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 obtained during the experimental study. - Contains the code of all software used during the experimental study: 1) Order control tool (software used to manually play picking commands, measure order completion times and manually register picking errors and dropped items); 2) Sensor control (Python code run on a Raspberry Pi to control infrared sensors and write timestamps of sensor interruptions into a database); 3) VR Model (Unity model for displaying the VR).