When tests are performed in medical scenarios, as well as many other everyday tests, the results are not always 100% accurate. Occasionally, tests will determine one thing when, in fact, the reality is that the opposite is true. This will result in either false positives and false negatives.
|False Positive||When the thing being tested for is mistakenly shown to be present when, in fact, it's not present.||A person is told that they have cancer when, in fact, they do NOT have cancer.|
|Fale Negative||When the thing being tested for is mistakenly shown to be absent and, in fact, it is present.||A home pregnancy test could tell a woman that she's NOT pregnant when, in fact, she actually is pregnant.|
How common are errors like this? It depends largely on the tests because different tests have varying levels of accuracy and sensitivity.
Most home pregnancy tests claim to be 99% effective at detecting pregnancy, which means that 99% of the time, these tests accurately detect a pregnancy when it's present and when the test has been conducted properly.
However, what if the woman does the test too early? Tests done too soon can reduce the effectiveness to around 90%, which means that the probability of a false negative--where the test says that she's not pregnant when really she is--raises to about a 10% likelihood, which is a significant amount. It would be better to have the false negative be closer to something like 1%, as the test claims.
False positives are typically more rare. Because these home pregnancy tests detect particular hormones, it's tough for the test to detect those hormones when they aren’t really there. Therefore, when a woman is not pregnant, a test will show this in about 98% of those cases, which means the false positive rate (a not-pregnant woman getting a positive pregnancy test result) is about 2%.
Of those 600 women, 90% would be correctly told that they were pregnant. These would be women who are going to have a baby and know it. The false negatives would be women who are pregnant and don't know it, so that's 60 out of 1000.
Of the 400 women who aren't pregnant, 98% will be correctly told, making 392 who will be correctly told that they're not pregnant and eight who will be incorrectly told that they are pregnant.
Combined, that's 68 out of 1,000 women here that have the incorrect result.
Source: Adapted from Sophia tutorial by Jonathan Osters.