As the name implies, descriptive statistics provides information about your data. We’ve already seen this with such things as averages and standard deviations.
But of course, you can go well beyond this—basically, by using the Bayes’ theorem. This approach is common in analyzing medical diseases, in which cause and effect are key—say for FDA (Federal Drug Administration) trials.
To understand how Bayes’ theorem works, let’s take an example. A researcher comes up with a test for a certain type of cancer, and it has proven to be accurate 80% of the time. This is known as a true positive.
But 9.6% of the time, the test will identify the person as having the cancer even though he or she does not have it, which is known as a false positive. Keep in mind that—in some drug tests—this percentage may be higher than the accuracy rate!
And finally, 1% of the population has the cancer.
In light of all this, if a doctor uses the test on you and it shows that you have the cancer, what is the probability that you really have the cancer? Well, Bayes’ theorem will show the way. This calculation uses factors like accuracy rates, false positives, and the population rate to come up with a probability:
- Step #1: 80% accuracy rate × the chance of having the cancer (1%) = 0.008.
- Step #2: The chance of not having the cancer (99%) × the 9.6% false positive = 0.09504.
- Step #3: Then plug the above numbers into the following equation: 0.008 / (0.008 + 0.09504) = 7.8%.
Sounds kind of out of whack, right? Definitely. After all, how is it that a test, which is 90% accurate, has only a 7.8% probability of being right? But remember the accuracy rate is based on the measure of those who have the flu. And this is a small number since only 1% of the population has the flu. What’s more, the test is still giving off false positives. So Bayes’ theorem is a way to provide a better understanding of results—which is critical for systems like AI.
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