In view of the uncertainty in containing the coronavirus, scientific findings and analyzes are considered an anchor to assess the situation around the pandemic and possible countermeasures. However, calculations with relative frequencies and conditional probabilities in particular often harbor the risk of being misinterpreted.
The most recent example is the infographic from the Robert Koch Institute (RKI), which is intended to help understand the test results of rapid antigen tests for SARS-CoV2. The graphic contrasts two scenarios: the targeted testing of people with corona symptoms and the testing of people with and without symptoms in mass tests.
Mass tests yield significantly more false positive results
For both cases, the RKI assumes a population of 10,000 people. In targeted testing, 1,000 people are infected with corona, in the scenario for the mass test there are five infected. The graphic then shows how many test persons received a positive or a negative test result.
The mass tests show: Only 0.01 percent of the test persons receive a negative test result, but are actually infected with Corona. In contrast, the risk of being mistakenly considered infected is 98 percent.
With targeted testing, the risk of a false negative test result increases to 2.2 percent. In contrast, the scenarios for false positive test results differ much more clearly. Here the risk drops to 18.4 percentage points – and is thus almost a fifth lower than in the mass tests.
“The unspoken message of this scenario comparison can hardly be overlooked: You should only be tested if there is a concrete suspicion or typical symptoms occur. But is the situation really that clear? ”Ask the unstatistics experts.
The classification of rapid tests
The proportion of five infected people per 10,000 tested in the mass test scenario is hardly likely in view of the current incidence values. Instead, an unreported number of 100 infected people among 10,000 mass tests would be more realistic. In this case, the risk of incorrectly receiving a negative test result is 0.2 percent, so it hardly increases noticeably.
“On the other hand, however, the effects are considerable,” explain the experts from the unstatistics. Accordingly, the risk of being mistakenly considered positive is 71.2 percent. The risk drops by more than a quarter due to the higher proportion of infected people – and the results in the mass test are no longer as bad as in the RKI example.
For the experts in unstatistics, the case is an example of why relative frequencies in particular are repeatedly misunderstood: “This is because calculating with conditional probabilities is very abstract”. Natural frequencies, on the other hand, made it easier to deduce the correct probability of illness from the test results.
Regardless of the circumstances, they still reduce the uncertainty about your own state of health – especially if the test result is negative. But even in this case, there is no one hundred percent protection. Because an infection can occur even a few days after a negative test result.
With the “Unstatistics of the month” The Berlin psychologist Gerd Gigerenzer, the Dortmund statistician Walter Krämer and RWI Vice President Thomas Bauer question both recently published figures and their interpretations every month.
You can find all “non-statistics” on the Internet at www.unstatistik.de. The book “Why fat doesn’t make you stupid and GM maize doesn’t kill – About the risks and side effects of unstatistics” is published by Campus Verlag.