Standard Deviation is a very useful concept if used with care and so I'm going to write a couple more blogs to help you understand more about how it is used in practice. The first one is how to interpret a standard deviation figure.

Probably a very useful way of interpreting a standard deviation is that, assuming that your underlying data is sampled from a Gaussian distribution (for these purposes a normal distribution), you expect approximately 68% of the values of your distribution to lie within one standard deviation of the mean of your distribution, and you expect approximately 95% of your distribution to lie within 2 standard deviations of the mean. Also by extension you can assume that 27% of your population will lie between one and 2 standard deviations from the mean, and 5% will lie more than 2 standard deviations from the mean.

So for example, imagine if your a distribution where the mean is 20 and the standard deviation is 5.

That means that the range within one standard deviation of the mean is 20 + or - 5 so between 25 and 15, and the range within 2 standard deviations of the mean is 30 to 10.

Therefore if you then take another reading the odds are 19 in 20 (95%) that the reading will be between 30 and 10.

Similarly this also helps you understand why a lower standard deviation also implies a 'tighter' or more defined distribution. If the standard deviation of the above distribution was actually 2.5 not 5 then 95% of the values of the distribution would like between 20 + or - (2 * 2.5) = 25 to 15. This is the same range within which only 68% of the values of our original distribution would lie.

This can also be shown pictorially. The illustrations at the bottom of this post illustrate this point for you.

Don't worry I will write a follow up blog post to give you some more detail on Gaussian distributions but for these purposes we are assuming that your data is sampled from a normal distribution.

That's it for this week's SPSS blog.