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

• S.P.P
In summary, "at the 2 to 3 sigma limit" refers to the standard deviation of a Gaussian distribution. It is a measure of the variability of data, with smaller sigma indicating less variability. For normally distributed data, 68% of the data falls within one sigma of the mean and 95% falls within two sigma. A measurement within three sigma is considered to be a good indication of the actual value.
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

Last edited:
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

S.P.P said:
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.

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.

## What does 2 - 3 sigma mean?

2 - 3 sigma refers to a statistical concept known as the standard deviation, which measures the spread of data around the mean. It is often used in scientific research to determine the reliability and confidence of experimental results.

## How is 2 - 3 sigma calculated?

To calculate 2 - 3 sigma, you first need to find the mean (average) of the data. Then, calculate the difference between each data point and the mean, square these differences, and find the average of all the squared differences. Finally, take the square root of this average to find the standard deviation.

## What does a 2 - 3 sigma range represent?

A 2 - 3 sigma range represents a range of data that falls within 2 - 3 standard deviations from the mean. This means that about 95% of the data points will fall within this range, and only about 5% of the data points will fall outside of it.

## Why is 2 - 3 sigma important in scientific research?

2 - 3 sigma is important in scientific research because it helps determine the reliability and significance of experimental results. If the results fall within this range, it is more likely that they are accurate and not due to chance or random variation.

## Can 2 - 3 sigma be used to determine causation?

No, 2 - 3 sigma cannot be used to determine causation. It can only show a correlation between variables, but it does not prove that one variable causes the other. Other factors and variables must be considered to establish causation in scientific research.

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