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The American Statistical Association's (ASA) efforts to improve statistics education, including the release of reports on undergraduate programs and teacher preparation. The document emphasizes the importance of teaching data science, real applications, and critical thinking skills in introductory statistics courses. It also recommends using real data, interactive software, and assessments to enhance student learning.
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Robert Carver (Stonehill College), Michelle Everson, co-chair (The Ohio State University), John Gabrosek (Grand Valley State University), Nicholas Horton (Amherst College), Robin Lock (St. Lawrence University), Megan Mocko, co-chair (University of Florida), Allan Rossman (Cal Poly
Citation: GAISE College Report ASA Revision Committee, “Guidelines for Assessment and Instruction in Statistics Education College Report 2016,” http://www.amstat.org/education/gaise.
Endorsed by the American Statistical Association
July 2016
Much has changed since the ASA endorsed the Guidelines for Assessment and Instruction in Statistics Education College Report (hereafter called the GAISE College Report) in 2005. Some highlights include:
(^1) http://www.ams.org/profession/data/cbms-survey/cbms2010-Report.pdf (^2) http://www.amstat.org/education/curriculumguidelines.cfm (^3) http://www.amstat.org/education/gaise/GAISEPreK-12_Full.pdf (^4) http://www.corestandards.org/ (^5) http://www.economist.com/printedition/2010-02- (^6) Silver, N. (2012) The Signal and the Noise: Why So Many Predictions Fail—but Some Don’t. New York: Penguin Books. Also see http://www.fivethirtyeight.com and http://www.gapminder.org. 7
8 http://magazine.amstat.org/blog/2015/10/01/asa-statement-on-the-role-of-statistics-in-data-science/ Jordan, M. (2016) Computational Thinking and Inferential Thinking: Foundations of Data Science eCOTS 2016. Also see at https://www.causeweb.org/cause/ecots/ecots16/keynotes/jordan.
prevalent. There has been a parallel development of “analytics” as the study of extracting information from big data—particularly with business and governmental applications.
Concurrent with these changes, the ASA has promoted effective and innovative activities in statistics education on several fronts, including the development and release of the following reports:
(^9) G.W. Cobb’s plenary at USCOTS 2005 presentation and later article http://escholarship.org/uc/item/6hb3k0nz. (^10) http://www.amstat.org/education/pdfs/guidelines2014-11-15.pdf (^11) http://www.amstat.org/education/SET/SET.pdf (^12) http://www.cbmsweb.org/MET2/met2.pdf (^13) http://www.amstat.org/education/pdfs/TeachingIntroStats-Qualifications.pdf
There is no single introductory statistics course. The variety of courses reflects a wide range of needs.
We believe that the six GAISE recommendations apply to the many variations of introductory statistics courses, although the specifics of how they are implemented in these courses will vary to suit the situation. Despite the fact that this report focuses on introductory courses, we believe that the GAISE recommendations also apply to statistics courses beyond the introductory level. We urge instructors to consider applying these recommendations throughout undergraduate statistics courses, including courses in statistical practice, statistical computing, and statistical theory.
Throughout the development of this report, we have tried to maintain realistic expectations while setting aspirational goals. We hope that this report can help instructors of introductory statistics improve their courses. We recognize that instructors face constraints that can make innovation challenging, but we believe that any statistics course can benefit from incremental changes that produce closer alignment with the six recommendations.
To facilitate innovation, this report includes substantially expanded and revised appendices that provide many examples of
The desired result of all introductory statistics courses is to produce statistically educated students, which means that students should develop the ability to think statistically.
The following goals reflect major strands in the collective thinking expressed in the statistics education literature. They summarize what a student should know and understand at the conclusion of a first course in statistics. Achieving this knowledge will require learning some statistical techniques, but mastering specific techniques is not as important as understanding the statistical concepts and principles that underlie such techniques. Therefore, we are not recommending specific topical coverage.
example, separately colored points and regression lines for males and females can be included in a scatterplot that relates age to height for children 3 years to 18 years).
Goal 4: Students should recognize and be able to explain the central role of variability in the field of statistics.
Variability is a key characteristic of data that underlies statistical associations and inference. Identifying the sources of variability in a statistical study is an important consideration. Graphical displays and numerical summaries help to illustrate and describe distributions of data (shape, center, variability, and unusual observations) and to select appropriate inference techniques. The role of sampling variability is the bridge to making comparisons and drawing inferences. At the introductory level, this includes an understanding of univariate (and perhaps bivariate) sampling distribution and/or randomization distribution models, and the role of features such as sample size, variability in the statistics, and distributional shape in these models. Understanding how results vary from sample to sample is a challenging topic for many students.
Goal 5: Students should recognize and be able to explain the central role of randomness in designing studies and drawing conclusions.
