There is a standard characteristic for measuring the degree of compliance in a group of evaluators r (with r > 2), and this characteristic is called Fleiss` kappa, k, [32, 31], often used in the statistics used. However,  showed that Kappa had its weaknesses. As we will see below, it is of a very passive nature. This is why we looked at other features of the evaluation agreement such as the Cochran Q test, the test statistics of the χ2 fit test of the assumption of an equal distribution of active notations, the average correlation coefficient and the coefficient of variation that can be calculated from the correlation matrix that contains the correlation coefficients of the scoring results of all the evaluator pairs. However, our calculations and comparisons have convinced us that these properties are not useful for conformity assessment. But we still used other statistics, which are explained below. The poet speaks to a tree as if they were their friend or lover: the small detail and domestic life of the spokesman here may represent the biggest problem of deforestation, climate agreements and an overall lack of esteem for trees. The poem ends on a triumphant note, supported by a full rhyme between “submerged” and “Elm” at the end of the poem: “Mastering the leaves. / The tree will remain. We tell him “no.” / Deep root by the bandage, Elm. The concept of kappa is based on pairwise comparisons and has its roots in the one-sided analysis of variance. Fleiss` Kappa can be expressed in different equivalent forms that highlight different aspects of the nature of this statistical characteristic. The first form is indicated in Eq (1).
(1) p0, the share of observed ratings being in line with the expected share of credit ratings. The formula for p0 is given by (2) Here eij nij / n, nij being the number of trees to which the same mark (“0” or “1”) was assigned by evaluators i and j. Eq (2) shows one aspect of kappa nature: p0 is an average closely related to concordance in pairwise comparisons. For the second term pe,  set (3), p = N1 / nr and N1 being the total number of characters “1” indicated in the experiment. The second form that Fleiss`kappa can take is (4), sj being the number of marks “1” of the tree j. The term sj (r – sj) is a good choice for characterizing concordance, as it uses extreme values in the cases sj = r / 2 and sj = 0 or sj = r. . .
Posted Oct 11th, 2021