I've been asked to analyse the distribution of a set of data, essentially a single column of random samples of a physical parameter which cannot be negative. The standard deviation that I usually calculate assumes that data are normally distributed, which in this case cannot be true.
Since I'm used to being asked to provide the standard deviation and mean of a dataset as a measure of the errors, I'd like to know whether there is an easily calculated parameter for a more appropriate distribution that would fulfil the same purpose?
I apologise if this question is ill-posed; I am not a statistician by training.
With many thanks,
Loruschorus
Best Answer
Standard deviation is a measure that can be calculated on any set of data regardless of its actual distribution. It is simply a measure of value dispersion in relation to the data set's mean.
Any normality assumption to which you are referring usually is only a concern when doing statistical inference. For instance, if you need to test whether a sample standard deviation is 'large' or if two sample standard deviations are the same, then the underlying distribution of the data is important.
So, if all you need for your analysis is to do is compute the standard deviation, then the standard deviation formula you have been using is sufficient.