Over the entire month of March, while testing at among the lowest rates in the country, Oklahoma officials identified 565 cases of coronavirus. 

On April 1, following the arrival of enough chemicals to process 10,000 tests, the state changed its approach dramatically. The state went from six test sites to 14. It dropped the requirement that patients be of a “vulnerable population.” No longer did it take a doctor’s permission to get tested. Any adult with symptoms would qualify. 

Oklahoma’s total shot to 988 in just three days. And still the state’s testing rate remained stubbornly low compared to some parts of the country.

Just how low was unclear Monday as officials announced that estimates of testing levels as of last week were massively undercounted.

Oklahoma’s experience highlights some fundamental facts to emerge from last week’s surge in coronavirus testing nationally: more testing makes a huge difference; the advent of more test kits has failed to eliminate the wide gap between some states and others; and even counting tests consistently is tough to do.

The uneven testing rate has left public health and medical professionals without a clear picture of how coronavirus is spreading.

"We've quickly devolved into an unknown," said Kacey Ernst, an infectious disease epidemiologist at the University of Arizona. "We don't have a pulse of how much transmission is out there."

Data compiled by the COVID Tracking Project, an independent website run by journalists, show that disparities persist despite a doubling of daily testing last week.

Ranking which states have the worst rates is hard because some are not consistently reporting every time they get a negative result. That means the public has an incomplete picture of how many people have been tested overall.

On Monday, Oklahoma officials said they have succeeded in capturing large numbers of negative results private labs had previously failed to report. The state now estimates having tested more than 13,000 tests, placing it at about one-fourth New York's level of testing per capita as of last week.

Texas more than doubled the number of tests it reported last week but still only reported 55,764 results. That’s a rate of 192 tests per 100,000 people, compared to a rate of nearly 1,400 per 100,000 in New York state.

Only three states -- New York, Louisiana and Washington -- have matched or exceeded the testing rate of South Korea, whose testing procedures experts hold out as a model for the world. 

Tests in those states also are far more likely to come back positive than in much of the country, suggesting that testing is occurring there largely in response to people showing up at healthcare providers with symptoms.

Experts say testing should be applied as a surveillance measure across states, to pinpoint hotspots early enough to keep people with no symptoms from spreading the virus. 

Some states that have yet to see high rates of disease managed to achieve much more aggressive testing. Alaska and New Mexico were able to test over 700 per 100,000 residents. That put them both in the Top 10 for testing rates nationally as of Friday.

But many other states with low rates of COVID-19 detection remain near the bottom for testing.

Some didn’t have labs to evaluate results; others did. Many ran into shortages of test kits and test chemicals; some shortages were deeper than others. The time it takes to get a test result has ranged from hours to weeks depending on where it’s performed.

States also vary in who they’ll test. Some states have required a doctor’s sign-off. Others make testing available to anyone with symptoms.

Oklahoma officials acknowledged last week that their numbers under-represented the extent of the virus’ spread. Shelley Zumwalt, a spokeswoman for the Oklahoma Department of Health, said the state was among the last to have a confirmed case. As a result, it was among the last to ask for help from the federal government, joining a glut of states desperate for supplies.

Another impediment: the remoteness of much of Oklahoma’s population. About a third of the state’s residents live in rural areas. 

“It's not so much that people don't have it, it's that we don't have resources in those rural areas to test people,” Zumwalt said.

In Georgia, where a February funeral is thought to have sparked an outbreak that engulfed the small town of Albany, testing remains sparse.

Some labs in Georgia are so overwhelmed, it can take 10 days for a patient to get test results. Medical workers conducting the tests are short on gear to protect themselves when collecting swabs for testing.

On Tuesday, Governor Brian Kemp announced a plan to partner with universities to ramp up testing. Once that plan is fully implemented, labs will be able to process 3,000 tests per day. At that rate, it will take one week to match the total done statewide since the pandemic started.

Not knowing how many people are infected in each state handcuffs policy makers deciding who needs to stay home, where additional medical resources are needed and which parts of the economy are going to be shut down. Failure to test widely and consistently also limits the ability of public health officials to find and quarantine infected residents, disease researchers said.

“If you could at least test everyone who wants a test, that would be better than worse,” said Jeffrey Townsend, a professor of biostatistics at Yale School of Medicine. “I think that is a point we should aim for.”

Matt Wynn is a data journalist on the USA TODAY investigations team, focusing primarily on public and consumer safety. Contact him at mwynn@usatoday.com or @mattwynn