1.
11/16/2016
Examples for Implementing Revised GAISE Guidelines (
Allan J. Rossman
Dept of Statistics
Cal Poly – San Luis Obispo

2.
11/16/2016
GAISE
Guidelines for Assessment and Instruction in Statistics Education
Recommendations for teaching introductory statistics at college level
Comparable PreK-12 guidelines
Developed, endorsed by American Statistical Association
2005 committee chaired by Joan Garfield
2016 committee chaired by Michelle Everson, Megan Mocko
Rossman
JMM Atlanta – January 2017

3. GAISE recommendations
Teach statistical thinking.
Focus on conceptual understanding.
Integrate real data with a context and purpose.
Foster active learning.
Use technology to explore concepts and analyze data.
Use assessments to improve and evaluate student learning.
Rossman
JMM Atlanta – January 2017

4. 1. Teach statistical thinking
Example: Sex discrimination?
Men: 533/1198 ≈ .445
Women: 113/449 ≈ .252
Does this provide evidence of discrimination against women?
Rossman
JMM Atlanta – January 2017

5. 1. Teach statistical thinking
Program A
Men: 511/825 ≈ .619
Women: 89/108 ≈ .824
Program F:
Men: 22/373 ≈ .059
Women: 24/341 ≈ .070
Rossman
JMM Atlanta – January 2017

6. 1. Teach statistical thinking
Engage in proportional reasoning
Take sample sizes into account
Consider where the data came from
Observational vs. experimental
Random sampling, random assignment, both, neither
Assess scope of conclusions
Generalizability, causation
Think about alternative explanations
Confounding variables
Rossman
JMM Atlanta – January 2017

7. 2. Focus on conceptual understanding
Example: Variability/Standard Deviation
Ambika records the ages of customers at The Avenue (on-campus snack bar) from 11am-2pm today, while Mary records ages of customers at McDonald’s (near freeway).
Sketch graphs for what the two distributions of customer ages gathered might look like.
Who will have the larger standard deviation of customer ages: Ambika or Mary? Explain.
Rossman
JMM Atlanta – January 2017

8. 2. Focus on conceptual understanding
11/16/2016
2. Focus on conceptual understanding
Example: Variability/Standard Deviation
Arrange these distributions of quiz scores in order from largest SD to smallest SD.
Rossman
JMM Atlanta – January 2017

9. 3. Integrate real data
Rossman
JMM Atlanta – January 2017

10. 3. Integrate real data Example: Facial prototyping
Do people tend to associate certain names with faces? (Lea, Thomas, Lamkin, & Bell, 2007)
Who is on the left: Bob or Tim?
Rossman
JMM Atlanta – January 2017

11. 4. Foster active learning
Example: Facial prototyping (cont)
What are two possible explanations for our observed sample result?
Which explanation can we easily model? How?
Use coin tosses to investigate
How often would such an extreme result occur by chance alone (if there were no facial prototyping)?
What conclusion can we draw?
Rossman
JMM Atlanta – January 2017

12. 5. Use technology to explore concepts
Example: Facial prototyping (cont)
In a recent class, 36 of 46 students put Tim on the left
Would such an extreme result be surprising if there were no facial prototyping?
Follow coin-tossing with technology simulation of 1000s of repetitions of 46 coin tosses
See where 36 falls in the distribution of number of heads/successes
Rossman
JMM Atlanta – January 2017

13. 5. Use technology to explore concepts
Example: Facial prototyping (cont)
Rossman
JMM Atlanta – January 2017

14. 5. Use technology to explore concepts
Example: Effect of outlier on least squares line
Rossman
JMM Atlanta – January 2017

15. 6. Use assessments to improve learning
At beginning of (nearly) every example/study
What are the observational units?
What are the variables? Which type is which variable? Which variable plays which role?
Is this an observational study or an experiment?
Did this study make use of random sampling, random assignment, both, or neither?
Rossman
JMM Atlanta – January 2017

16. 6. Use assessments to improve learning
At end of (nearly) every example
Is there strong evidence of an effect or difference? Explain. Interpret p-value.
How large is the effect or difference? Explain. Interpret confidence interval.
Is it reasonable to draw a cause-and-effect conclusion? Explain why or why not.
Is it reasonable to generalize the results to larger group? Explain why or why not.
Rossman
JMM Atlanta – January 2017

