| > The difference between deep red and orange is a lot bigger than the difference between dark blue and slightly less dark blue. That may be true, but is it better? Does the scatterplot underemphasize differen densities, or does the density plot overemphasize them? I think the scatterplot is more intuitive. There are 21 equal steps between 0 and 100% black. Two points are twice as dark as one, four points are twice as dark as two. Darker means more, lighter means less. Compare that to shifting from blue to red. Does the shift from orange to red indicate the same density difference as the shift from blue to orange? To decide you need to consult the color scale. The scatterplot is intuitive, and requires no scale. > The hexbin has lower spatial resolution, it's true, but I'd argue that the spatial resolution you get in a scatterplot is illusory. It doesn't reflect the underlying probability distribution, only the particular sample. The spatial resolution of a scatterplot represents empirical reality. Each point corresponds to a single observation, with no probability distribution implied or imposed. The density plot, in contrast, imposes a probability distribution, which may or may not reflect the true distribution of the population. The larger the bins, the more likely the displayed pattern is 'illusory'. |
tl;dr; I'm a Bayesian, you are a Frequentist (at least with regards to plotting).