#Sigma symbol how to

However, how to use this yardstick depends on the situation. 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. Two sigmas above or below would include about 95 percent of the data, and three sigmas would include 99.7 percent. 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.

The standard deviation is just the square root of the average of all the squared deviations. In the coin example, a result of 47 has a deviation of three from the average (or “mean”) value of 50. The deviation is how far a given data point is from the average. 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. You’ll get quite a few 45s or 55s, but almost no 20s or 80s. You’ll get almost as many cases with 49, or 51. But if you do this test 100 times, most of the results will be close to 50, but not exactly. 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. 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. The unit of measurement usually given when talking about statistical significance is the standard deviation, expressed with the lowercase Greek letter sigma (σ).

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.

Sigma symbol