1. 9.1 WELCOME TO COMMON CORE HIGH SCHOOL MATHEMATICS LEADERSHIP SUMMER INSTITUTE 2014 SESSION 9 26 JUNE 2014 WHAT A DIFFERENCE A (STATISTICAL) TEST MAKES

2. 9.2 TODAY’S AGENDA  Homework review and discussion  Group presentations: Grade 9, Lessons 3 and 17  Break  Grade 9, Lesson 19: Interpreting Correlation  A glimpse forward: Statistical Tests  MKT assessment  Closing remarks

3. 9.3 A FEW MOMENTS FROM XKCD…

4. 9.4 A FEW MOMENTS FROM XKCD…

5. 9.5 A FEW MOMENTS FROM XKCD…

6. 9.6 ACTIVITY 1 HOMEWORK REVIEW AND DISCUSSION Table discussion Discuss your write ups for the Day 8 homework tasks:  Compare your strategies with others at your table  Reflect on how you might revise your own solution and/or presentation

7. 9.7 Day 8 homework:  See the Problem Set for Lesson 2. Complete Problem 2 (the Obedience School for Dogs)  Reflection on teaching: Based on your current progress with the resources, reflect on the following: Do you feel you are able to identify lessons for the students you will teach next fall? Explain how you think your students may react to this material. Do you feel prepared or comfortable in presenting selected lessons to your students? Explain. What topics or lessons are you the most uncomfortable with at this time? Explain why you selected these lessons. ACTIVITY 1 HOMEWORK REVIEW AND DISCUSSION

8. 9.8 LEARNING INTENTIONS AND SUCCESS CRITERIA We are learning to…  Identify the differences between correlation and causation  Describe the nature of correlation in a data set  Compare data sets and determine whether differences are statistically significant

9. 9.9 LEARNING INTENTIONS AND SUCCESS CRITERIA We will be successful when we can:  Interpret the value of a correlation coefficient as a measure of the strength and direction of a linear relationship  Provide multiple explanations for why correlation does not imply causation, using contextual data sets  Define statistical significance and identify appropriate tests of statistical significance using contextual data sets

10. 9.10 ACTIVITY 2 GRADE 9, LESSON 3 (MICHELLE, LINDSAY, ALLISON) ESTIMATING CENTERS & INTERPRETING THE MEAN AS A BALANCE POINT ENGAGE NY /COMMON CORE GRADE 9, LESSON 3

11. 9.11 ACTIVITY 3 GRADE 9, LESSON 17 (HEATHER, MELISSA, JENNY) ANALYZING RESIDUALS ENGAGE NY /COMMON CORE GRADE 9, LESSON 17

12. 9.12 ACTIVITY 4 GRADE 9, LESSON 19 INTERPRETING CORRELATION ENGAGE NY /COMMON CORE GRADE 9, LESSON 19

13. 9.13 ACTIVITY 4 LESSON 19: INTERPRETING CORRELATION Put the three scatter plots in order from weakest to strongest correlation.

14. 9.14 ACTIVITY 4 LESSON 19: INTERPRETING CORRELATION Which of these two has a stronger linear relationship?

15. 9.15 ACTIVITY 4 LESSON 19: INTERPRETING CORRELATION  In your small groups, complete and discuss Exercises 13-17.

16. Break

17. 9.17 S-ID.6  Represent data on two quantitative variables on a scatter plot, and describe how the variables are related.  Fit the function to the data; use functions fitted to data to solve problems in the context of the data. Use given functions or choose a function suggested by the context. Emphasize linear, quadratic, and exponential models.  Informally assess the fit of a function by plotting and analyzing residuals.  Fit a linear function for a scatter plot that suggests a linear association. S-ID.7  Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data. S-ID.8  Compute (using technology) and interpret the correlation coefficient of a linear fit. S-ID.9  Distinguish between correlation and causation. ACTIVITY 4 LESSON 19: INTERPRETING CORRELATION

18. 9.18 ACTIVITY 5 A GLIMPSE FORWARD WHEN ARE DIFFERENCES STATISTICALLY SIGNIFICANT? CONTENT FOR A CAPSTONE STATISTICS COURSE

19. 9.19 ACTIVITY 5 STATISTICAL TESTS & SIGNIFICANT DIFFERENCES  When is a difference statistically significant?  If we had two populations’ responses to the same question, how could we know whether the differences were “noise” or real?

20. 9.20 ACTIVITY 5 STATISTICAL TESTS & SIGNIFICANT DIFFERENCES You have a curfew of midnight. What choice best describes what you will probably do? a. You don’t call and come home when it suits you. b. You finally call after you are already late and make excuses. c. You call to tell your parents you will be late. d. You get home on time.

21. 9.21 ACTIVITY 5 STATISTICAL TESTS & SIGNIFICANT DIFFERENCES You have a curfew of midnight. What choice best describes what you will probably do? a. You don’t call and come home when it suits you. b. You finally call after you are already late and make excuses. c. You call to tell your parents you will be late. d. You get home on time. Home on TimeNot Home on TimeTotal Milwaukee Sample20 (0.33)40 (0.66)60 Sweden Sample14 (0.25)42 (0.75)56 Total3482116

22. 9.22 ACTIVITY 5 STATISTICAL TESTS & SIGNIFICANT DIFFERENCES Basic tests for statistical hypothesis testing:  z-test comparing populations means, assumes a normal distribution, standard deviations known  t-test comparing populations means, relaxed conditions and assumptions, standard deviation not known  Chi-square test categorical data, assumes a normal population (Pearson’s, Fisher’s exact, Yates…) A basic version of most tests can be done online or with Excel.

23. 9.23 ACTIVITY 5 STATISTICAL TESTS & SIGNIFICANT DIFFERENCES On TimeNot on TimeTotal MKE20 (0.33)40 (0.66)60 SWE14 (0.25)42 (0.75)56 Total3482116

24. 9.24  How can you distinguish between linear and nonlinear associations in data by looking at a scatter plot?  What are the characteristics of linear, quadratic, and exponential relationships and/or associations in data?  How can you tell whether a linear model is a good fit to data? ACTIVITY 4 REFLECTING ON STANDARDS ALIGNED TO LESSONS 12, 13 & 15 Closing questions for lessons 12, 13 & 15

25. 9.25 LEARNING INTENTIONS AND SUCCESS CRITERIA We are learning to…  Identify the differences between correlation and causation  Describe the nature of correlation in a data set  Compare data sets and determine whether differences are statistically significant

26. 9.26 LEARNING INTENTIONS AND SUCCESS CRITERIA We will be successful when we can:  Interpret the value of a correlation coefficient as a measure of the strength and direction of a linear relationship  Provide multiple explanations for why correlation does not imply causation, using contextual data sets  Define statistical significance and identify appropriate tests of statistical significance using contextual data sets

27. 9.27 A FEW WORDS ON THE GRADUATE PROJECT…

28. 9.28 ACTIVITY 6 STATISTICS KNOWLEDGE ASSESSMENT MKT Assessment Go to: http://bit.ly/UWM-LOCUS or http://dev- artist.gotpantheon.com/take/xaYNkXbEm8http://bit.ly/UWM-LOCUShttp://dev- artist.gotpantheon.com/take/xaYNkXbEm8 Access code: xaYNkXbEm8

29. Thank you! See you in the fall: September 17 Location TBD