Careful With Trailing Averages

January 1st, 2022
covid-19
With covid, it is common for people to look at seven day trailing averages. For example, the MA Covid Dashboard has "the seven day average of percent positivity is 18.42%". While this isn't exactly wrong, it's not a good fit for a rapidly rising number. Here's how it's usually presented:

This gives the impression that 18.4% is the number for 12/30, but it's clearer to think of it as a number for 12/27. That way it represents our best guess of how things were on the 27th by looking three days into the future and three days into the past to average out fluctuations:

On the other hand, these variations are clearly not noise; it's a weekly cycle. People are much more likely to test positive on the weekend than during the week:

Monday 89%
Tuesday 85%
Wednesday 96%
Thursday 93%
Friday 113%
Saturday 172%
Sunday 145%

(Average ratio by day of week comparing daily test positivity to the seven day average of test positivity centered on that day.)

This makes sense: weekend testing will include a larger proportion of people who are getting tested because they are sick.

Instead of trying to average this pattern away, we can use it, scaling each day by the inverse of its average departure from the 7d average:

This gives us a metric that is as responsive as the daily numbers with less of the day-by-day variation from from measuring different populations on different days. It's not perfect, you can see it getting things wrong by treating Thanksgiving and Christmas like normal days, but it's pretty good.

When case numbers are changing quickly, this responsiveness is helpful. Using the most recent seven days we'd get a test positivity of 18%, but the most recent weekday-adjusted daily number is 23% (+25%).

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