For experienced AP Stats teachers, we know what the second semester is all about: Statistical Inference! And for AP Statistics, this means that students will be doing a whole lot of confidence intervals and significance tests. With more than 10 inference procedures for students to learn, it is critical to establish a consistent structure for students to use for statistical inference scenarios. If we can get our students into consistent habits of thinking and process, the last few months of the course can be a breeze. This year we are going to try a brand-new approach to inference:

## The 4C Method for Inference

1. **CHOOSE:** Choose the inference procedure and set it up.

2. **CHECK:** Check the appropriate conditions.

3. **CALCULATE:** Perform the calculations.

4. **CONCLUDE:** Interpret results in the context of the problem.

## CHOOSE: The First Step is the Most Important

At the end of the course, we want our students to be able to read an AP Exam question and quickly decide what type of inference procedure is needed. Before checking any conditions, before any calculations, and before any conclusions, students must decide what type of confidence interval or __significance test__ is required. This decision ultimately sets up which conditions and formulas that will be used later.

This is exactly why we should identify the inference procedure first!

NOTE: The most recent AP Exam rubrics have also made this the first item to look for when grading!

## CHECK: Check Conditions, Ask “So What?”

Once we have chosen the inference procedure and set it up, it is time to check the conditions to be sure that all of our work will be worth it. While it is important that students know how to check each condition, we think it is equally important that they understand why we check the condition. We call this the “so what” and you will see them in red here.

NOTE: The “so what” is NOT required for full credit on the AP Exam rubrics. But it is interesting to notice that recent AP Exams have started to include the “so what” as part of the model solution.

## CALCULATE: Formulas by Thinking, Not Memorizing

Instead of going directly to the STATS menu on the calculator, we want our students thinking about what it means to calculate a confidence interval or to calculate a test statistic and *P*-value. For this reason, we have students write out a general formula first and then build the specific formula that goes with the inference procedure chosen. To finish out, they plug in numbers and come up with an answer.

**NOTE:** The formulas are not required for full credit on the AP Exam. For full credit on a confidence interval, students need only provide the correct interval. For full credit on a significance test, students need only provide the correct test statistic and *P*-value.

## CONCLUDE: Put it in Context

Here students will give a full interpretation of their confidence interval OR give a full conclusion for a significance test (which includes an __interpretation of the ____P____-value__).

NOTE: The *P*-value interpretation is not required for full credit on the AP Exam.

Using this new 4C Method for Inference, we are 99% confident our students will show a statistically significant improvement in their understanding of inference (dad jokes). Give it a try and let us know how it goes.

## DOWNLOAD: The 4C Method for Inference Templates

## 4C Method Refreshed Lessons

CED Unit 6: Inference for Proportions

CED Unit 7: Inference for Means

CED Unit 8: Chi-square Tests

CED Unit 9: Linear Regression Inference

**Note:** We recently learned that an open source textbook, Advanced High School Statistics, has been using a 5-step framework of I + 4C: Identify, Choose, Check, Calculate, Conclude, since 2019. We were totally unaware of this, but we'd like to give a shout out to them! You can download their book for free at http://__openintro.org/ahss____.__

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