Transcript 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 LEADERSHIP
SUMMER INSTITUTE 2014
SESSION 9 • 26 JUNE 2014
WHAT 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
ACTIVITY 1
HOMEWORK REVIEW AND DISCUSSION
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.
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
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 4
GRADE 9, LESSON 19
INTERPRETING CORRELATION
ENGAGENY/COMMON CORE GRADE 9, LESSON 19
9.13
ACTIVITY 4
LESSON 19: INTERPRETING CORRELATION
Put the three scatter plots in order from weakest to strongest correlation.
9.14
ACTIVITY 4
LESSON 19: INTERPRETING CORRELATION
Which of these two has a stronger linear relationship?
9.15
ACTIVITY 4
LESSON 19: INTERPRETING CORRELATION
 In your small groups, complete and discuss Exercises 13-17.
Break
9.17
ACTIVITY 4
LESSON 19: INTERPRETING CORRELATION
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.
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
34
82
116
Total
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
ACTIVITY 4
REFLECTING ON STANDARDS ALIGNED TO LESSONS 12, 13 & 15
Closing questions for lessons 12, 13 & 15
 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?
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
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 6
STATISTICS KNOWLEDGE ASSESSMENT
MKT Assessment
Go to: http://bit.ly/UWM-LOCUS or http://devartist.gotpantheon.com/take/xaYNkXbEm8
Access code: xaYNkXbEm8
Thank you!
See you in the fall:
September 17
Location TBD