SWBAT evaluate statistical significance when comparing two statistics

What is mathematical significance and how do you figure it out? This lesson introduces statistical significance.

20 minutes

*There is a video narrative that further explains the pedagogy for this section of the lesson in my resources. You will want to have copies of the handout "Significance" for this lesson and may want to use my "Data Sets", both of which are in my resources. * I begin this lesson with two short data sets on the front board and challenge my students to determine if the data sets are similar or different. I expect several students to suggest that they're similar based on measures of center and spread, and that there will be other students who will disagree. **(MP3)** *For those students who aren't actively participating I use directed questions like "Joe, do you agree with what Sally said?" followed by "Why do you agree/disagree?" and "Is there any other information you need to make this decision?"*. As the discussion winds down and/or begins to become repetitious I suggest that maybe there's a better way to compare these data sets. Generally someone says that the decision would be easier if we knew the source for the data, **(MP1)** so I explain that a teacher a my previous school has several sections of Algebra II and wanted to compare the scores for two of his classes. I ask if there are any other questions or suggestions than repeat my statement that there's a better way.

I tell my students that the phrase is "Statistical Significance", ask them to write the phrase in their notes and tell them that they will be creating a definition throughout this lesson. I then give each student a copy of the Significance handout and tell them they have ten minutes to read though it and prepare to ask questions about any of the new terms if necessary. **(MP6) ***(I have an assortment of graphic organizers available to my students and have included copies in my resources).* As they're working I walk around offering encouragement and assistance as needed. After ten minutes I randomly select a student to summarize the reading, then select additional students to build on that summary. I continue to ask and answer questions then use the fist-to-five method to determine how well my students think they understand this material. I finish this section by asking my students if they think we can use statistical significance to evaluate the data on the board.

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30 minutes

You will need copies of the Data Set handout and the Significance Tables (one side each - one paper) for this section of the lesson and your teams will need their graphing calculators for the last problem. I tell my students that they will be working with their right-shoulder partner for this part of the lesson to become familiar with significance tables and will use their graphing calculators to determine if our data sets are statistically significantly different. **(MP1, MP5)** I pass out the handout and ask students to review it with their partners, then ask if there are any questions. If needed I take student questions then tell my students that they have approximately 20 minutes to complete the activity. While they are working I walk around giving encouragement and assistance and redirecting as needed.

After 20 minutes (or when all the teams are finished) students swap papers (making sure their names are on them) with the teams to their left and right, so that each team has two different papers to look at. I tell my students that they will each be checking a paper so they need to work independently for this section of the lesson. I pass out color pencils and while I review the answers and take class questions I have the students independently checking their classmates paper, writing in correct answers if needed. When we've completed the corrections I tell my students to put their names on the paper in colored pencil and return the corrected papers to their owners. *(This is an example for my students of attending to precision, not in their own calculations but in making corrections to a classmates' paper.) ***(MP6)** *There is a copy of the answer key in this section resources. *

5 minutes

The closure piece for this lesson goes back to the first activity where we were trying to determine if two sets of data were truly different. I want my students to look at the results they got for the last problem on the worksheet and using that p-value and the significance level of 0.05 write a brief explanation of whether or not the data sets are statistically significantly different at the bottom of that worksheet. I encourage my students to refer back to the first handout they got to help them write an appropriate statement. **(MP6)** Before I collect these papers I also encourage my students to review all they've written for their definition of statistical significance and modify that definition as needed based on what they've learned.