Status of Weighted Agreement Statistics Between Two Raters in Ordinal Data Affected by Sample size and Number of Categories

The aim of this study is to introduce weighted inter-rater agreement statistics used in ordinal scales, compare weighted agreement statistics along with the Spearman correlation coefficient and reveal their status of being affected by the sample size and number of categories. For this purpose, data for different sample sizes and number of categories were produced for the cases when there is no relationship or when there is low, medium, or high relationship between the two raters, and the aforementioned weighted agreement statistics were calculated. It can be said that Cohen’s kappa, Scott’s π, and Krippendorff’s alpha coefficients provide similar results with the correlation coefficients, and they get values very close to the correlation coefficient value in the B-P agreement statistics. However, it can be said that Gwet’s AC2 statistic, especially for a category number of 3, differs from the correlation coefficient value in cases where there is no/low correlation between the raters, and a moderate level of agreement can be mentioned between the raters, albeit by chance. While investigating the agreement between two raters in ordinal scales, it is recommended to be careful in cases when only the number of categories is three and to use Gwet’s AC2 agreement statistics. In other cases, it can be said that the concepts of agreement and relationship can be used interchangeably with peace of mind