## Day 42 - Lesson 3.8

##### Learning Targets
• 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 significant.

##### Activity:

Today’s lesson is a big one: statistical significance. We front loaded this with students by explaining the importance of the day before we got started. Also, statistical significance can be a difficult concept to grasp so we also made sure students know that it’s ok if it takes them a little while to understand it. Students need to develop perseverance and as teachers we have to give them permission to struggle so they don’t shut down when they get stuck.

In today’s activity, we’re looking at the results from the putting experiment.  We have the distance of the ball from the hole for 10 putts each for the short putter and the long putter.   The students calculated the mean distance for each type of putter and then found the difference between them.

After the groups find the difference, lead the class in a discussion about how do 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 concept of simulating the experimental results by explaining that we will assume the putter length has no impact on the putt.  Take the person 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.

Give each group a set of 20 cards, one for each putt.  Have the students write the distances of the putts on the cards, shuffle the cards and split them in to two groups.  Groups should assign one group as the short putts and the other group as the long putts and then find the difference in means.  As a class, create a dotplot of all the differences.  Mark the original difference in means and decide if this is enough evidence to make a conclusion.  We will use the 5% cutoff for statistical significance.

##### Teaching Tip:

Originally we tried this activity by having students use the applet to simulate the difference in means.  We felt that students were struggling to understand what the applet was doing and therefore had a hard time understanding the concept. We changed the lesson to the simulation with the note cards to give students a concrete understanding.  We are really happy with the change.  Students had a much deeper and thorough understanding of the simulation and randomization distribution.

Bonus: If you have time, try the online only Bonus Lesson 3.8A: Blocking.  This is a great lesson to use the Dog Blocking activity.