The mathematical understanding of “random” ( not synonymous with haphazard or unplanned) is fundamental to the role that randomness plays in statistical studies. Distinction of probabilistic sampling techniques from non-probabilistic ones help to recognize when it is appropriate for the results of surveys and experiments to be generalized to the population from which the sample was taken. Similarly, 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.
Understanding the role of models in statistics is a critical skill for being able to investigate the distribution of data values and the relationships between variables. The first recommendation of the GAISE report is to teach statistical thinking. One of the key features of statistical thinking is to understand that variables have distributions. Models help us describe the distribution of variables, especially the distribution of one or more variables conditional upon the values of one or more other variables.
It is important to understand that two variables may be associated and that statistical models can be used to assess the strength and direction of the association. Bivariate models that relate two variables – such as the regression model relating a dependent quantitative response variable to an independent quantitative explanatory variable – are building blocks for more complicated multivariable models. 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.
Statistical inference involves drawing conclusions about a population from the information contained in a sample. Often this involves calculation of sample statistics to make inferences about population parameters either through estimation (for example, a confidence interval to estimate the proportion of voters who have a favorable impression of the President of the United States) or testing (for example, a hypothesis test to determine if the mean time to headache relief is less for a new drug than a current drug). At least as important as calculating confidence intervals and p- values is understanding the concepts underlying statistical inference. Understanding the limitations of inferential procedures, including checking assumptions, and the effect of sample size and other factors, are important to assessing the practical significance of results and that if you conduct multiple tests, some results might be significant just by chance. Being able to identify which inferential methods are appropriate for common one-sample and two-sample parameter problems helps develop statistical thinking skills. Providing ample opportunity to practice drawing and communicating appropriate conclusions from inferential procedures allows students to demonstrate understanding of statistical inference.
Goal 8: Students should be able to interpret and draw conclusions from standard output from statistical software.
Modern data analysis involves the use of statistical software to store and analyze (potentially large) datasets. While there may be value to performing some calculations by hand, it is unrealistic to analyze data without the aid of software for all but the smallest datasets. At a minimum, students should interpret output from software. Ideally, students should be given numerous opportunities to analyze data with the best available technology (preferably, statistical software).
Goal 9: Students should demonstrate an awareness of ethical issues associated with sound statistical practice.
As data collection becomes more ubiquitous, the potential misuse of statistics becomes more prevalent. Application of proper data collection principles, including human subjects review and the importance of informed consent, are central to the effective and ethical use of statistical methods. Relying on statistical methods to inform decisions should not be confused with abusing data to justify foregone conclusions. With large datasets containing many variables, especially from observational studies, understanding of confounding and multiple testing false positive rates becomes even more relevant.
the statistical process that will allow them to solve unfamiliar problems and to articulate and apply their understanding” (p.885). These authors argue that we should refrain from teaching our students merely how to follow recipes and should instead teach them how to really cook. Using a “cooking analogy,” they explain that someone who can really “cook” not only understands how to follow recipes but can make easy adjustments at a moment’s notice by knowing exactly what to focus on and look for when attempting to assemble not just a single dish but a full meal.
The following carpentry story provides another illustration of statistical thinking and an alternative to the “cooking analogy:”
In week 1 of the carpentry (statistics) course, we learned to use various kinds of planes (summary statistics). In week 2, we learned to use different kinds of saws (graphs). Then, we learned about using hammers (confidence intervals). Later, we learned about the characteristics of different types of wood (tests). By the end of the course, we had covered many aspects of carpentry (statistics). But I wanted to learn how to build a table (collect and analyze data to answer a question) and I never learned how to do that. We should teach students that the practical operation of statistics is to collect and analyze data to answer questions.
As a part of the overarching emphasis to teach statistical thinking, we propose that the introductory course teach statistics as an investigative process of problem-solving and decision- making. We also propose that all students be given experience with multivariable thinking in the introductory course. We expand on each of these ideas below.
We urge instructors to emphasize the investigative nature of statistics throughout their courses. We hope that doing so can avoid the unfortunate, but not uncommon, reality that many students leave their introductory course thinking of statistics only as a disconnected collection of methods and tools.
In their early work on statistical thinking, Wild and Pfannkuch (1999) summarize the investigative cycle with the acronym PPDAC (Problem, Plan, Data, Analysis, Conclusion). A nice illustration of this cycle appears in classrooms throughout New Zealand: http://new.censusatschool.org.nz/wp-content/uploads/2012/11/data-detective1.pdf.
Another way of thinking about the statistical investigative cycle is provided in the GAISE PreK- 12 Report (Franklin et al. 2007), where this process is laid out in four stages:
We do not advocate one particular conception of the investigative process, nor do we recommend a specific number of stages or steps in this process; we do strongly recommend that instructors emphasize the investigative nature of the field of statistics throughout their introductory course. 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.
