Type 1 and Type 2 Errors
Day 92 - Lesson 9.1
Interpret a Type I error and a Type II error in context. Give a consequence of each error in a given setting.
**NOTE: This lesson can be moved to the day before the Lesson 9.3 power lesson without any disruption. We tried this with students and it worked quite well. **
Activity: Should Rockford Switch to Bottled Water?
This Activity is based on a real event that happened in a town close to the high school where TheStatsMedics teach. Many of our students were aware of the water pollution and this made the lesson relevant for students.
Experience First, Formalize Later
In this Activity, students get to grapple with the potential consequences of using significance tests to make decisions, but without all the formal vocabulary. In the debrief, we formalize the learning by introducing the language of Type 1 and Type 2 errors and also showing them this table:
Joint Probability or Conditional Probability
As a preview of what will come later in Lesson 9.3, you can inform students that the “Correct conclusion” in the top right corner of this table is the power of the significance test. Students always ask what we call the “Correct conclusion” in the lower left of the chart. We tell them that this is the agility of the test (yes, we made this up).
When we start talking about the probability of making a Type 1 or Type 2 error (and later power), it is important to clarify a common misconception. These probabilities are NOT joint probabilities, they are CONDITIONAL probabilities.