Anonymously collect the differences in heart rate from each student, and keep the differences separated by groups. Display the results. These results will be used later in the lesson.

The goal of this discussion is for students to think about how to analyze the data from the two groups. Here are some questions for discussion:

• “How could you graphically represent the data?” (I could make a histogram showing the distribution of the data from each group.)
• “What are some ways you could analyze the data?” (I could calculate and compare the mean and standard deviation of each data set, or compare the shapes of the two histograms.)
• “How would you find a randomization distribution for this data?” (I could record all of the values in a spreadsheet and then randomly choose half of them to be the counting group and the other half to be the silent group. Then I would find the means of those two groups and subtract them. I would repeat this many times.)

Anonymously collect the differences in heart rate from each student, and keep the differences separated by groups. Display the results. These results will be used in the next activity.

If students are confused about the values as they are analyzing the data, consider asking:

• “What do the values you are considering represent in the context of the problem?”

• “How might organizing and labeling the information used for this analysis help you understand your work?”

The goal of this discussion is for students to share their analysis of the results of the randomization experiment. For groups that are too small to create a good histogram, display the example here for all to see. Otherwise, display the histogram from the class data.

Here are some questions for discussion:

• “Where does the difference between the mean heart rates of the 2 treatment groups fall in the randomization distribution?” (For “The Counting Experiment,” it falls right in the middle, which means it would not be such an unlikely occurrence even if the treatment had no effect. For “The Partial Experiment,” it is far from the typical values, which means it is inconsistent with the treatment having no effect on heart rate, and we can conclude the treatment did have some effect on heart rate.)
• “What size difference between the mean heart rates of the 2 treatments would cause you to conclude that the difference was not likely to have occurred by chance even if the treatment had no effect on heart rate? Explain your reasoning.” (For “The Counting Experiment,” I think a difference greater than 8 or less than -8 would have allowed me to say it’s doubtful the treatment had no effect. This is because most of the values resulting in the randomization distribution were greater than -8 or less than 8. For “The Partial Experiment,” I think a difference greater than 10 or less than -10 would have allowed me to say it’s doubtful the treatment had no effect.)
• “Do you think counting affects heart rate? Explain your reasoning.” (I think it might, but this experiment was not able to provide evidence in support of that claim. But nor did it provide any evidence against it.)
• “Do you think doing only part of the activity affects heart rate? Explain your reasoning.” (I do think it affects heart rate because the relatively large difference in means we found is not likely to have occurred had there been no effect.)
• “Were these experiments failures? Explain your reasoning.” (No, they are not failures. Just because one fails to find evidence of a claim does not mean that the experiment failed. Perhaps the size of the impact on heart rate was too small for our experiment to detect.)