June 6, 2019
The Guidelines for Assessment and Instruction in Statistics Education
The GAISE report (2016) was produced by a committee of leading statistical educators and endorsed by the ASA and AMATYC. It gives specific recommendations and some examples about best practices in teaching statistics.
Goals for intro stats
- Goal 1. Students should become critical consumers of statistically-based results reported in popular media, recognizing whether reported results reasonably follow from the study and analysis conducted.
- Goal 2. Students should be able to recognize questions for which the investigative process in statistics would be useful and should be able to answer questions using the investigative process.
- Goal 3. Students should be able to produce graphical displays and numerical summaries and interpret what graphs do and do not reveal.
- Goal 4. Students should recognize and be able to explain the central role of variability in the field of statistics.
- Goal 5. Students should recognize and be able to explain the central role of randomness in designing studies and drawing conclusions. Random assignment in comparative experiments allows direct cause-and- effect conclusions to be drawn while other data collection methods usually do not.
- Goal 6. Students should gain experience with how statistical models, including multivariable models, are used. While the details of these more complicated models may be beyond most introductory courses, it is important that students have an appreciation that the relationship between two variables may depend on other variables. Multivariable relationships, illustrating Simpson’s Paradox or investigated via multiple regression, help students discover that a two-way table or a simple regression line does not necessarily tell the entire (or even an accurate) story of the relationship between two variables.
- Goal 7. Students should demonstrate an understanding of, and ability to use, basic ideas of statistical inference, both hypothesis tests and interval estimation, in a variety of settings.
- Goal 8. Students should be able to interpret and draw conclusions from standard output from statistical software packages.
- Goal 9. Students should demonstrate an awareness of ethical issues associated with sound statistical practice.
Main recommendations
- Recommendation 1: Teach statistical thinking.
- “We should model statistical thinking for our students throughout the course, rather than present students with a set of isolated tools, skills, and procedures.”
- Teach statistics as an investigative process of problem-solving and decision-making
- “Mentioning the investigative process at the beginning of the course but then treating various course topics in a compartmentalized manner does not help students to see the big picture. We recommend that throughout the entire introductory course, instructors illustrate the complete investigative cycle with every example/exercise presented, starting with the motivating question that led to the data collection and ending with the scope of conclusions and directions for future work.”
- Give students experience with multivariable thinking.
- Recommendation 2: Focus on conceptual understanding.
- Focus on students’ understanding of key concepts, illustrated by a few techniques, rather than covering a multitude of techniques with minimal focus on underlying ideas.
- Pare down content of an introductory course to focus on core concepts in more depth.
- Perform most computations using technology to allow greater emphasis on understanding concepts and interpreting results.
- Recommendation 3: Integrate real data with a context and a purpose.
- The report has 15 bullet points under this recommendation.
Recommendation 4: Foster active learning.
Recommendation 5: Use technology to explore concepts and analyze data.
- Recommendation 6: Use assessments to improve and evaluate student learning.
- “Assessments need to focus on understanding key ideas, and not just on skills, procedures, and computed answers.”
What to leave out …
- Probability theory
- Constructing plots by hand
- Basic statistics
- Drills with z-, t-, \(\chi^2\), and F-tables.
- Advanced training on a statistical software program.
Technology and GAISE
- Interactive Applets
- “Interactive applets can be used to emphasize important statistical concepts without being encumbered by lots of calculations.”
- “Applets work well with the query first method. This means that the students try to answer the conceptual questions first on their own and then again after using the applet.”
- Under “Future Direction of Applets and Interactive Visualizations,” the report emphasizes the Shiny system the StatPREP Little Apps use.
- Statistical Software
- Accessing Real Data online (Observational, Experimental, Survey)
- Using Games and Other Virtual Environments
- Real Time Response Systems
Changing professional standards about p-values and significance
From Nature, March 2019, “Retire statistical significance”
“How do statistics so often lead scientists to deny differences that those not educated in statistics can plainly see? For several generations, researchers have been warned that a statistically non-significant result does not ‘prove’ the null hypothesis (the hypothesis that there is no difference between groups or no effect of a treatment on some measured outcome). Nor do statistically significant results ‘prove’ some other hypothesis. Such misconceptions have famously warped the the literature with overstated claims and, less famously, led to claims of conflicts between studies where none exists.”
The American Statistician March 2019
“The ASA Statement on P-Values and Statistical Significance stopped just short of recommending that declarations of ‘statistical significance’ be abandoned. We take that step here. We conclude, based on our review of the articles in this special issue and the broader literature, that it is time to stop using the term ‘statistically significant’ entirely. Nor should variants such as ‘significantly different,’ ‘p < 0.05,’ and ‘nonsignificant’ survive, whether expressed in words, by asterisks in a table, or in some other way.
“In sum, ‘statistically significant’ — don’t say it and don’t use it.”
“Statistics education will require major changes at all levels to move to a post ‘p < 0.05’ world. We are excited that, with support from the ASA, the US Conference on Teaching Statistics (USCOTS) will focus its 2019 meeting on teaching inference.”
What does this mean for teaching?
One area of consensus …
More emphasis on confidence intervals and effect size.
The two articles on education from the TAS March 2019 volume
Content Audit for p-Value Principles in Introductory Statistics, Maurer, K., Hudiburgh, L., Werwinski, L., and Bailer J.
- Evaluate the coverage of p-value principles in the introductory statistics course using rubrics or other systematic assessment guidelines.
- Discuss and deploy improvements to curriculum coverage of p-value principles.
- Meet with representatives from other departments, who have majors taking your statistics courses, to make sure that inference is being taught in a way that fits the needs of their disciplines.
- Ensure that the correct interpretation of p-value principles is a point of emphasis for all faculty members and embedded within all courses of instruction.
Beyond Calculations: A Course in Statistical Thinking, Steel, A., Liermann, M., and Guttorp, P.
- Design curricula to teach students how statistical analyses are embedded within a larger science life-cycle, including steps such as project formulation, exploratory graphing, peer review, and communication beyond scientists.
- Teach the p-value as only one aspect of a complete data analysis.
- Prioritize helping students build a strong understanding of what testing and estimation can tell you over teaching statistical procedures.
- Explicitly teach statistical communication. Effective communication requires that students clearly formulate the benefits and limitations of statistical results.
- Force students to struggle with poorly defined questions and real, messy data in statistics classes.
- Encourage students to match the mathematical metric (or data summary) to the scientific question. Teaching students to create customized statistical tests for custom metrics allows statistics to move beyond the mean and pinpoint specific scientific questions.