After the initial surge in coronavirus cases in the United States in March, the seven-day average of new daily cases fell to just over 20,000 in early June. That decline became central to Vice President Pence’s argument that the country wasn’t seeing a new wave of infections last month — but since June 9, the average has trended back up. Higher and higher, in fact, with the seven-day average passing 50,000 this week.

President Trump argues that the increase is a function of testing. It has been pointed out repeatedly that this isn’t the case, including by The Post nearly a month ago. As more data comes in, Trump’s repeated insistence on this point makes it more and more obviously wrong. That’s particularly true since states that have seen increases in cases are more likely to also see increases in coronavirus-related deaths — deaths that are not occurring simply because the patients were tested.

Much of the national surge is a function of increased case totals in a handful of states. In fact, the 10 states that have seen the biggest increases in their own averages since June 9 now account for nearly 28,000 additional new cases per day — most of the 31,000 case-per-day increase in the national average. The eight states, plus the District of Columbia, that have seen the biggest downward shift since June 9 are seeing more than 1,400 fewer cases per day than they did on that date.

Relative to June 9 (and using data through July 7), here’s how the daily average of new cases has changed in those 19 locations and nationally.

Again, Trump’s claim is that this is a function of more testing. Test more, find more cases, see numbers rise. And, again, that’s not true. Yes, there has been increased testing in the 10 states where the average number of cases has increased the most. But in the majority of places where case totals have dropped, testing has gone up as well.

More important is the rate of positive tests.

Let’s say, theoretically, that you increased testing in a state from 100,000 a day to 300,000 a day. Perhaps you were catching 10,000 new cases a day when testing 100,000 people, a number that goes up to 15,000 when you test 300,000. There’s a 50 percent increase in new cases, which might be a function of more testing. But notice that while 10 percent of tests came back positive originally (10,000 out of 100,000), now only 5 percent do (15,000 out of 300,000).

If, instead, you increased from 100,000 tests to 200,000 and saw positive tests increase from 10,000 to 30,000, you’re seeing a jump from 10 percent positive to 15 percent. A greater density of positive results might be a function of where you’re testing — and it might be a function of a spreading virus.

In the 10 states with the biggest increases in the daily case average, the rate of positive tests has gone up across the board. In some cases, such as Arizona and Florida, the increase has been substantial. In the eight states, plus the District of Columbia, that saw the biggest decreases in the daily average since June 9, the rate of positives has uniformly decreased.

Again, those drops in the rate of positive tests occurred in some states where the level of testing went up (including in Connecticut, Illinois, Massachusetts and Virginia), along with the District of Columbia. What’s more, in the states where the number of new cases increased the most, the rate of increase in new cases consistently exceeded the rate of new tests. Meaning that even as testing expanded, the rate of new cases expanded faster.

The big question that has accompanied the recent surge in cases is the extent to which we might see an increase in coronavirus-related deaths. So far, the picture is muddy, in part because of the lag time between tests being confirmed positive and a patient’s death. But in seven of the 10 states where new cases increased the most, so did the seven-day average in the number of new deaths. In four of those states, the increase was over 10 percent.

By contrast, only one state among those seeing the biggest decreases in new cases saw an increase in deaths: Virginia.

This, too, isn’t entirely clear-cut. Testing more people may mean catching more people who are dying of the virus, whose deaths might not have been attributed to it previously. But the more likely explanation, particularly given the spread across multiple states, is that this number reflects an actual increase in coronavirus-linked deaths.

Particularly when we compare the change in new cases and new deaths since June 9 across states. The correlation isn’t perfect, but it’s clearly the case that states that saw increases in new cases were also more likely to see increases in new deaths.

This makes sense, of course. If the virus is spreading, which it is, more people are getting sick. And while the mortality rate from the virus is down, that still means that people will die.

The data from July 7 indicate that, for the first time in three months, the seven-day average of new deaths was up more than 12 percent day-over-day.

That may not be a permanent trend, and we hope that it is not. But it is also not a function of testing.