Obscuring Truth: PHMDC's Foggy Statistics

Each week, Public Health of Madison and Dane County's (PHMDC's) publishes its Data Snapshot, a summary report that presents a select view of how COVID-19's impacts on Dane County.

The November 11th Snapshot, which encompasses data for the two weeks from October 25th to November 7th, indicates that:

"Percent positivity was 3.4% and an average of 3,232 tests were conducted per day."

Within this Snapshot, PHMDC provides neither the actual number of COVID tests performed nor cases of infection detected. They mention only that "percent positivity was 3.4%," making it difficult for anyone to estimate the number of cases actually detected. In fact, PHMDC creates the impression that 3.4% of Dane County was infected in the last two weeks. That impression is false.

Some quick math allows us to determine how many tests were done and how many cases of COVID detected. Let's start with the tests.

How Many Tests Were Performed?

Since there are 14 days in this period, we can figure the approximate total number of tests administered by multiplying the average number of tests PHMDC cites by 14:

3,232 tests per day X 14 days = 45,248 tests

For PHMDC to report a whole number like 3,232 means that they almost certainly rounded up or down. We don't know the exact average. PHMDC doesn't tell us. However, the average must lie between 3,231.5 and 3,232.499999.

The total COVID tests given from October 25th to November 7th must therefore be between 45,241 and 45,254.

The actual number of tests performed is basic information that PHMDC should include in its Snapshots, but doesn't. This leaves those reading the Snapshot unsure of exactly what the underlying facts about the number of tests are.

How Many Cases of Infection Were Detected?

To derive the number of COVID cases detected, we take the total number of tests we initially calculated and multiply it by the "3.4% positivity rate" cited in the November 11th Snapshot:

45,248 tests X 0.034 positivity = 1538.432 cases

If we round positivity out to a single digit, we can only say that the actual positivity is between 0.0335 and 0.0344999999. We know this because if the positivity rate were any higher, PHMDC would have to say it was 3.5; if the positivity rate were any lower, PHMDC would have to say 3.3. Let's dig in a little deeper to understand better.

The lower bound on the number of cases is the minimum number of tests in the 14-day period times the smallest percentage that could be rounded up to 3.4%:

45,241 X 0.0335 = 1515.5735 cases

However, you can't have a fraction of a case, so the number of cases cannot be lower than 1,516. If it were 1,515 then the positivity rate would be 1,515 / 45,241 = 0.03348732 and the positivity rate would have been reported as 3.3%.

Similarly the upper bound on the number of cases is the maximum number of tests in the period times the largest percentage that could be rounded down to 3.4%:

45,254 X 0.0344999999  = 1561.2630 cases

Since you still can't have a fraction of a case, though, the number of cases cannot be more than 1561. If it were 1562 then the positivity rate would be 1562 / 45,254 = 0.03451628 and the positivity rate would have been reported as 3.5%.

The number of cases PHMDC uses in its own calculations, then, must be between 1515 and 1561. That's about all we could say about the number of tests and cases based on the PHMDC Snapshot. So...

Between 1,515 and 1,561 COVID cases were detected in Dane County from October 25th to November 7th

Why would PHMDC essentially bury this data? Why would they fail to state the exact number of tests performed and cases of infection detected?

Ambiguity, vagueness, and uncertainty increase anxiety and fear in a population. PHMDC should go out of its way to state facts plainly in its Snapshots. Fogginess is not a virtue when relaying a statistical narrative. Being imprecise and vague when reporting facts results in lack of trust. It makes one wonder whether things are being purposely obscured and what the motives may be for doing so. We will take at motives further in a future article.

For now, make it a point to talk to your Dane county supervisor, Madison alder, and PHMDC director Janel Heinrich about putting basic underlying facts like the exact number of tests and the exact number of cases detected in future Snapshots. Tell them that PHMDC should be straight with the public about the basic facts informing its Snapshot narrative.