More on that work on age adjustment. I keep asking myself where is it in the Stats curriculum do we teach students this stuff? A class session focused on that analysis teaches students so much more about statistical thinking than anything we have in the textbooks.
I’m not sure. This sort of analysis is definitely statistics, but it doesn’t fit into the usual model-estimate-s.e. pattern of intro stat. Nor does it fit into the usual paradigm of exploratory data analysis which focuses on scatterplots. If we were to broaden exploratory analysis to include time series plots, that would work—but still this would miss the point, in that the usual focus would then be on the techniques of how to make the graph, not on the inquiry. From a conceptual point of view, the analysis I did is not so different from regression. It’s that lumping and splitting thing. And then there’s the age adjustment which is model-based but not in the usual way of intro statistics classes.
There’s an appeal to starting a class with examples such as this, where sample sizes are huge so we can go straight to the deterministic patterns and not get distracted with standard errors, p-values, and so forth.
When I taught intro stat, I did use various examples like this. Another one being the log-log graph of metabolism of animals vs. body mass, where again the point was the general near-deterministic relationship, with the variation around the line being secondary, and estimates/s.e./hyp-test not coming in at all). Deb and I have a bunch of these examples in our Teaching Statistics book.
It’s not hard to cover such material in class, but there does seem to be a bit of a conceptual gap when trying to link it to the rest of statistics, even at an introductory level but at other levels as well. In our new intro stat course, we’re trying to structure everything in terms of comparisons, and these sorts of examples fit in very well. But where the rubber meets the road is setting up specific skills students can learn so they can practice doing this sort of analysis on their own.
Kaiser follows up with a more specific question:
Also, on a separate topic, have you come across a visual display of confidence intervals that is on the scale of probabilities? It always bugs me that the scale of standard errors is essentially a log scale. Moving from 2 to 3 and from 3 to 4 are displayed as equal units but the probabilities have declined exponentially.
My reply: I like displaying 50% and 95% intervals together, as here:
P.S. Regarding the age-adjustment example that Kaiser mentioned: it just happens that I posted on it recently in the sister blog:
Mortality rates for middle-aged white men have been going down, not up.
But why let the facts get in the way of a good narrative?
It’s frustrating to keep seeing pundits writing about the (nonexistent) increasing mortality rate of middle-aged white men. It’s like Red State Blue State all over again. Just makes me want to scream.