The gold standard for discovery is 5-sigma

To physicists, the gold standard for a discovery is what they call a "5-sigma" bump, where sigma is a measure of bumpiness known as a standard deviation. A bump that high means that the odds are less than 1 in 3.5 million that it was produced by chance.

A "sigma event" is an event that takes place when the observation is at least 3 standard deviations away from the mean.

P( Z < -3) + P(Z > 3) 
= 0.001349898 + 0.001349898
= 0.002699796

4 sigma
2 * P(Z < - 4) = 6.334248e-05

5 sigma
2 * P(Z < -5) = 5.733031e-07

6 sigma
2 * P(Z < -6) = 1.973175e-09

From <http://5sigmabump.tumblr.com/>