Data collection has become an increasingly important problem in robotic manipulation, yet there still lacks much understanding of how to effectively collect data to facilitate broad generalization. Recent works on large-scale robotic data collection typically vary many environmental factors of variation (e.g., object types, table textures) during data collection, to cover a diverse range of scenarios. However, they do not explicitly account for the possible compositional abilities of policies trained on the data. If robot policies can compose environmental factors from their data to succeed when encountering unseen factor combinations, we can exploit this to avoid collecting data for situations that composition would address. To investigate this possibility, we conduct thorough empirical studies both in simulation and on a real robot that compare data collection strategies and assess whether visual imitation learning policies can compose environmental factors. We find that policies do exhibit composition, although leveraging prior robotic datasets is critical for this on a real robot. We use these insights to propose better in-domain data collection strategies that exploit composition, which can induce better generalization than naive approaches for the same amount of effort during data collection. We further demonstrate that a real robot policy trained on data from such a strategy achieves a success rate of 77.5% when transferred to entirely new environments that encompass unseen combinations of environmental factors, whereas policies trained using data collected without accounting for environmental variation fail to transfer effectively, with a success rate of only 2.5%. We provide videos at http://iliad.stanford.edu/robot-data-comp/.