University of Minnesota

Newsletter for the Section on Statistical Education

Volume 7, Number 1 (Winter 2001)

How many statistics instructors learn that their former students have applied their statistical skills to earn over $100,000 playing a lottery game? This happened to Robin Lock, Professor of Mathematics at St. Lawrence University in New York. Lock's former student and a friend applied their knowledge of probability in figuring out that the expected value of a Quick Draw lottery game at a local restaurant was greater than $0 during a special promotion.

According to Lock, these students "first raised enough cash to start play with little chance of going bust before the law of large numbers took effect to assure their expected winnings." They computed the probabilities and expectations by hand, then simulated the game many times on a computer to confirm the long run behavior. Putting the theory into practice for the remaining three days of the promotion netted the pair a profit of more than $100,000, matching almost exactly what the theory had predicted. Lock noted "Not only did they understand the application of mathematical expectation to this problem, but they had confidence in what they learned and the free time to sit all day in the restaurant playing the game." After hearing about these students' success, Lock invited them to visit his class and share the information about how they worked out the expected value, simulated the game, and decided how much to gamble.

This is just one of the many stories Robin Lock enjoys telling to his colleagues, and this interview resulted from my desire to write down and share some of these stories with a broader audience. Many people are most familiar with Robin Lock as the master of data surfing on the web. His website (http://it.stlawu.edu/~rlock) is bookmarked by most statistics educators, and he updates it regularly, adding copies of the numerous talks he gives at conferences and workshops.

How did Lock first become interested in data sets and archiving data? His Ph.D. in mathematics and statistics from the University of Massachusetts, Amherst included only theoretical mathematics and statistics courses. Towards the end of his graduate program he attended a talk given by statistician Mike Sutherland, called "My favorite data sets." This was the first time Lock really came into contact with data sets and statistical software, and he thought applied statistics looked like fun. This talk spurred an interest in real data sets that has continued to be a focus of his professional work.

Ten years after Sutherland's talk, in 1990, Lock produced a data disk for The Statistics in Liberal Arts Colleges Workshop (SLAW). SLAW is a group that has been meeting every summer for many years to share ideas and resources as well as to discuss issues related to being a statistician in a mathematics department at a liberal arts college. The group had been discussing the need to have more real data sets available that could be shared and used with students. Lock collected and assembled data sets on a disk for this group. Having attended the third International Conference on Teaching Statistics in New Zealand, he was inspired by a session there on sharing data. However, the data exchange was difficult due to problems with different formats and platforms.

Continuing his mission to collect and share interesting data, Lock initiated a column in the ASA *Graphics and Computing Newsletter* on data sets, and helped to create the Data Sets and Stories section of the *Journal of Statistics Education* when that journal started in 1993. In addition to writing about data, he began to give talks and presentations about data sets as well. His 1996 ASA talk on Data Surfing won an award that year for the best contributed paper in a statistics education session.

Lock uses many web resources in his class, in addition to data sets. For example, he found the "Guessing Correlation" game (matching correlations to scatterplots) at the University of Illinois website, and began using it in class, playing until the students guessed one wrong. Now students are encouraged to play the game outside of class. Anyone who makes it on the leader board of top scorers (perhaps needing more than 100 correct guesses in a row) before the next quiz gets a free point on that quiz. Although this isn't much of an incentive, students play into the early morning, sending Lock email messages or phone messages when they reach the list and earn their extra credit point.

Many instructors enjoy using a version of "Let's make a deal" as an activity when teaching probability. Students can either simulate the game in class using cards to represent the three doors (behind which are two goats and one car) or can use a web version of the game. One time when Lock played the game with his students, he instructed them to sit on either side of the room, according to their belief that "staying" or "switching" was a better strategy to use in winning the car after one door is revealed. As they played the game and collected data, students could change to the other side of the room if their belief changed. After a while all but one student had moved to the "switch" side of the room. When Lock asked the one remaining student why he hadn't changed his seat despite all the evidence gathered that to switch was the best strategy, this student responded, "because if I move we'll have to stop playing the game."

Lock has other favorite activities that he uses in class in addition to "Let's make a Deal". He uses a loaded dice activity, where he has a red die (a fair die) and a white die (that has been altered to two fives and no two). This activity is used before a unit on tests of proportions. He has the students roll the two dice, so that red is against white, and tally which die shows the higher number (ignoring ties). A box is passed around so that each student has a turn to roll the pair of dice 10 times, while class is proceeding.

This provides a total of 300-350 rolls, which is needed for the power of the test to be sufficient. Then he performs a test of proportions with the resulting data. The class tests the hypothesis that the Red die wins 50% of the time. (With the altered white die, it really wins 40% of the time). This experiment provides strong evidence that the null hypothesis is false, and a small p-value is produced. Students are asked: what went wrong? After students give their guesses, Lock shows them the "fixed" die. He claims, "If nothing else, after this activity they know how to fix dice."

During the past year Lock was named Jack and Sylvia Burry Professor of Statistics at St. Lawrence University and became a fellow of the American Statistical Association. He continues to share his expertise in teaching statistics with colleagues in the USA at the Joint Statistical Meetings as well as at the international conferences on teaching statistics. He especially enjoys the ICOTS conferences because "everyone you talk to is interested in teaching." Having attended these conferences in British Columbia, Morocco, and Singapore, in addition to New Zealand, Lock is looking forward to actively participating in ICOTS 6, which will be held South Africa in 2002.

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