# Best way to define where the data is no longer normally distributed

I thought I'd first give a brief description of what my data is so that it's easier to understand what my problem is. I have a dataset which goes as follows:- binned mass differences of compounds vs binned pearson correlation coefficients vs frequency

I've calculated the differences of the masses of compounds and then calculated the pearson correlation coefficient values of those mass differences to see whether some of those mass differences derive from compounds that are of the same parent compound (i.e. fragmented compounds etc). I did this by using some other data that I won't talk about here but it's sound. Now, I want to look at the frequency of the mass differences across the pearson correlation coefficient bins to see at which point of the correlation coefficient do we begin to see an increase in mass differences that derive from the same compound and to compare datasets obtained from different instruments and biological matrices etc to see whether this makes a difference. From plotting the maximum value of frequency against the pearson correlation coefficient bins, I get this graph here:-

Going up is the frequency and going across is the pearson correlation coefficient bins (there's 40 bins that stretch from -1 to +1, meaning they go up in 0.05, like -1 to -0.95, -0.95 to -0.9 etc). As you can see, the data is normally distributed for pretty much half the data (up until 20, which represents the bin -0.05 to 0 etc), but it reaches a point where it begins to go back up and it no longer follows a normal distribution (around 30). Is there a way of somehow using the distribution of data to define a cut off point as to when the data no longer follows normal distribution? So like plotting a Gaussian curve onto the data and looking at the point at which the data deviates from the curve etc. Hope this makes sense.

Edit: I don't know if this would be a good way of doing it, but if we used the first half of the data and mirrored it to generate a mean and std etc, is it possible to somehow then define an equation for that normal distribution curve and somehow use that to see which points from the original data (the points in the second half) deviates from the normal distribution and where this begins?

• Your correlations are bounded whereas a Gaussian (normal) isn't. Looking bell-shaped isn't sufficient to define a normal distribution. Why not just focus on identifying a change in slope? Apr 13, 2015 at 13:51
• Yeah I was contemplating on doing just that, could you write that as an answer so I can accept it? Cheers Apr 13, 2015 at 14:23
• I don't think I want to say more! Apr 13, 2015 at 14:25

• Probably it would: the mode (i.e. $\mu$) may not correspond. Anyway you can give it a try and see if the two distibutions are very shifted. Apr 13, 2015 at 13:59