Today's blog post comes from AP Stats guru Daren Starnes. Daren has taught AP Statistics since the course launched in 1996-97. He has served as a reader, table leader, and question leader for the AP Statistics exam for 20 years. Daren has led over 200 workshops for statistics teachers, both online and in-person. He is also lead author of two popular statistics textbooks.
Most introductory statistics courses include a substantial chunk of inference content for students to digest. This foray through inference usually occupies the last 40% or so of the course. To truly master inference, students must develop conceptual understanding of the underlying logic of confidence intervals and significance tests. They need to achieve an articulate grasp of concepts like margin of error, P-value, statistical significance, Type I and Type II error, and power. That’s no small task! In addition, students need to develop fluency in constructing confidence intervals and performing significance tests in various settings.
Challenges for Learning Inference:
Distinguishing populations, samples, parameters, statistics, and sampling distributions
Understanding the logic of confidence intervals and significance tests
Carrying out inference procedures reliably
Checking conditions for inference procedures (and knowing why they are checking them)
Calculating accurately—by hand or using technology
Determining the appropriate scope of inference based on how the data were collected
Crafting clear, precise statistical explanations
Deciding which inference method to choose
Solutions for Teaching Inference:
1. Use dynamic applets.
Use technology to develop students’ understanding of key concepts. For instance, the sampling distributions applet at Online Statbook is an excellent tool for motivating the central limit theorem. Several applets at www.rossmanchance.com are ideal for student investigation of the underlying logic of confidence intervals and significance tests. The relatively new Art of Stat site has a nice collection of interactive applets, including my new favorite applet for exploring the relationship between Type I error, Type II error, and power. And the suite of stapplet.com applets allows students to analyze data, calculate probabilities, and perform simulation-based and traditional inference.
2. Introduce inference concepts early and often.
Why wait until the second half of the course, when students have just been walloped by probability, random variables, and sampling distributions? It is natural to discuss inference whenever data are obtained from random sampling or a randomized experiment. That is likely the case throughout the units on exploring data and collecting data near the beginning of the course. Margin of error can be explored when students are presented with data from a sample survey. Likewise, students can be introduced to the ideas of P-value and statistical significance in the context of a randomized experiment. Hands-on and technology-based simulations allow students to investigate the idea of a confidence interval or a significance test without getting bogged down in the formalities. Informal inference can be inserted throughout the units on probability, random variables, and sampling distributions. The key is to ask questions like, “How unlikely would it be to obtain a result at least as surprising as the one observed in this study by chance alone?”
3. Give students lots of practice and feedback.
Give students frequent practice communicating their statistical thinking and receiving timely, specific feedback about clarity and precision. Don’t let students off the hook by asking only questions that encourage rote memorization of definitions or that encourage “template” responses. Of course, knowing the meaning of statistical terminology and being able to provide an interpretation that includes all key elements are good starting points for many students. But they aren’t sufficient for demonstrating mastery of concepts and skills. The AP Statistics exam features questions every year that require students to apply their understanding in a novel context or nonroutine way. (See Free Response Question #6, also known as the Investigative Task, on each exam for one such example.)
I look forward to digging deeper into several ideas shared in this blog post as part of the upcoming "Teaching Inference with Confidence” online workshop sponsored by Stats Medic.