Semi-automated parts-to-picker systems are becoming more popular in order picking, making efficient rack designs for fast searching and picking more important. Virtual reality (VR) using modern head-mounted devices (HMD) is a promising technology for the human-centred planning of order picking at single racks. However, state-of-the-art HMDs come with several limitations. For evaluating the usability of HMDs, it is of interest whether these limitations lead to different workload and measured times in VR compared to a real environment. An experimental setup consisting of a real rack and an equally sized virtual representation (using the HTC Vive HMD) has been developed for a randomized controlled study with 112 participants and 10 professional order pickers. This dataset contains the raw data from the experiments as well als the code for the statistical analysis.