What is the significance of the 2 - 3 sigma limit in statistical measurements?

[S.P.P]

Hi all,

I'm reading some journal articles and in many of them, when they quote a result, they add 'at the 2 to 3 sigma limit.' I realize this is some sort of statistical quantity, but what exactly does it mean, and do lower values of sigma mean better results?

Thanks

 

[Mindscrape]

It is related to the standard deviation of a Gaussian distribution. Typically, 68.4 percent of the data will fall within one standard deviation. Essentially what it means is that if you get data that is two or three sigma away, there is a good chance you screwed up.

Look at rules for normally distributed data.
http://en.wikipedia.org/wiki/Standard_deviation

 

[OlderDan]

Hi all,

I'm reading some journal articles and in many of them, when they quote a result, they add 'at the 2 to 3 sigma limit.' I realize this is some sort of statistical quantity, but what exactly does it mean, and do lower values of sigma mean better results?

Thanks

σ (sigma) is the symbol used for the standard devition, which is a measure of the variability of data in some set or the width of some probability distribution. Smaller σ means less variability (data points are closer together). For the normal distribution, which is a probability density function, 68% of the probability is within one σ of the mean and 95% is within 2σ. If you randomly pick one data point from a set that is normally distributed, there is a 95% probability that its value is within 2σ of the average value.

 

[MasterEngAPEE]

Gausian Distribution simplified means that if you measure the same thing many times and make a vertical bar for each measurement value you can get, the bar graph will have a bell shape centered around the actual measurement. The width compared to the height of the bell shaped graph can be described with a statistical measurement called standard deviation or sigma. Basically, this is a measurement of how much the measurements vary around the actual value.

Now three sigma is 3* the standard deviation, which statistically mean that 99.73% of the time a measurement is made it will be within 3*the standard deviation of the actual value. It is thus a way to compare how good the measurement method is.

In similar ways 2 sigma means within 95% of the actual value and 6 sigma means as close to always as is resonable to ever need.