Referential communication provides a sophisticated way in which animals can communicate information about their environment. Previously, research demonstrated that honey bee stop signals encode predator danger in their fundamental frequency and danger context in their duration. Here, we show that these signals also encode danger in their vibrational amplitude. Stop signals elicited by the more dangerous predator, the large hornet (Vespamandarinia) had significantly 1.5-fold higher vibrational amplitudes than those elicited by the small hornet predator (Vespavelutina). We measured the freezing vibrational response thresholds, and show that these natural signals exceed response thresholds. Finally, with artificial playbacks of the vibratory stop signal, we demonstrate that these signals referentially encode the danger that foragers experience at food source. Stop signals elicited by the larger and significantly more dangerous predator (V.mandarinia) were significantly 1.4-fold more inhibitory than stop signals elicited by the smaller and less dangerous predator (V.velutina). This dataset contains all of the data used for the statistical analyses reported in this paper and to generate the figures.