Today in AP Statistics we continued the Great Candy Review by comparing Starburst proportions to the skittles proportions; specifically, we started trying to decide if the proportion of orange starbursts *could be* equal to the proportion of orange skittles.

The activity covers both 1-sample proportion tests (by assuming that 20% of skittles are orange, as we surmised, and comparing our starburst sample proportion to 0.2) and then 2-sample proportion tests by dropping that assumption and comparing our actual samples, but before I dove into the tests I decided to spend some time dwelling on *power*.

This is my first time teaching this course, and I haven’t always figured out until too late what aspects to prioritize. Power is hard, it comes near the end of a chapter, and I skimmed it.

Big. Mistake.

Really thinking about the power of a test, even calculating it, turns out to be an *extremely good way* to really think about the underlying concepts of statistical inference. It took us 30-45 minutes to really get through the first two pages of the packet, which I didn’t expect, but I saw light bulbs going on all over the room as we slowly grasped the big picture. When students really understood the power of the test – when they realized that **even if our friend is wrong** there is a 75% chance we won’t be able to “prove” it with these techniques and understood why… well, they were obviously annoyed, but they also clearly understood the limitations and execution of inference tests better than they have all year.

It was a good moment.

Next class we will actually take a sample of starbursts and conduct the tests. I doubt we will be able to decide with high confidence that they proportions different (even though they really ARE) and now, hopefully, students will understand better why.