Weekly Deaths have a Normal Distribution

You can use '#-of-standard-deviations-from-the-mean' to detect improbable events

When looking at data there is a center of data and it is often estimated by the mean value. The standard deviation measures how spread out the other values are from the mean. When you have a normal distribution, then you can use the number of standard deviations from the mean, or the Z score, to detect improbable events.

Anything beyond 3 standard deviations from the mean is considered so extreme as to require follow-up analysis. In this previous Substack, I mentioned how a standard deviation of week-specific death is about 3.7% of the mean value — so that you can detect improbable events using a deficiency, or an excess, of 11% either way.

Any single week with over 11% excess death — or one with deaths over 11% below what is expected — would be improbable. Here is the analysis that shows weekly deaths are normally distributed, justifying the use of the number of standard deviations:

The blue dots are actual weekly death counts for 313 weeks in a row in the US (2014-2019). The light-shaded trend line relates those deaths to the Z score. Because dots lined up so well (R-square of 0.959), death counts are approximately normal, and using standard deviations to evaluate death counts is appropriate.

Here is the same graph with notes in it:

The highest weekly death (top right dot) was the beginning of 2018 when there was severe flu, and the death count was 4 standard deviations above the mean of all 313 weeks. Because it was only 1 out of 313 weeks observed, the probability of a week with death that is that high is under one-third of 1%.

A four-standard-deviation increase in weekly death is a really big deal.