Want to know to what degree political demonstrations produced results in elections? Track the rain. The rain? It actually makes a beautiful example of what's termed an instrumental variable. Read Dan Kopf's excellent Quartz summary or the full article by Andreas Madestam, Daniel Shoag, Stan Veuger, and David Yanagizawa-Drott from Harvard and Stockholm Universities.
Whether it rains at protest locations can scarcely have anything directly to do with ultimate election results, but it unquestionably relates to turnout for each demonstration. If the size of turnout relates to election results, then the rain should, statistically (if not causally), relate to them as well. "If the absence of rain means bigger protests, and bigger protests actually make a difference, then local political outcomes ought to depend on whether or not it rained [on protest days]...As it turns out, protest size really does matter."
"Fifty-eight percent of national variation in hospital readmission rates was explained by the county in which the hospital was located," announce Jeph Herrin et al. in Community Factors and Hospital Readmission Rates, published in 2014 in Health Services Research. Sound odd to you? After all, for most readmission studies the percent explained is in single digits. Being able to account for 4 or 5% of the variation translates to an ability to assess individual risk that can meaningfully aid in clinical decisions. Even Harlan Krumholz and his team of 17 researchers and statisticians, the ones whose predictive models underpin the national readmission penalty system, have usually explained only 3-8%. And those models have taken into account about 50 input variables.
It turns out that Herrin et al. took their data on 4,073 hospitals and broke it down by 2,254 counties. There were almost as many counties as hospitals themselves. And many counties contained only a single hospital.
Now, suppose the authors had divided the 4,073 hospitals into, say, 4 groups defined by region, and found that the 4 groups had sizeable differences in readmission rate. That would have been a meaningful way to summarize the data. Even with somewhat more groups -- say, one for each of the 50 states -- that might have been meaningful, though the data would have been spread pretty thin for some states. But to "explain" differences using 2,254 groups? It's not a far cry from simply listing the readmission rates of all 4,073 hospitals and claiming victoriously to have "explained" 100% of the variance in the hospital-to-hospital rate. Sounds like a feat for Captain Obvious. It's tautology. With such an approach, any apparent "explanation" of the outcome is empty.
One reason why this matters a great deal is that, to the extent that some geographic factor is considered responsible for this outcome, hospital performance will no longer be. So if county legitimately explained 58% of the variance, then hospital performance, it might be argued, couldn't account for more than 42%. This is the incorrect conclusion that was reported in unqualified fashion by news outlets such as Becker's Hospital Review.
The article by Herrin and colleagues makes contributions in other ways, of course, but the chief findings are very misleading. Watch for dialogue, in Health Services Research or elsewhere, on how to interpret the results. The upshot should be quite a bit more nuanced and moderated than what we've seen above. And if you're interested in the role of socioeconomic factors in hospital readmission, you'll find some eye-opening results out of Missouri at Reinforced Care, Inc.