# Starting the Second Semester: Liar’s Logic

Day one of semester two. In this “regular” stats class, we’ve basically spent the first semester on issues in descriptive statistics; it’s time to turn towards inferential stats. Not that we will leave all things descriptive behind. I can’t separate them. And neither will we arm ourselves with traditional, frequentist, Normal-based tests and interval estimates.

I prepared a bunch of slides as an easy intro to the semester; my idea was to give them an overview of the big issues. One thing I did right: the first draft of these slides began with presentation of the issues and ended with some short activities to illustrate them. When I realized how wrong that was, I moved the activities and interaction into the midst of the presentation so that you never went more than about two slides without breaking to do something else.

What I would do better: some ending wrap-up that did something to cement things, such as having them write about the big ideas or at least call out a few new concepts or vocabulary words. Instead, we started the homework—not as a pad, but to make sure they knew how to use Fathom Surveys (it’s been a couple of months). We could have done both, but it was OK.

The main thing I wanted to accomplish was to give some basis for the principles of inference. A plan in an AP class—on the first day of the year—might be to do a full-fledged inference activity such as Martin v Westvaco from Statistics in Action. You’d do that using randomization (cards or chips). But here that would be too much too soon. So I did Liar’s Logic, which you might want to know about.

### Liar’s Logic

This is a whole-class game in three phases. First, I don’t call it “Liar’s Logic” in front of the class. It’s Guess My Number.

Phase 1: This is the guess-my-number game you have played ever since elementary school. I choose a whole number between 1 and 100 inclusive, and you have to find it using only yes-or-no questions.

This doesn’t take too long, and we can then ask how they did it. Today, they claimed they used the process of elimination, which fits just fine.

Phase 2: We‘ll play the same game except (I explain) there is a small change; see if you can figure out what it is.

Play begins, except this time, I occasionally lie. I mostly tell the truth, but make sure that after a few turns, they are faced with contradictory information. The game would never end, so if they don’t ask if I’m lying, I stop the game and tell them. Today, they actually asked if I was lying, and I said “yes.”

Wonderful disequilibrium ensued. We made the point that this was a stupid game, because I could make it so that you would never finish.

Phase 3: Same game, but with a different change. After every question, I will secretly roll a die. If I get a six, I’ll lie. Otherwise, I’ll tell the truth.

Students rapidly developed the strategy of asking the same question multiple times. The point being that although there is still lying involved, you can finish the game. At the end, they asked “is it 45?” five times and got four yesses and one no.

Yet, no matter how confident you are, you can never be completely sure. I said that one of our tasks this semester is to put numbers on that confidence.

I’m hoping that this will become one of those “touchstone” moments I can refer back to; you know, where I can just say, “remember 45?” and use that situation to talk about probability or confidence levels.

Other topics included:

• Habits of mind, especially being skeptical
• Meaning of inference in everyday life (infer/imply) and science (going from specific to general)
• Importance of thinking about alternative explanations (we used some stats from the news for this)

Whew.

## Author: Tim Erickson

Math-science ed freelancer and sometime math and science teacher. Currently working on various projects.