What does 3-sigma confidence mean in astronomy measurements?

[cepheid]

In this statement:

"[WMAP data suggest] a lower limit on reionization of z > 6.7 with 3$\sigma$ confidence."

What is the meaning the of the 3-sigma part in this context? See also my other thread here:

https://www.physicsforums.com/showthread.php?t=261118

Based on the responses there, I still don't quite understand what this sigma business is all about.

 

[Vanadium 50]

What they mean is if the true value were 6.7, and you performed a large number of different measurements, one would expect about 1 in 400 of them to fluctuate to a result at least as extreme as what was measured.