As we think about engaging students in the investigative process, we hope to create mental habits such as the six mental habits described by Chance (2002):
De Veaux and Velleman (2008) reiterate this approach in their suggestion that introductory statistics courses should involve students in the process of proposing questions, testing assumptions, and drawing conclusions from data. Statistics involves an investigative process of problem-solving and decision-making, which makes it a fundamental discipline in advancing both scientific discoveries and business and personal decisions.
One way of incorporating the investigative process into a first statistics course is to ask students to complete projects that involve study design, data collection, data analysis, and interpretation. We can also attempt to include activities in our courses that involve students in different parts of the investigative cycle. We might further share examples of real studies that are reported in the news or in journal articles and engage our students in discussion of the conclusions drawn from these studies and whether such conclusions are valid in light of the methods used to gather and explore the data.
When students leave an introductory course, they will likely encounter situations within their own fields of study in which multiple variables relate to one another in intricate ways. We should prepare our students for challenging questions that require investigating and exploring relationships among more than two variables.
Kaplan (2012) has criticized the tendency for the introductory course to focus on simple questions about how two groups differ or about how two variables are correlated. Such
Earlier, we highlighted important learning objectives that an instructor hopes their students will achieve. It can be challenging to present material in a way that facilitates students’ development of more than just a surface level understanding of important concepts and ideas.
Certainly, an introductory course will involve some computation, though most should be facilitated by technology. It is desirable for students to be able to make decisions about the most appropriate ways to visualize, explore, and, ultimately, analyze a set of data. It will not be helpful for students to know about the tools and procedures that can be used to analyze data if students don’t first understand the underlying concepts. Having a good understanding of the concepts will make it easier for students to use necessary tools and procedures to answer particular questions about a dataset.
Procedural steps too often claim students’ attention that an effective teacher could otherwise direct toward concepts. Students with a good conceptual foundation from an introductory course will be well-prepared to study additional statistical techniques in a second course.
Using real data in context is crucial in teaching and learning statistics, both to give students experience with analyzing genuine data and to illustrate the usefulness and fascination of our discipline. Statistics can be thought of as the science of learning from data, so the context of the data becomes an integral part of the problem-solving experience. The introduction of a data set should include a context that explains how and why the data were produced or collected. Students should practice formulating good questions and answering them appropriately based on how the data were produced and analyzed.
Using real data sets of interest to students is a good way to engage students in thinking about the data and relevant statistical concepts. Neumann, Hood and Neumann (2013) explored reflections of students who used real data in a statistics course and found the use of real data was associated with students’ appreciating the relevance of the course material to everyday life. Further, students indicated that they felt the use of real data made the course more interesting.
(or drastically reduce) some lectures and Appendix F has additional suggestions specifically geared to implementing this recommendation in large classes.
Technology has changed the practice of statistics and hence should change what and how we teach. By technologies, we refer to a range of hardware and software that can do far more than handle the computational burden of analysis. By adopting the best available tools (subject to institutional constraints), we allow students to do analysis more easily and therefore open up time to focus on interpretation of results and testing of conditions, rather than on computational mechanics. Technology should aid students in learning to think statistically and to discover concepts. It should also facilitate access to real (and often large) datasets, foster active learning, and embed assessment into course activities.
Statistics is practiced with computers and usually with specially designed computer software. Students should learn to use a statistical software package if possible. Calculators can provide some limited functionality for smaller datasets, but their use should be supplemented with experience reading typical computer results. Regardless of the tools used, it is important to view the use of technology not just as a way to generate statistical output but as a way to explore conceptual ideas and enhance student learning. We caution against using technology merely for the sake of using technology or for pseudo-accuracy (carrying out results to many decimal places). Not all technology tools will have all desired features.
When computers are not available to all students at all times, experience with computers could include one or more of the following:
For example, an instructor might demonstrate how to estimate a regression equation using a statistical package, then provide students with copies of the resulting regression table and residual plots, and ask students to summarize the results and assess model conditions. Alternatively, an instructor might create an exploratory graph, elicit questions or suggestions from the class, modify the graph in real time, and share the results from the final analysis.
Technology tools should also be used to help students visualize concepts and develop an understanding of abstract ideas by simulations. Some tools offer both types of uses, while in other cases, a statistical software package may be supplemented by web applets.
We note that technology continues to evolve rapidly. Many smart phones or tablets can provide access to online statistical software when sufficient internet access is available. We also note that institutions and courses vary widely in funding and the resources necessary to support this recommendation. The catchphrase should be “use the best available technology.”
(See Appendix D for in-depth discussion and examples.)