Hello everyone,
Type II error is an error that occurs when you accept the null hypothesis when in the real sense, it is false. It accepts the results of a test as negative when they are positive or false (False negative). Peter Donnelly explains this type of error with a scenario of HIV test results. A test for HIV is 99% accurate. Let’s say in a group of a million, 900,000 people test negative. Because the test is 99% accurate, out of the 900,000 people, there is the probability that close to 9,000 people are positive but tested negative.
In the scenario above, most people only think about the false positive. We hope that just in case a medical test (HIV, Cancer, or any other terminal illness) is positive, we are lucky enough that it is a false positive. Donnelly, in his video, explains how hard it is to get a false positive compared to a false negative because the chances of getting the disease by itself are low. None of the errors are better than the other; I believe it depends on the statistical decision being made. For example, in the scenario above, although we seem to be more concerned about a false positive, a type II error is worse. It means you have the disease, and you might end up finding out when it is too late.
In the case of the lousy statistician, the lawyers or the jury would have noticed the argument was wrong if they had the right decision-making skills. Therefore, I still think statistical thinking is vital for the general population, and as I said in my previous discussion, it is something everyone should learn to do correctly. Because it helps reach the correct conclusions and identify when statistical errors are being made.
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