Inference for Experiments (Lesson 4.7)
Chapter 4 - Day 9
Outline an experiment that uses a completely randomized design.
Explain the concept of statistical significance in the context of an experiment.
Use simulation to determine if the difference between two means or two proportions in an experiment is statistically significant.
In this lesson, we continue thinking within the anchored putting context that was used to introduce the chapter, as well is in Lesson 4.6. In this lesson, students will examine some actual results from an experiment to try to determine if there is convincing evidence that long putters work better.
This lesson is not the first time that students have informally thought about statistical significance. In fact, the very first lesson in the course (Can Joy Smell Parkinson’s?) used a similar simulation approach to what we will use in this lesson.
Notice there is a STOP sign at the bottom of page 1, indicating to students that they should stop here and wait for the formal debrief with the teacher before moving to page 2. For page 2, teachers have two options:
Have students try this on their own in groups. Each group would have 1 person in charge of a computer to run the simulation (or phones also work).
Show students the applet using the teacher computer and work through page 2 as a whole class.
At the bottom of page 1 of the activity, lead the class in a discussion about how we know if this difference is big enough. If students have a tough time thinking about this, you may want to pose the question with exaggerated values. For example, if the difference were only 1 cm, would that be enough? What if it were 10 cm?
Introduce the simulation of the experiment by explaining that we will assume the putter length has no impact on the putt (this will later become a null hypothesis). Consider the student who putted 2 cm from the hole with the short putter. Perhaps they would have been 2 cm away no matter which putter they used.
Important Note: Many students will struggle with the immediate jump to technology for doing the simulation. One possible solution is to write the 20 values for the distance to the hole on individual index cards. Shuffle up the index cards and then randomly assign them into two piles. Find the mean for each pile and then the difference of means. Put this difference of means on the dotplot. Now the computer applet is going to go through this exact same process, but much more quickly.