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Exercises and Questions for Electronic Assessment of Statistical Concepts

In the United States most introductory courses in applied statistics emphasize definitions, computations, and procedure. Hence instructors in these Stat 101 courses may ask their students to define a median, to use a formula to compute a correlation coefficient, or to follow a six-step procedure to test a pair of hypotheses. With the current technology there is no need for students to memorize definitions, as they have done in the past. By using the Internet in a wireless environment (or by using the Help available in many statistical software packages), students may easily obtain a definition of any term found in a first course. With today’s electronic calculators (or statistical software), they do not need to use a formula for computation. Nor do they need to follow a complicated procedure to obtain an estimate of a p-value from a table, when a sequence of clicks produces an exact p-value. Instead most statistical educators recommend that Stat 101 should stress concepts. It should not be a course whose learning objectives are blind memorization, elementary arithmetic computation, and successful implementation of procedures. One influential report that makes this recommendation is the Guidelines for Assessment and Instruction in Statistics Education (GAISE) College Report (Garfield et al (2005)). The third of its six recommendations states that the course should “stress conceptual understanding rather than mere knowledge of procedures”. Included in this report are references to some important statistical concepts such sampling distributions, statistical significance, and confidence intervals, but there is no definition of a statistical concept. From conversations with many statistical educators in recent years, the author believes that such an idea is similar to United States Supreme Court Justice Potter Stewart’s explanation of “hard-core” pornography: "I shall not today attempt further to define the kinds of material I understand to be embraced . . . [b]ut I know it when I see it . . .”. In an attempt to determine the core statistical concepts, a survey of 57 statisticians was administered at the 2004 Joint Statistical Meetings (McKenzie (2004). The most mentioned core concepts were variability, association vs. causation, randomness, significance (statistical vs. practical), data collection methods (experiments, observations, surveys) and sampling distributions (law of large numbers, CLT (central limit theorem). But, even when such concepts can be identified, they are rarely emphasized for a number of reasons.