In order to navigate in a social environment, a robot must be aware of social spaces, which include proximity and interaction-based constraints. Previous models of interaction and personal spaces have been inspired by studies in social psychology but not systematically grounded and validated with respect to experimental data. We propose to implement personal and interaction space models in order to replicate a classical psychology experiment. Our robotic simulations can thus be compared with experimental data from humans. Thanks to this comparison, we first show the validity of our models, examine the necessity of the interaction and personal spaces and discuss their geometric shape. Our experiments suggest that human-like robotic behavior can be obtained by using only correctly calibrated personal spaces (i.e., without explicit representation of interaction spaces and therefore, without the need to detect interactions between humans in the environment).