Calculation of simple rates for new COVID cases and deaths has revealed that mask mandate states have performed no better than states in which masks have been voluntary.  Advocates for the mandate are looking for a confounding variable that — when properly controlled — will reveal the heroic performance of mask mandates as life-saving actions taken by enlightened governments.  Almost certainly, they will settle on population density as the knight in shining armor designated as Defender of the Mandate.

Already, some are beginning to contend that high population density is the main cause of COVID diffusion.  Once this is controlled for, they claim, the effectiveness of the mask mandate will be established. 

This is the hope.  What follows is a dose of reality.

This table positions each state's cumulative COVID death rate according to its level of population density.

Each red dot is an individual state, and the red line running through them all is a regression line calculated to indicate the trend.  From zero out to roughly 300–500 people per square mile, there is no discernible evidence that population density has any effect at all.  On the other hand, from that point on, there is a much closer association between the two variables: the few states with very high population densities do have correspondingly high COVID death rates.  Based on this, the best hypothesis might be that there is a density threshold below which density doesn't matter but above which it does.  We will look at the five boroughs of more densely populated New York City.

Manhattan is the heart of the city and the most densely populated part.  The other four boroughs have much lower population densities but still greatly surpass the densities in individual states.

The following table includes a population density figure for each of the five boroughs (next to last column).

The top row in a table appearing at a different URL provides COVID death rates for the five boroughs.

The first table gave the population density of each borough; the second provided their COVID death rates.  Here is a list of the five boroughs in descending order of population density.  Data on COVID death rates are given in deaths per 10,000 rather than deaths per 100,000 so that the numbers compare directly with those for states at the beginning of this report.

When plotted on a graph, no suggestive pattern emerges — nothing to indicate that the COVID death rate increases with population density.

Manhattan has a population density that is twice as high as any other borough, yet its COVID death rate is much lower than that of any other.  Staten Island is by far the least densely populated of the boroughs, yet its COVID death rate surpasses two of the other four.

Population density varies a lot between boroughs.  It is eight times higher in Manhattan than it is in Staten Island, even twice as high as in Brooklyn, the second most densely populated borough.  If population density is responsible for variations in COVID death rates, these magnitudes of difference should be sufficient to reveal it.  Yet there is zero evidence that more heavily populated boroughs have experienced higher COVID death rates.

On the other hand, COVID death rates are higher in these five densely populated boroughs than in the much less densely populated states.  However, the influence of population density on COVID death rates appears to diminish with higher density levels.  Increases in death rates certainly don't keep pace with what the graph of states would suggest if the regression line were extrapolated out to, say, 75,000 people per square mile.

An analysis of smaller territories ought to more effectively identify any relationship between population density and COVID death rate.  We believe that contagion is governed by very local interactions ("six feet to stop the spread"), so the relevance of population density ought to increase when we take things down to the local level.  City boroughs are more local than states, but let's go one step farther: ZIP code areas in a single borough. 

Let's look at the density data for the twelve ZIP codes of Staten Island.  Staten Island is a reasonable choice because its number of ZIP codes is manageable, and also because it appears to have generally elevated death rates.  The shape, size, and position of Staten Island ZIP code areas is shown in the lower left of this New York City map.  The map, incidentally, is showing how COVID death rates vary from one ZIP code to the next.

In the following table, the ZIP codes for Staten Island are listed in descending order of population density.  Staten Island ZIPs have fairly elevated density levels relative to all the others in the New York metropolitan area.

And here is a simple graph to visualize these data:

There is no tendency for the more densely populated ZIP code areas to have higher COVID death rates.  Furthermore, their death rates fall in a range similar to that of the other four boroughs — even though those boroughs have average population densities many times higher than Staten Island's.

This study finds nothing to indicate that density and death rate are related.  Where is the scientific evidence that controlling for population density will reveal the effectiveness of mask mandates?

Mask mandates are authoritarian and cost people time, money, and convenience.  Not just a few people; everybody in the country.  One can argue over the significance of these disadvantages for the people, but it would be dishonest to deny them altogether.  This being so, those who impose the disadvantages have an obligation to present scientific evidence that their mandate works.

From now on, merely asserting that population density raises COVID transmission must be dismissed as unscientific if unaccompanied by credible data specifying how much.

Image: qimono via Pixabay, Pixabay License.

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