Two pairs of bivary results (ui, vi) and (uj, vj) that respond (5) or (6) are considered concordant or discordant; That is, the ui and vi are either larger or the two smaller than uj and vj. Thus, the perfect positive (negative) correlation by Spearman`s Rho corresponds to the perfect concordance (Diskordanz); that is, concordant (discordant) pairs (ui, vi) and (uj, vj) for all 1≤i<j≤n. Since ui and vi are linearly related, the Pearson correlation can be applied, resulting in p⌢=1, indicating a perfect correlation. However, the data clearly do not indicate a perfect match; In fact, the two judges hardly agree. Kappa is a way to measure compliance or reliability and correct the number of times assessments may coincide by chance. Cohens Kappa,[5] which works for two evaluators, and Fleiss`Kappa,[6] an adaptation that works for any fixed number of evaluators, improve the common probability by taking into account the amount of concordance that one might expect by chance. The original versions had the same problem as the common probability, as they treat the data as nominal and assume that the evaluations are not natural; If the data do have a rank (ordinary measurement level), this information is not fully taken into account in the measurements. There are several operational definitions of "inter-board reliability" that reflect different views on what a reliable agreement between evaluators is. [1] There are three operational definitions of the agreement: Weinberg R, Patel YC.

Simulated intraclassical correlation coefficients and their transformations into z. J Stat Comput Simul. 1981; 13(1):13–26. There are several formulas that can be used to calculate compliance limits. The simple formula given in the previous paragraph, which works well for samples greater than 60,[14] is as follows: comparing (1) and (4), it is clear that ρ⌢ is really the Pearson correlation when applied to the rankings (qi, ri) of the initial variables (ui, vi). Since rankings are only about the order of observations, the relationships between rankings are always linear, regardless of whether the initial variables are linearly related. Thus, not only does Spearmans Rho have the same interpretation as Pearson correlation, but also applies to nonlinear relationships. Example 1. Suppose that ui and vi are perfectly correlated and follow the nonlinear relationship ui=vi9. Let us continue to think that vi follows a standard normal distribution N (0, 1) with an mean 0 and a variance 1.

Next, the product-moment correlation is: Konishi S. Normalizing and variable transformations for intraclassical correlations. Ann Inst Stat Math. 1985; 37 (1):87-94. Villages de crèches alpha[16][17] is a versatile statistic that evaluates the concordance between observers who categorize, evaluate or measure a certain amount of objects in relation to the values of a variable. It generalizes several specialized conformity coefficients by accepting any number of observers, applicable to nominal, ordinal, interval and proportional levels, capable of processing missing data and being corrected for small sample sizes. To see it, indicate μu (μv) and σu2 (σv2) the mean (of the population) and variance (population) of the variable ui (vi). . . .