Sure, you can't show that it's true for everybody but having a result like: "only 0.1% chance that it occurred by random if 2/3 of the population reacts this way and way less if it's half of the population" is very nice result to have.
If something occurs for 16 randomly chosen people (or even 15/16 or 14/16) you are virtually certain it occurs for very significant part of the population which is often the goal of the study - to justify further research.