The wide variation in scores over time for high scoring restaurants is fine, when you think about the generating mechanism. There are a series of possible offences, and the high scoring restaurants will be doing many of them at some time, but not necessarily at every visit. So for each there will be a binomial probability at each visit. There will also be different points for each, building in further variability, so probably the variance is a function of the mean at least and probably mean squared. It would be interesting to fit the data and see what the relationship is.

Excluding the closed restaurants might make sense, if your goal is assessing the likelihood that an open restaurant will have a poor inspection record. It's like properly ignoring Monty's opened door in the Monty Hall problem.

I'm not sure I agree with using box plots for your first chart (though I can't tell if you're recommending it for this situation, or just pointing it out as an example).

All it tells me is that all the restaurants graded A have scores grouped towards the low end of the range, which is the definition of a grade A. Hence, you're showing the correlation and distribution that is implicit in the scoring mechanism. The more interesting question is what is the distribution and proportion of restaurants with each score/grade. (That said, group "4" is interesting to compare here.)

But I do agree with the use of box plots for the comparison of other categorizations.

Sage: great comment. I'd not have put up the first boxplot if Group 4 weren't there. It serves to show that Group 4 is a mixture of everything else. Also, I want to say that data analysts should always prepare this chart to check for any data errors; if something is miscoded, you can see right away there is an outlier on this chart.

Derek: One misstep in the original article is to have removed Group 4 without comment. It is a best practice to always state (in a footnote) if the data has been altered.
If we can distinguish between those restaurants closed for health reasons from those closed for other reasons, then it is better to include the former group in the analysis, as you're implying.

Ken: that's an interesting way of thinking about a model for this. I was getting at a more basic point, which is that any grading system that fluctuates so much from year to year is bound to be quite worthless... is it measuring some transient thing (as you suggested) or something fundamental about each restaurant?

In your explanation of box plots (I think) you've omitted to explain what the whiskers represent. Are they min & max in this case?

Which software did you use to generate the box-plot charts at the bottom?

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