October 1999 Statistical Thinking with Spreadsheets By Malcolm Getz This is a regular column sponsored by INFORMED, the INFORMS Forum on Education. Contact Armann Ingolfsson at armann.ingolfsson@ualberta.ca The spreadsheet is a language useful for exploring statistics. It offers many advantages for an introduction to statistical thinking. Students can learn statistics faster and enjoy it more by learning to think in a spreadsheet. In a spreadsheet, the contents of cells are nouns and the functions and procedures are verbs. The chart procedure is one set of verbs. A student who learns to use a chart verb gains a powerful tool for exploring statistics. By applying the editing adjectives, a student can make a chart carry the student's own esthetic. By making a variety of charts, a student can learn how to critique charts. With mastery of basic charting, a student can deploy charts in a variety of settings to explore features of the statistical landscape. The arithmetic functions are another useful set of verbs. A student can learn quickly to count, sum and average. Although the spreadsheet offers only modest advantage over a calculator at summing and averaging, by learning the spreadsheet verbs, the student develops a facility that can be readily extended. Indeed, once a student understands a new statistic (and verifies it with the simple functional verbs) the student can easily learn more advanced spreadsheet verbs like skew and slope. In a spreadsheet, the random number generators are verbs that allow a user to simulate an idea. A student can learn to flip a coin by rounding the RAND() function. Drag the coin flip formula over a hundred cells, and the sheet will flip a hundred coins at once. Simulation provides a powerful class of verbs for drilling deeply into the statistical mountains. As in learning other languages, one builds vocabulary by using it. The charting skills are useful in summarizing simulations. They are also useful in understanding verbs like ANOVA and regression. They can even be used in resampling. A first course in statistics taught with spreadsheets begins by forming simple sentences. Enter numbers as nouns, apply the sort and plot verbs, draw meaning in words. Invite students to immediately form their own sentences. Students can create spreadsheet projects that use the spreadsheet tools in clever ways. Doing original projects builds mastery and enthusiasm. Student can learn to gain mastery of more statistical ideas if key skills thread through the course. Charting is one such thread to be introduced early and extended throughout the course. Functions form a second thread from the simple count and sum functions to the rich procedures in the data analysis tool set. Simulation is a third thread that students can grasp more readily if simple simulations appear early. For many years, I invited students to use spreadsheet simulation to understand the behavior of samples by completing a spreadsheet project. With open-ended instructions, too few students could figure out what to do. With tight instructions, the students simply followed the steps in rote fashion, getting little insight. Now, I recognize that simulation is a vocabulary set similar to charting. By introducing early a simple simulation like a coin flip, students gain a comfort level with the idea of simulation. When students come to sampling, they can more readily deploy the basic simulation verbs to understand samples. Simulation then works best when woven as a thread through the course. As with any language, the key to learning the spreadsheet is to have students use the language. By inviting students to create spreadsheet projects on topics of their own choice, they must internalize the spreadsheet grammar sufficiently to use it for their own purposes. I assign a project due in the second week of the course. Observe something, turn the observations into numbers, compute descriptive statistics, and plot a relative frequency polygon. The choice of topic matters; more interesting topics get better grades. I assign students in teams of two to work together in learning spreadsheet, but each turns in his or her own project. Completing this first project is like writing one's own first sentence in French. After that point, students are much less concerned with the minutiae of menus and options. They know the tools are at hand. Entering numbers, applying some functions and drawing conclusions becomes a comfortable way to work. I have written a textbook in CD form for students to learn statistics while working in a spreadsheet ("e.stat for business and economics," South-Western College Publishing, 2000). The pages of explanatory text have figures embedded as in any text; however, in "e.stat" the figures click through to live Excel spreadsheets. More than 300 such spreadsheets and more than 500 problems present the concepts normally found in a first course in statistics. Readers are encouraged to work directly in the spreadsheet, to chart, compute, simulate and summarize conclusions in blocks of text. Many of the problems provide data sets downloaded from websites, making it easy for students to click a web address to get updated or related data. I project "e.stat" in class and work with the worksheets actively in class. Students study "e.stat" on their own, use it in taking computer-based tests or use it while completing projects. Some instructors say that students will want a printed text for comfort. My students compare what they have learned with what their friends learned in similar statistics classes that use print. They are amazed with the greater number of statistical ideas they have mastered, the ease with which they can employ the ideas for analysis, and the fun they have had in charting, designing and executing hypothesis tests and regressions. The analogy here is to learning French in an oral-oral, immersion setting. French comes faster, lasts longer, has more meaning and is more fun than in the old style of reading-only pedagogy. Learning statistics is easier, more useful and more fun when one uses spreadsheet as the language of discourse. It also helps that students want proficiency in spreadsheet for other purposes. Malcolm Getz is an associate professor of Economics at Vanderbilt University. E-mail: Malcolm.Getz@vanderbilt.edu Table of Contents OR/MS Today Home Page OR/MS Today copyright © 1999 by the Institute for Operations Research and the Management Sciences. All rights reserved. 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