Friel and O'Connor (1999) used a previously published data set that examined 37 brands of peanut butter to introduce students to graphing within a real-world context. Following the discussion of the data set, students discussed what characteristics make good peanut butter (e.g., should not be too salty), conducted their own taste test between two brands, and graphed the resultant data using several different methods (e.g., stem-and-leaf plots, boxplot).
There are limited published demonstrations devoted to illustrating the normal curve. Existing examples tended to focus on providing students with real life illustrations of the normal distribution. For example, Brooks (2000) had students take a field trip to a nearby beach to examine the dimension of pebbles on the beach. Students recorded measurements for over 800 pebbles, calculated descriptive statistics, and plotted the data using a histogram and boxplot. Brooks noted that the exercise provided students the opportunity to explore a naturally occurring normal distribution and the importance of random sampling, proper graphing, and working together to achieve a common goal.
There are numerous additional published central tendency exercises designed to capture student's attention and get them involved in the learning process. For example, Tyrrell (2003) described a novel way of illustrating income data—he linked an individual's height to their income level. Tyrrell represented someone making the average income as being almost six feet tall. Someone making the minimum wage was only 9 inches tall as opposed to the richest individuals who stood at over 230 feet tall. Tyrrell used a public United Kingdom income database and images available through Microsoft Excel to create this illustration. He reported that the technique proved useful when he discussed the impact of outliers on income data. Educators have also used sample word counts from novels (Salzinger, 1990), music (Lesser, 2001), opinion questionnaires (Connor, 2003), simulated union strikes (Shatz, 1985), and climate data (Lindquist & Hammel, 1998) to teach the mean, median, and mode.
There has been a growing body of research devoted to the role of variation in several different areas such as the graphical representation of data (Meletiou & Lee, 2002), correlation and regression (Nicholson, 1999), teaching chance and data analysis (Watson & Kelly, 2002), repeated samples (Reading & Shaughnessy, 2004), and in the comparison of data sets (Ben-Zvi, 2002; Makar & Confrey, 2004). However, Reading and Shaughnessy lamented that statistics courses overemphasize central tendency and minimize the importance of variability. Indeed, Gould (2004) remarked, "The conceptualization of data as 'signal versus noise'…teaches students that the central tendency, however it's measured, is of primary importance and variability is simply a nuisance. A noisy one at that" (p. 7). Trice, Trice, and Ogden (1990), Gelman and Glickman (2000), and Melton (2004) provided several additional exercises to illustrate variation in the classroom.
Additional demonstrations and techniques are available on the topics such as the relationship among Pearson's r and variability, reliability, and validity (Huck, Wright, & Park, 1992; Odom & Morrow, 2006); understanding the coefficient of determination (Barrett, 2000); teaching Pearson's r without reliance on cross-products (Huck, Ren, & Yang, 2007); and quantifying students' qualitative understanding of the scatterplot (Holmes, 2001).
A similar exercise proposed by Stern (1999) examined the relationship between the number of shoes owned and gender. Yoshiwara and Yoshiwara (2000) invited instructors to use examples in class that incorporated bicycles, birds, bats, and balloons into examples designed to illustrate linear regression and other algebra problems. Chan (2001) proposed that instructors could use the concept of the breakdown point in linear regression to illustrate the influence that extreme data points have on ordinary least square (OLS) regression results. Dietz (1989) encouraged instructors to add a nonparametric alternative (e.g., Theil's estimator of slope and intercept) to simple linear regression when teaching a section or course on nonparametric statistics. She felt that these nonparametric estimators of slope and intercept were "robust, efficient, and easy-to-calculate alternatives to least squares" (p. 35). Additional materials exist for the teaching of the linear regression with unbalanced (Little, 1982) and clustered (Hedeker, Gibbons, & Flay, 1994) data.
Statistical educators have also provided examples to illustrate regression to the mean. For example, Cutter (1976) provided a means to illustrate regression to the mean using two sets of dice tosses. Levin (1982) modified Cutter's original demonstration by using two decks of playing cards instead of dice sums to reduce the artificiality of the exercise. Karylowski (1985) offered an additional modification by introducing psychological content to the demonstration by having students test individuals on a personality measure. After determining the cutoffs for the high and low groups (e.g., upper and lower 25%), the instructor had students retest the subjects on the same personality measure. Karylowski noted that the constituency of both extreme groups would change (i.e., regress to the mean) after the second testing session. Watkins (1986) offered a series of trivia questions that instructors could use to illustrate the regression to the mean among college students. Becker and Greene (2005) provided information on how various Nobel Laureates (e.g., Daniel Kahneman, Milton Friedman) have addressed regression to the mean throughout their careers.
Stockburger (1982) created three computer simulation exercises to illustrate the mean, normal curve, and correlation coefficients. He reported that students who used these exercises were significantly more successful on subsequent assignments than those students that did not utilize the simulations. Educators have also created programs to illustrate nonnormal data sets (Walsh, 1992), correlation (Goldstein & Strube, 1995; Mitchell & Jolley, 1999; Strube, 1991), regression and heteroscedasticity (Bradley, Hemstreet, & Ziegenhagen, 1992), and scatterplots (Goldstein & Strube, 1995; Hassebrock & Snyder, 1997).
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