# How to find statistical significance between binned data?

I have created a histogram of velocities for thousands of moving objects. I have bin sizes of 1 based on object weight. So bins 1-20, for weight 1gram to 20 grams. So that's the "x-axis".

The y-axis, or height of the bins is based on averages of velocities for these objects. I take all the 1 gram objects and find their average velocity, and that is the height of the 1 gram bin. Then the same for all the 2 gram bin, find their average velocity and plot that as the bin height.

My question is, how can I find if there is a significance between the bins. First of all, finding significance between 20 bins is a LOT of comparisons, is there an easy way to do that?

But even if I can just compare 2 or 3 at a time that would be useful. So I can say the 1 gram objects have a significantly different velocity than the 2 gram objects.

• If you have a lot of data, you should avoid binning them. Consider using a non-parametric smoother to show the bivariate relation between these data. And consider also that tons of data circumvents the need for traditional testing: you are getting closer to simply showing people what your study is capable of producing with descriptive statistics. It is more powerful than tests. Commented Nov 18, 2016 at 18:27