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Another Thing I Thought I’d Never Have to Explain on Econbrowser: Confidence Interval

Summary:
Mr. Steven Kopits takes issue with the Harvard School of Public Health led study’s point estimate of (4645) and confidence interval (798, 8498) for Puerto Rico excess fatalities post-Maria thusly: Does Harvard stand behind the study, or not? That is, does Harvard SPH believe that the central estimate of excess deaths to 12/31 is 4645, or not? Does it stand behind the confidence interval, or not? Is there still a 50+ probably that the death toll comes in over 4600? If there is, then the people of PR need to start looking for the 3,250 missing or the press needs to assume PR authorities are lying. Those are the implied action items. Or should we just take whatever number HSPH publishes in the future and divide by 3 to get a realistic estimate of actual? Let’s show a detail of the graph

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Mr. Steven Kopits takes issue with the Harvard School of Public Health led study’s point estimate of (4645) and confidence interval (798, 8498) for Puerto Rico excess fatalities post-Maria thusly:

Does Harvard stand behind the study, or not?

That is, does Harvard SPH believe that the central estimate of excess deaths to 12/31 is 4645, or not? Does it stand behind the confidence interval, or not? Is there still a 50+ probably that the death toll comes in over 4600? If there is, then the people of PR need to start looking for the 3,250 missing or the press needs to assume PR authorities are lying. Those are the implied action items.

Or should we just take whatever number HSPH publishes in the future and divide by 3 to get a realistic estimate of actual?

Let’s show a detail of the graph previously displayed (in this post):

Another Thing I Thought I’d Never Have to Explain on : Confidence Interval
Figure 1: Estimates from Santos-Lozada and Jeffrey Howard (Nov. 2017) for September and October (calculated as difference of midpoint estimates), and Nashant Kishore et al. (May 2018) for December 2017 (blue triangles), and Roberto Rivera and Wolfgang Rolke (Feb. 2018) (red square), and Santos-Lozada estimate based on administrative data released 6/1 (large dark blue triangle), end-of-month figures, all on log scale. + indicate upper and lower bounds for 95% confidence intervals. Orange triangle is Steven Kopits estimate for year-end as of June 4. Cumulative figure for Santos-Lozada and Howard October figure author’s calculations based on reported monthly figures.

The middle paragraph shows a misunderstanding of what a confidence interval is. The true parameter is either in or not in the confidence interval. Rather, this would be a better characterization of a 95% CI:

“Were this procedure to be repeated on numerous samples, the fraction of calculated confidence intervals (which would differ for each sample) that encompass the true population parameter would tend toward 95%.”

In other words, it is a mistake to say there should be a 50% probability that the actual number will be above the point estimate. But that is exactly what Mr. Kopits believes a confidence interval means. He is in this regard incorrect. From PolitiFact:

University of Puerto Rico statistician Roberto Rivera, who along with colleague Wolfgang Rolke used death certificates to estimate a much lower death count, said that indirect estimates should be interpreted with care.

“Note that according to the study the true number of deaths due to Maria can be any number between 793 and 8,498: 4,645 is not more likely than any other value in the range,” Rivera said.

Once again, I think it best that those who wish to comment on estimates should be familiar with statistical concepts.

Menzie Chinn
He is Professor of Public Affairs and Economics at the University of Wisconsin, Madison

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