringing together a p value based on a large number of trampled permutations. Another objective of our document is to provide MATLAB software for calculating exact and approximate p values for the Mantel and Within Row gradient indices. The following two tables show how these dies work. The third dimension, service, is not used in this example. In our second example, Q – 3 visual confusion matrixes are used, based on data originally collected by Cho, Yang and Hallett (2000), and then analyzed by Brusco (2002) and Brusco and Steinley (2012). The data refer to the detection of structured materials No. 20 at different distances: the A 1, A 2 and A 3 dies correspond to distances of 8.2, 15.5 and 22.9 m respectively. Because confusion matrixes were already standardized in lines, there was no need to apply additional standardization. The results of the analysis of the confusion matrixes of structured materials are presented in Table 5. It is immediately clear that the significance tests associated with the mantelca.m and triadca .m programs are all significant at the level α .00005.

This high degree of statistical significance in relation to our results in example 1 is largely due to the greater number of stimuli (n -20 in example 2 vs. No. 9 in example 1). As importance has grown, statistical significance is almost assured, and so it is differences in the strength of the indexes of agreement that contribute to differences. The match between the three S dies is generally strong, whether the size of the mantle or gradient is used in the row. The lowest adequacy is between the A 1 and A 3 dies, of which (No. 1 (A 1, A 3) – 0.5561) and (A 1, A 3) – 0.6156). This is not surprising, as the A 1 and A 3 dies are stops over the shortest or longest distances. When measuring the concordance with the mantle index, the measured correspondence between the average distance and the longest distance (A 2, A 3) – 0.8351) is much greater than the correspondence between the shortest distance and the average distance (A 1.A 2) – 0.7252). However, using the match measurement within the series, the chords are very similar, with the agreement between the shortest distance and the average distance (No. 2 (A 1, A 2) – 0.7488) being slightly better than the agreement between the average distance and the longest distance (A 2.A 3) – 0.7459).

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