There is a prevailing belief that interruptions using cellular phones during face to face interactions may affect severely how people relate and perceive each other. We set out to determine this cost quantitatively through an experiment performed in dyads, in a large audience in a TEDx event. One of the two participants (the speaker) narrates a story vividly. The listener is asked to deliberately ignore the speaker during part of the story (for instance, attending to their cell-phone). The speaker is not aware of this treatment. We show that total amount of attention is the major factor driving subjective beliefs about the story and the conversational partner. The effects are mostly independent on how attention is distributed in time. All social parameters of human communication are affected by attention time with a sole exception: the perceived emotion of the story. Interruptions during day-to-day communication between peers are extremely frequent. Our data should provide a note of caution, by indicating that they have a major effect on the perception people have about what they say (whether it is interesting or not . . .) and about the virtues of the people around them.