Supporting data for Atkinson, Mills, and Smith manuscript. Languages differ in their complexity. One possible explanation for this observation is that differences in social factors influence linguistic complexity: languages which are typically used for esoteric communication in small-scale "societies of intimates" exhibit greater complexity as a result of the communicative contexts in which they are employed. We use the techniques from referential communication studies across three experiments to assess the effects of two social group factors thought to influence the esotericity of communication --- group size and amount of communally-shared knowledge --- on the brevity and transparency of linguistic conventions. While we find the more exoteric contexts initially result in longer labels and a greater reliance on more literal descriptive terms, there is no effect of either factor in the longer term, and so no support for the idea that the structure of linguistic conventions is shaped by the groups in which they develop. This dataset contains the labels produced by the participants in Experiments 1 and 2 and the GLMM model outputs.ams_labels.csv: description data from Experiments 1 and 2 ams_key.txt: key for ams_labels.csv