related question Which is the best visualization for contingency tables?

My application area is computational advertising (observational data; looking at e.g. CTR Click Through Rate - proportion of user clicks per number of impressions [user views] presented).

I am interested in plotting (for a non-technical audience) the dependence of CTR on various other variables, for example hour of day.

The issue I have is that there may be a wide range of frequencies - so plotting the actual observed CTR (as a bar plot) for a given factor level may not be very meaningful. I have toyed with putting confidence bands, but I don't find this very intuitive either, i.e. that the wide band somehow should be used to mentally 'adjust' for the actual CTR plotted.

I have seen (but have no experience of) mosaic plots but they seem to have the same problem - you have to mentally discount the size according to the Pearson residual colour.

What I was thinking was maybe to use a Bayesian? approach- namely to use some average CTR (and associated variance?) as prior and then plot the posterior estimates.

Does this make any sense? If so could someone point me at the relevant methodology.

What alternatives are there?

  • $\begingroup$ There's no obligation to colour the tiles of a mosaic plot by residuals. $\endgroup$ – Nick Cox Jan 26 '17 at 10:28
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    $\begingroup$ A square root scale often helps with counts. I've used that on the graphs discussed in my answer to the cited thread. $\endgroup$ – Nick Cox Jan 26 '17 at 10:31

If I understand your problem correctly you have tables with very unequal marginal distributions. Maybe you can go old-school and standardize the table:

Yule, G. Udny (1912). "On the Methods of Measuring Association Between Two Attributes". Journal of the Royal Statistical Society. 75 (6): 579–652. doi:10.2307/2340126

There are some examples and an implementation in Stata here: http://maartenbuis.nl/software/stdtable.html


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