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Guidelines for Effective Stats Education: Introductory Course Recommendations, Exams of Statistics

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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Guidelines for Assessment and Instruction
Guidelines for Assessment and Instruction Guidelines for Assessment and Instruction
Guidelines for Assessment and Instruction
in Statistics Education (GAISE)
in Statistics Education (GAISE)in Statistics Education (GAISE)
in Statistics Education (GAISE)
College Report
College ReportCollege Report
College Report
2016
20162016
2016
Committee:
Committee:Committee:
Committee:
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
– San Luis Obispo), Ginger Holmes Rowell (Middle Tennessee State University), Paul Velleman
(Cornell University), Jeffrey Witmer (Oberlin College), and Beverly Wood (Embry-Riddle
Aeronautical University)
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
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Download Guidelines for Effective Stats Education: Introductory Course Recommendations and more Exams Statistics in PDF only on Docsity!

Guidelines for Assessment and InstructionGuidelines for Assessment and InstructionGuidelines for Assessment and InstructionGuidelines for Assessment and Instruction

in Statistics Education (GAISE)in Statistics Education (GAISE)in Statistics Education (GAISE)in Statistics Education (GAISE)

College ReportCollege ReportCollege ReportCollege Report 2016 201620162016

Committee:Committee:Committee:Committee:

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

  • San Luis Obispo), Ginger Holmes Rowell (Middle Tennessee State University), Paul Velleman (Cornell University), Jeffrey Witmer (Oberlin College), and Beverly Wood (Embry-Riddle Aeronautical University)

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

Contents

  • Committee:
  • Executive Summary
  • Introduction
  • Goals for Students in Introductory Statistics Courses
  • Recommendations
  • Suggestions for Topics that Might be Omitted from Introductory Statistics Courses
  • References
  • APPENDIX A: Evolution of Introductory Statistics and Emergence of Statistics Education Resources
  • APPENDIX B: Multivariable Thinking
  • APPENDIX C: Activities, Projects, and Datasets
  • APPENDIX D: Examples of Using Technology
  • APPENDIX E: Examples of Assessment Items
  • APPENDIX F: Learning Environments

IntroductionIntroductionIntroductionIntroduction

Background

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:

  • More students are studying statistics. According to the Conference Board on Mathematical Sciences (CBMS) survey, 508,000 students took an introductory statistics course in a two- or four-year college/university in the fall of 2010, a 34.7% increase from
    1. More than a quarter (27.0%) of these enrollments were at two-year colleges^1. Nearly 200,000 students took the Advanced Placement (AP) Statistics exam in 2015, an increase of more than 150% over 2005. In addition, many high school students took the AP course without taking the exam or took a non-AP statistics course. At the undergraduate level, the number of students completing an undergraduate major in Statistics grew by more than 140% between 2003 and 2013 and continues to grow rapidly^2.
  • Many students are exposed to statistical thinking in grades 6 – 12 , because more state standards include a considerable number of statistical concepts and methods. Many of these standards have been influenced by the GAISE PreK – 12 report developed and endorsed by the ASA^3. In particular, the Common Core^4 includes standards on interpreting categorical and quantitative data and on making inferences and justifying conclusions.
  • The rapid increase in available data has made the field of statistics more salient. Many have heralded the flood of information now available. The Economist published a special report on the “data deluge” in 2010^5. Statisticians such as Hans Rosling and Nate Silver have achieved celebrity status by demonstrating how to garner insights from data^6.
  • The discipline of Data Science has emerged as a field that encompasses elements of statistics, computer science, and domain-specific knowledge^7. Data science has been described as the interplay between computational and inferential thinking^8. It includes the analysis of data types such as text, audio, and video, which are becoming more

(^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.

