How to add percentages

Percentage calculation

The problem with large-scale tests.
A test (for example a disease test) gives the correct answer in 99% of the cases, but the wrong answer in 1% of the cases. In Germany (80 million inhabitants) 100,000 are sick, all people are tested. Then the following results:
  • Of the 100,000 sick, 99,000 are recognized as sick, 1,000 are mistakenly believed to be healthy.
  • Of the 79,900,000 healthy people, 1%, i.e. 799,000 people, are mistakenly believed to be sick.

    Conclusion: A total of 99,000 + 799,000 people (ie 898,000 people) are declared sick - of these, however, only 99,000 (ie about 11%) are really sick.

To distinguish one speaks of Error of the first kind (the percentage of sick people mistakenly believed to be healthy) and dated Error of the second kind (the percentage of healthy people who are mistakenly considered sick): In our example we assumed that both errors are 1%, but in practice these percentages will be different - the only thing that applies is: no test is infallible, it always occurs Errors of the first and second kind).
To assess whether a test makes sense, the (of course only estimated) ratio of the number x of sick people to the number y of healthy people plays an essential role.
(In our example, 1% of y was significantly greater than 99% of x - in such a case the test makes little sense; especially if the testing itself should have possible side effects.)