I have a dataset that is generated via binning of a continuous variable. The bin sizes are custom and uneven but they are non overlapping and cover the whole relevant part of the number line.
A lot of the distribution comparison tests I know assume that the distributions that are being compared are continuous, is there a rigorous way to do this comparison, and say with a certain confidence that the histograms are different?
Let’s say I measure a continuous variable with a certain cadence. Over the first time window I will have N_1 observations of this variable. These N_1 observations of the real valued variable, for data engineering and computational reasons, are converted to a histogram, so instead N_1 variables I have k bins that are fixed and each having a certain number of counts that add up to N_1. Similarly for the second time window, I have k bins each containing certain number of counts that add up to N_2. I would like to be able to say, for example, the variable I am measuring “on average” have increased