  • More and better technology options for education have become widely available. These include course management systems, automated homework systems, technology for facilitating discussion and engagement, audience response systems, and videos now used in many courses. Applets and other applications, such as Shiny apps coded in the R programming language, that are designed to explore statistical concepts have come into widespread use. Many general-purpose statistical packages have developed functions specifically for teaching and learning.
  • Alternative learning environments have become more popular. These include online courses, hybrid courses, flipped classrooms, and Massively Open Online Courses (MOOCs). Many of these environments may be particularly helpful for supporting faculty development.
  • Some have called for an update to the consensus introductory statistics curriculum to account for the rich data that are available to answer important statistical questions.
  • Innovative ways to teach the logic of statistical inference have received increasing attention. Among these are greater use of computer-based simulations and the use of resampling methods (randomization tests and bootstrapping) to teach concepts of inference^9.

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:

  • Curriculum Guidelines for Undergraduate Programs in Statistical Science^10 , which identifies the increased importance of teaching data science, real applications, more diverse models and approaches, and the ability to communicate;
  • Statistical Education of Teachers^11 , a report that provides recommendations for preparing teachers of statistics at elementary, middle, and high school levels, and is meant to accompany the influential Mathematical Education of Teachers report^12 ;
  • Qualifications for Teaching Introductory Statistics^13 , a statement produced by a joint committee of the ASA and Mathematical Association of America, which recommends that statistics teachers have at least the equivalent of two courses in statistical methods and some experience with data analysis beyond the material taught in introductory courses;

(^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

Scope

There is no single introductory statistics course. The variety of courses reflects a wide range of needs.

  • Some introductory courses address statistical literacy , while others focus on statistical methods. This distinction is sometimes referred to as courses for consumers versus those for producers of analyses.
  • Introductory statistics courses target many different student audiences. There are different needs at different institutions, from elite universities to community colleges, with varying access to technology and support. Some statistics courses aim for a general student audience, while others are targeted at students in the life sciences, at business students, at future engineers, or at mathematics majors. There is a demand in some of these fields for examples and topical coverage tailored to the specific needs of the applied discipline.
  • Prerequisites differ among introductory statistics courses, the primary distinction being that some require calculus but most require no more than high school algebra.
  • Class sizes range from small courses of a dozen students that might be taught in a computer lab to large lecture courses for hundreds of students to massively open online courses (MOOCs) taught to thousands asynchronously.

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.

Support for Implementation

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

  • activities and datasets to illustrate active learning of statistical thinking,
  • assessment items, instruments, assignments, and rubrics,
  • technology tools for exploring concepts and analyzing data, and
  • suggestions by which the guidelines can be fulfilled in various learning environments (face-to-face, flipped, online, etc.).

Goals for Students in Introductory Statistics CourseGoals for Students in Introductory Statistics CourseGoals for Students in Introductory Statistics CourseGoals for Students in Introductory Statistics Coursessss

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.

  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.
  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.
  3. Students should be able to produce graphical displays and numerical summaries and interpret what graphs do and do not reveal.
  4. Students should recognize and be able to explain the central role of variability in the field of statistics.
  5. Students should recognize and be able to explain the central role of randomness in designing studies and drawing conclusions.
  6. Students should gain experience with how statistical models , including multivariable models, are used.
  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.
  8. Students should be able to interpret and draw conclusions from standard output from statistical software packages.
  9. Students should demonstrate an awareness of ethical issues associated with sound statistical practice.

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.

Teach statistics as an investigative process of problem-solving and decision-making.

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:

  1. Formulate questions.
  2. Collect data.
  3. Analyze data.
  4. Interpret results.

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):

  1. Understand the statistical process as a whole.
  2. Always be skeptical.
  3. Think about the variables involved.
  4. Always relate the data to the context.
  5. Understand (and believe) the relevance of statistics.
  6. Think beyond the textbook.

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.

Give students experience with multivariable thinking.

