Day 108: Errors in Decision-Making
We spent some time today talking about decision errors in AP Statistics. It was clear from the opener that my stats apprentices were not so clear about what Type I and Type II errors are and how to state them. Although I knew in my subconscious that the probabilities of these errors are conditional probabilities, I’ve never used this approach in developing the conceptual understanding of the errors with my kids. I did today and I’m really pleased with the results (as far as I know!)
We also talked about the seriousness of the errors, so I had students look at two scenarios and the related error statements. Then they decided which they thought was more serious by voting with their bodies. They moved to one side of the room or the other depending on which they thought was more serious; then they debated their choice using correct vocabulary.
In addition, we wrote up our first significance test for one proportion in the 4-step way. Typical presentation, but I did spend time developing the difference in the Normal condition and the standard deviation calculation between confidence intervals and significance tests. It was a great way to re-enforce the difference between confidence intervals (which give plausible values of the parameter) and significance tests (which has the claimed parameter). Through the discussion we determined which value to use in the Normal condition and the standard deviation (P0 vs. p-hat): p-hat for confidence intervals since it is our best unbiased estimator of the true population value and P0 for significance tests since it is the mean of the sampling distribution of all p-hats.
We finished the problem by determining which error we might have made. Also talked about interpreting possible errors BEFORE running the significance test vs. the error we might actually have made AFTER we run the test. Great conceptual discussions!