In this video, explore the difference between descriptive and Bayesian statistics.
- [Instructor] Previously in this course, I have described what is known as descriptive statistics. Descriptive statistics, as the name implies, provides facts about your data. Some of those facts could include measures such as medians, means, variance, and standard deviations. You can then use these facts about your data to make estimates at a known confidence level. For example, you might think that most of your customers live within a 25-mile radius, plus or minus three or four miles, with about 95% confidence. You might also be wondering, what else is there? It turns out there's a lot, an entirely different branch of statistics.
Let me give you an example of the type of analysis that you can do. Let's assume that you take a test for the flu and that it comes back positive. The test has the following characteristics, and these characteristics will allow you to assess the overall accuracy of the test. The first is that the test returns the correct result 85% of the time. So if you have the flu, 85% of the time it it will say yes indeed, you have it. However, the test does identify healthy individuals as having the flu 10% of the time, so that's what's known as a false positive.
Also, there is a base rate, or background rate, where about 1% of the population actually has the flu. So given all of that information, what is the probability that you do have the flu after your test came back positive? We can analyze the data using something called Bayes' rule where you combine the accuracy, false positives, and base rate to find the result. So if 1% of the population has the flu and the test is 85% accurate but there's a 10% false positive rate, then a positive test means that the probability you have the flu is 7.91%.
And to give you a preview of what's going to happen in future movies, the 1% base rate, that is, the population that has the flu, is the cause of the actual probability of you having the flu being so low. Now of course, I do want to emphasize that this calculation is based on the single test. Once you perform more tests with different levels of accuracy, then you can be more certain of your result.
- Distinguish between the mean, median, and mode.
- Describe the relationship between variance and standard deviation.
- Identify a nondirectional hypothesis.
- Point out the difference between COVARIANCE.P and COVARIANCE.S.
- Explain correlation.
- Analyze Bayes’ rule.