Measuring and making decisions for social reciprocity

Social reciprocity may explain certain emerging psychological processes likely to be founded on dyadic relations. Although indexes and statistics have been proposed to measure and make statistical decisions regarding social reciprocity in groups, these tools were generally developed to identify association patterns rather than to quantify the discrepancies between what each individual addresses to his or her partners and what is received from those partners in return. Additionally, social researchers' interest extends beyond measuring groups at the global level because dyadic and individual measurements are also necessary for proper descriptions of social interactions. This study is concerned with a new statistic for measuring social reciprocity at the global level and with decomposing that statistic in order to identify which dyads and individuals account for a significant part of asymmetry in social interactions. In addition to a set of indexes, some exact analytical results are derived, and a way of making statistical decisions is proposed.