Darkness triggers Dishonesty

A new study shows that dim lighting makes it seem as no one is watching us and it triggers moral transgressions in many people.
 
The research showed that when people are concealed away from others, they feel as if they are wearing hoods of some sort or that they are in hiding, making it more likely for them to commit bad behavior or commit criminal activity.
 
It went on to say, like Hide and Seek when we are children, it is like no one can see us even if we are are sitting out in the open. The same can be said for adults when they are in a dimly light or dark room.
 
They did an experiemnt with 84 college students. They were placed in a room, one dark, one well lit. In it, was two envelopes, one with ten dollars, the other empty. They were asked to pick two numbers that added up to 20 from each of 20 matrices. For each pair of numbers correctly chose, they got to keep 50 cents from that 10 bucks.
 
Result: The participants scored the same in both rooms, well lit and dark. In the dim room though, they cheated more than their counterparts. In the well lit room it showed 7.8 matrices correctly, while the dim or dark room showed 11.5 correct responses, resulting in a $1.85 difference.
 
They they did another experiment to prove their theory. This time students would wear sunglasses and of course without, while playing a money game. In the game, they would have to allocate a part of $6 to a random stranger. Those wearing the shades acted more selfishly, giving less than their counterparts, with an average of $1.81. While those in nothing gave about $2.71.
 
As a result, it showed that those who participated with sunglasses felt a bigger sense of anonymity than those with none. For instance, those wearing them were more likely to agree on average with statements like: I was anonymous during the study, my choice went unnoticed.
 
They were too, disagreeable with statements like: I was watched during the study; and others were paying attention to how I behaved during it.
 
It showed that dim lighting has a negative influence on people causing bad reactions, thoughts, and behaviors.
 
The question though is how high the error in this experiment can there be? The difference of $1 in this small scale stands out, but would it make a difference if it was a larger group or more money was used?