arossman@calpoly.edu 11/16/2016 Examples for Implementing Revised GAISE Guidelines (www.amstat.org/education/gaise) Allan J. Rossman Dept of Statistics Cal Poly – San Luis Obispo arossman@calpoly.edu www.amstat.org/education/gaise

arossman@calpoly.edu 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 www.amstat.org/education/gaise

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

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

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

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

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

2. Focus on conceptual understanding arossman@calpoly.edu 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 www.amstat.org/education/gaise

3. Integrate real data Rossman JMM Atlanta – January 2017

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

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

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

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

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

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

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

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

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

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

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

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

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

1a. Investigative process Rossman JMM Atlanta – January 2017

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

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

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

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

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

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

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

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