In this paper the author addresses some issues concerning statistical inference when assessing agreement between two observers, in case of data measured on either categorical or continuous scale. Firstly, the paper deals with the problem of assessing agreement between two raters while the ratings are given separately on a 2-point nominal scale, and the properties of a modified version of Cohen’s kappa statistic (Sinha et al., 2006) are considered. Secondly, simulation studies concerning testing statistical hypotheses in the continuous case are presented.