Social reciprocity may explain certain emerging psychological processes, which are likely to be founded on dyadic relations. Although some indices and statistics have been proposed to measure and make statistical decisions regarding social reciprocity in groups, these were generally developed to identify association patterns rather than to quantify the discrepancies between what each individual addresses to his/her partners and what is received from them in return. Additionally, social researchers are not only interested in measuring groups at the global level, since dyadic and individual measurements are also necessary for a proper description of social interactions. This study is concerned with a new statistic for measuring social reciprocity at the global level and with decomposing it in order to identify those dyads and individuals which account for a significant part of asymmetry in social interactions. In addition to a set of indices some exact analytical results are derived and a way of making statistical decisions is proposed.