Explained: Sigma

[Tank]

Explained: Sigma

It's a question that arises with virtually every major new finding in science or medicine: What makes a result reliable enough to be taken seriously? The answer has to do with statistical significance -- but also with judgments about what standards make sense in a given situation.

The unit of measurement usually given when talking about statistical significance is the standard deviation, expressed with the lowercase Greek letter sigma (σ). The term refers to the amount of variability in a given set of data: whether the data points are all clustered together, or very spread out.

In many situations, the results of an experiment follow what is called a "normal distribution." For example, if you flip a coin 100 times and count how many times it comes up heads, the average result will be 50. But if you do this test 100 times, most of the results will be close to 50, but not exactly. You'll get almost as many cases with 49, or 51. You'll get quite a few 45s or 55s, but almost no 20s or 80s. If you plot your 100 tests on a graph, you'll get a well-known shape called a bell curve that's highest in the middle and tapers off on either side. That is a normal distribution.

The deviation is how far a given data point is from the average. In the coin example, a result of 47 has a deviation of three from the average (or "mean") value of 50. The standard deviation is just the square root of the average of all the squared deviations. One standard deviation, or one sigma, plotted above or below the average value on that normal distribution curve, would define a region that includes 68 percent of all the data points. Two sigmas above or below would include about 95 percent of the data, and three sigmas would include 99.7 percent.

So, when is a particular data point — or research result — considered significant? The standard deviation can provide a yardstick: If a data point is a few standard deviations away from the model being tested, this is strong evidence that the data point is not consistent with that model. However, how to use this yardstick depends on the situation. John Tsitsiklis, the Clarence J. Lebel Professor of Electrical Engineering at MIT, who teaches the course Fundamentals of Probability, says, "Statistics is an art, with a lot of room for creativity and mistakes." Part of the art comes down to deciding what measures make sense for a given setting...

If you are ever going to understand statistics this is one of the most important concepts/terms. Have a read. If you want to 'blag' at stats just know the term  

[pytheas]

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"Why Most Published Research Findings Are False" is a food for thought paper on this topic

http://www.plosmedicine.org/article/info%3Adoi%2F10.1371%2Fjournal.pmed.0020124

Also, many real life data are not gaussian, parametric or normal.

Indeed abi, abi who?  abi-normal

lots of tests to check your "normality" distribution and the power of your argument

But ultimately as my favorite prof said  a near infallable way to step securely on the ground  goes:

"if you need stats to see the effect, its probably not relevant"

[Ecurb Noselrub]

IQ tests are usually interpreted in terms of standard deviations or sigmas.  I've seen articles that describe a standard deviation as 15 points, so one standard deviation above the average (100 by definition) is 115, while 2 SD's is 130, 3 is 145, etc.  According to the bell curve distribution in the OP, it would take an IQ of 140 or so to get into the top 2%.  I'm interested - who here qualifies?