How to Capture Synchronization in Triads in One Single Measure: Development of the AMPC Measure and an Associated Significance Test

Interpersonal synchronization is a concept often studied in psychology. Whereas most research focuses on dyads, triadic systems such as family triads warrant increased attention. A crucial challenge in taking a triadic view on synchronization is how to quantify it, since a statistical measure that captures the level of triadic synchronization in one value, while discarding dyadic synchronization only, is lacking so far. The current paper therefore investigated three existing measures that show potential to capture triadic synchronization and proposes two novel ones. We also present a significance test that allows to investigate whether the observed triadic synchronization in a triad is stronger than can be expected by chance, while accounting for potential auto-dependence in the data. By means of a simulation study, we tested (1) how the measures react to different potential synchronization patterns; (2) the Type I error rate and the power of the significance test. The results showed that only one measure, i.e., the newly proposed adapted multiplication of pairwise correlations (AMPC), can effectively capture triadic synchronization, while discarding dyadic synchronization. We then applied the AMPC measure to intensive longitudinal data on attachment-related measures in families, showing that AMPC can detect meaningful triadic synchronization in empirical data.