Simple question about certainty/confidence in astronomy

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The discussion clarifies the meaning of "3-sigma" in the context of WMAP data regarding reionization, indicating a statistical confidence level. A 3-sigma confidence implies that if the true value is 6.7, approximately 1 in 400 measurements would yield results as extreme as the observed data. This level of confidence is commonly used in scientific measurements to assess the reliability of results. Understanding sigma levels is crucial for interpreting the significance of astronomical findings. The explanation emphasizes the importance of statistical analysis in confirming scientific hypotheses.
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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.
 
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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.
 

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