17. 6. Use assessments to improve learning
Example: Uniform colors
457 matches in 2004 Olympics: 248 won by wrestler in red, 209 by wrestler in blue
Test whether one uniform color (red, blue) tends to win Olympic wrestling matches significantly more than the other color.
How would test statistic, p-value, confidence interval, conclusion change if you analyzed proportion of wins for blue rather than red?
Rossman
JMM Atlanta – January 2017

18. 6. Use assessments to improve learning
Example (adapted from Jay Lehman):
Which would be larger – the mean weight of 10 randomly selected people or the mean weight of 1000 randomly selected cats? Explain briefly.
Which would be larger – the SD of the weights of 10 randomly selected people or the SD of the weights of 1000 randomly selected cats? Explain briefly.
Rossman
JMM Atlanta – January 2017

19. 6. Use assessments to improve learning
Example (easy to grade):
For each of the following, indicate whether it can SOMETIMES or NEVER take a negative value.
Standard deviation
Correlation coefficient
Slope coefficient
Inter-quartile range
p-value
Rossman
JMM Atlanta – January 2017

20. 6. Use assessments to improve learning
Example (harder to grade):
The purpose of a confidence interval is to estimate the unknown value of a population parameter based on a statistic calculated from a sample.
Convince me that you understand this by describing an example of a situation (not shown in class or the textbook) in which you might do this. Be sure to clearly identify the variable, population, parameter, sample, and statistic.
Rossman
JMM Atlanta – January 2017

21. New emphases in GAISE revision
Teach statistical thinking
Teach statistics as investigative process of problem-solving and decision-making
Give students experience with multivariable thinking
Rossman
JMM Atlanta – January 2017

22. 1a. Investigative process
Logic of
Inference
Scope of
Significance
Estimation
Generalization
Causation
6. Look back and ahead
1. Ask a research question
Research Hypothesis
2. Design a study and collect data
3. Explore the data
4. Draw inferences
5. Formulate conclusions
Rossman
JMM Atlanta – January 2017

23. 1a. Investigative process
Rossman
JMM Atlanta – January 2017

24. 1b. Multivariable thinking
Example: Sex Discrimination?
Simpson’s paradox
Example: Cat Jumping
Labeled scattterplot
Rossman
JMM Atlanta – January 2017

25. 1b. Multivariable thinking
Example: Starting Salaries by Time in College (from 2016 AP Statistics Exam)
Does staying in college longer tend to produce higher starting salaries?
Rossman
JMM Atlanta – January 2017

26. Goals for introductory students
Become critical consumers.
Be able to apply investigative process.
Produce and interpret results of graphical displays and numerical summaries.
Recognize and explain fundamental role of variability.
Recognize and explain central role of randomness in designing studies and drawing conclusions.
Rossman
JMM Atlanta – January 2017

27. Goals for introductory students (cont)
Gain experience with statistical models, including multivariable ones.
Demonstrate understanding of, and ability to apply, statistical inference in variety of settings.
Interpret and draw conclusions from standard output of statistical software.
Demonstrate awareness of ethical issues associated with sound statistical practice.
Rossman
JMM Atlanta – January 2017

28. Topics that might be omitted
Probability theory
Counting rules
Rules for probabilities of unions and intersections
Constructing plots by hand
Basic statistics learned in grades 6 – 12
Drills with probability distribution tables
Advanced training with statistical software packages
Rossman
JMM Atlanta – January 2017

29. GAISE Appendices Evolution of Introductory Statistics
Multivariable Thinking
Activities, Datasets, and Projects
Examples of Using Technology
Examples of Assessment Items
Learning Environments
Rossman
JMM Atlanta – January 2017

30. Applicability of GAISE?
To all kinds of introductory statistics courses
Statistical literacy vs. methods
All types of student majors
All class sizes
All learning environments: face-to-face, online, hybrid
All institution types: universities, colleges, two-year colleges, high schools
Beyond introductory courses
Rossman
JMM Atlanta – January 2017

31. www.amstat.org/education/gaise arossman@calpoly.edu Thanks! Rossman
JMM Atlanta – January 2017