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The probability (ranging from zero to one) that the results observed in a study (or results more extreme) could have occurred by chance. Convention is that we accept a p value of 0.05 or below as being statistically significant. That means a chance of 1 in 20, which is not very unlikely. This convention has no solid basis, other than being the number chosen many years ago. When many comparisons are bing made, statistical significance can occur just by chance. A more stringent rule is to use a p value of 0.01 ( 1 in 100) or below as statistically significant, though some folk get hot under the collar when you do it.

A short article on the power of chance might help.