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.

9.1

WELCOME TO COMMON CORE HIGH SCHOOL MATHEMATICS LEADERSHIPSUMMER INSTITUTE 2014

SESSION 9 • 26 JUNE 2014WHAT A DIFFERENCE A (STATISTICAL) TEST MAKES

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

9.3

A FEW MOMENTS FROM XKCD…

9.4

A FEW MOMENTS FROM XKCD…

9.5

A FEW MOMENTS FROM XKCD…

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

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

9.8

LEARNING INTENTIONS AND SUCCESS CRITERIA

We are learning to…

Identify the differences between correlation and causationDescribe the nature of correlation in a data setCompare data sets and determine whether differences are

statistically significant

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

9.10

ACTIVITY 2 GRADE 9, LESSON 3 (MICHELLE, LINDSAY, ALLISON)

ESTIMATING CENTERS & INTERPRETING THE MEAN AS A BALANCE POINT

ENGAGENY/COMMON CORE GRADE 9, LESSON 3

9.11

ACTIVITY 3 GRADE 9, LESSON 17 (HEATHER, MELISSA, JENNY)

ANALYZING RESIDUALS

ENGAGENY/COMMON CORE GRADE 9, LESSON 17

9.12

ACTIVITY 4GRADE 9, LESSON 19

INTERPRETING CORRELATION

ENGAGENY/COMMON CORE GRADE 9, LESSON 19

9.13

ACTIVITY 4LESSON 19: INTERPRETING CORRELATION

Put the three scatter plots in order from weakest to strongest correlation.

9.14

ACTIVITY 4LESSON 19: INTERPRETING CORRELATION

Which of these two has a stronger linear relationship?

9.15

ACTIVITY 4LESSON 19: INTERPRETING CORRELATION

In your small groups, complete and discuss Exercises 13-17.

Break

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 4LESSON 19: INTERPRETING CORRELATION

9.18

ACTIVITY 5 A GLIMPSE FORWARD

WHEN ARE DIFFERENCES STATISTICALLY SIGNIFICANT?

CONTENT FOR A CAPSTONE STATISTICS COURSE

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?

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.

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 Time Not Home on Time Total

Milwaukee Sample 20 (0.33) 40 (0.66) 60

Sweden Sample 14 (0.25) 42 (0.75) 56

Total 34 82 116

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.

9.23

ACTIVITY 5 STATISTICAL TESTS & SIGNIFICANT DIFFERENCES

On Time Not on Time Total

MKE 20 (0.33) 40 (0.66) 60

SWE 14 (0.25) 42 (0.75) 56

Total 34 82 116

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 4REFLECTING ON STANDARDS ALIGNED TO LESSONS 12, 13 & 15

Closing questions for lessons 12, 13 & 15

9.25

LEARNING INTENTIONS AND SUCCESS CRITERIA

We are learning to…

Identify the differences between correlation and causationDescribe the nature of correlation in a data setCompare data sets and determine whether differences are

statistically significant

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

9.27

A FEW WORDS ON THE GRADUATE PROJECT…

9.28

ACTIVITY 6STATISTICS KNOWLEDGE ASSESSMENT

MKT AssessmentGo to: http://bit.ly/UWM-LOCUS or http

://dev-artist.gotpantheon.com/take/xaYNkXbEm8

Access code: xaYNkXbEm8

Thank you!See you in the fall:

September 17Location TBD