Statistics can be a frustrating class for a lot of students because the rules often seem arbitrary and the formulas seem to come out of nowhere. You can stay on top of the work if you stay focused on the big picture. Here are two key ideas I stress to my Stats students at the beginning of every year:
- Statistics deals with uncertainty. Unless we have the entire population in front of us (a very rare occurrence!), we can only make educated guesses about the data and the likelihood of particular events. In every other math class you’ve ever taken, you can find the exact answer. In statistics, you can only make predictions or calculate probabilities. All of the formulas we learn in Statistics are used to help us describe how the data varies and to make estimates for how likely an event is.
- Statistics is not intuitive. In most of your math classes, you can usually tell if the answer you’ve gotten is reasonable or not. In Statistics, your best guess for what a particular probability should be may be way off the actual answer. That means if you have set up a problem incorrectly, you don’t get any feedback to help you. You have to learn which formula to use in which situation and then trust your calculator. That can be very scary!
My favorite example of how statistics is not intuitive is a famous problem known as the Birthday Paradox. Let’s say all of the students in your Statistics class were chosen at random from a large population. What is the probability that two students in the class share the same birthday? When I pose this question to my Stats students, I get guesses that range from 1% to about 20%. These seem like very “reasonable” guesses, but it turns out they are not very accurate. Do a search on “birthday paradox” and you’ll be surprised at what the actual answer is!
One final note about all the formulas in Stats: In most high school and undergraduate Stats classes, you learn the formulas without learning where they come from. That’s because the derivations often require difficult or tricky calculus or math analysis operations. But you can learn how to apply the formulas without knowing how to derive them, so most Stats classes are set up this way. If you are overwhelmed by all the formulas, keep a list handy that reminds you when each formula is used. This will help you tame your Statistics class.