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

  • Offer students considerable practice with selecting an appropriate technique to address a particular research question, rather than telling them which technique to use and merely having them implement it.
  • Use technology and show students how to use technology effectively to manage data, explore and visualize data, perform inference, and check conditions that underlie inference procedures.
  • Assess and give feedback on students’ statistical thinking (also see Recommendation 6 below) as they progress through the course. In the appendices to this report, we present examples of projects, activities, and assessment instruments and questions that can be used to develop and evaluate statistical thinking.

Recommendation 2: Focus on conceptual understanding.

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.

Suggestions for teachers:

  • View the primary goal as to discover and apply concepts.
  • 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.
  • Although the language of mathematics provides compact expression of key ideas, use formulas that enhance the understanding of concepts, and avoid computations that are divorced from understanding.

Recommendation 3: Integrate real data with a context and a

purpose.

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.

Suggestions for teachers:

  • Use real data from studies to enliven your class, motivate students, and increase the relevance of the course to the real world.
  • Use data with a context as the catalyst for exploration, generating the questions, and informing interpretations to conclusions.
  • Make sure questions used with data sets are of interest to students so they can be easily motivated. Take the time to explain why we are interested in this type of data and what it represents. Note: Few data sets interest all students, so instructors should use data from a variety of contexts.
  • Use class-generated data to formulate statistical questions and plan uses for the data before developing the questionnaire and collecting the data. For example, ask questions likely to produce different shaped histograms, or use interesting categorical variables to investigate relationships. It is important that data gathered from students in class does not contain information that could be embarrassing to students and that students’ privacy is maintained.
  • If data entry is a part of the course, get students to practice entering raw data using a small data set or a subset of data, rather than spending time entering a large data set.
  • Use statistical software to analyze larger datasets that are available electronically.
  • Use subsets of variables in different parts of the course, but integrate the same data sets throughout. (Example: Use side-by-side boxplots to compare two groups, then use two- sample t-tests on the same data. Use histograms to investigate shape, and then later in the course to verify conditions for hypothesis tests. Encourage students to explore how multiple variables in the data set relate to one another.)
  • Minimize the use of hypothetical data sets to illustrate a particular point or to assess a specific concept.
  • See the Appendices C, D, and E for examples of good ways to use data in class activities, homework, projects, tests, etc.

(or drastically reduce) some lectures and Appendix F has additional suggestions specifically geared to implementing this recommendation in large classes.

Suggestions for teachers:

  • Ground activities in the context of real data with a motivating question. Do not “collect data to collect data” for its own sake.
  • Consider the student need for physical explorations ( e.g. , die rolling, card drawing) prior to the use of computer simulations to illustrate or practice concepts.
  • Encourage predictions from students about the results of a study that provides the data for an activity before analyzing the data. This motivates the need for statistical methods. (If all results were predictable, we would not need either data or statistics.)
  • Avoid activities that lead students step-by-step through a list of procedures. Instead, allow students to discuss and think about the data and the problem.
  • When planning activities, be sure there is enough time to explain the problem, let the students work through the problem, and wrap-up the activity during the same class period.
  • Consider low-/no-stakes peer assessment (where students comment on or rate a classmate’s work) within class to provide quick feedback and to improve the quality of final assessments.

Recommendation 5: Use technology to explore concepts and

analyze data.

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:

  • A brief introduction to a statistical software package, for example in a computer lab.
  • Watching an instructor demonstrate the use of a statistical software package in the context of a statistical investigation.
  • Reading generic “computer output” designed to resemble computer package results, but not specifically reproducing any of the major packages. This can be coupled with questions that probe student understanding. ( e.g. , what is the regression equation?)

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.”

Some technologies available:

(See Appendix D for in-depth discussion and examples.)

  • Interactive applets
  • Statistical software
  • Web-based resources, including o sources of experimental, survey, and observational data o online texts o data analysis routines
  • Games and other virtual environments
  • Spreadsheets
  • Graphing calculators

Suggestions for teachers:

  • Perform routine computations using technology to allow greater emphasis on interpretation of results.