Confirmation bias (or myside bias) is a tendency for people to prefer information that confirms their preconceptions or hypotheses, independently of whether they are true. People can reinforce their existing attitudes by selectively collecting new evidence, by interpreting evidence in a biased way or by selectively recalling information from memory.
Confirmation bias refers to a type of selective thinking whereby one tends to notice and to look for what confirms one's beliefs, and to ignore, not look for, or undervalue the relevance of what contradicts one's beliefs. For example, if you believe that during a full moon there is an increase in admissions to the emergency room where you work, you will take notice of admissions during a full moon, but be inattentive to the moon when admissions occur during other nights of the month. A tendency to do this over time unjustifiably strengthens your belief in the relationship between the full moon and accidents and other lunar effects.
Ironically, we know that the full moon does influence behavior in humans as well as tides and other waterways. See the work of Sensitive Chaos, or study Russell's Solalign System of non-linear multi-modal sensory integration. In the timber industry, during a full moon, certain types of trees in must be stamped as "full moon" wood upon harvest, because the sap has risen up the tree, making it weaker and wetter. Timber cannot be floated down stream in a full moon very easily, because the moon causes the water to rise- pushing the logs to the outer banks where they tend to run aground.
With this sort of knowledge, when you hear a statistician crunching numbers and telling you that "the full moon phenomenon" of increased crime and odd human behavior is an illusion of 'confirmation bias' you may consider him to be an irrational skeptic. Other studies have shown that there are behavioral alterations connected to the full moon that will influence crime statistically.