Researchers studying video material being produced for children measure its immersiveness by placing a TV tuned to a selected commercial channel in the same room. How often does the distracting TV succeed in stealing the attention of the child? You can try this. If necessary, you can develop an app to do something similar on the same phone which supports the game.

Thanks @Srinivasan Ramani for your suggestion. My experiment is related to business management, so I'm looking for a self-reporting scale.