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Description of the Random Behavior Exercise for the Instructor

Three different levels of difficulty/involvement are woven into this web exercise. Level 1 would be appropriate for an advanced placement high school senior, junior college student, or an introductory course college student who wants just the basics. By skipping all the level 2 and 3 verbiage, the student guickly discovers he/she can't behave randomly, but he/she won't become aware of the subtleties and complexities surrounding randomness.

Level 2 is most appropriate for introductory college-level courses or second courses in psychology. Level 2 exposes students to some of subtle and complex issues concerning randomness, probability and social inference (cognition).

Level 3 would be appropriate for upper-level/major student because it assumes the student has had a statistics/math course and is highly motivated to explore, think, and learn about abstract, difficult-to-think-about concepts. Working all the way through level 3 will take most students between 1 and 1.5 hours.

The exercise begins with some definitions of randomness along with optional digressions about definition problems, flawed lotteries, and chaos theory. Next, students input an imaginary sequence of 100 coin flips and learn about 4 ways to assess randomness (distribution of heads/tails, number of runs, length of runs, and serial dependencies or autocorrelation). Students can test their understanding of these randomness tests by taking an interactive quiz.

Next, they request an analysis of their imagined sequence, and they receive results of the 4 statistical tests in a table. The exercise provides explanations for why the imagined sequences usually fail randomness tests, describing the gambler's and hot hand fallacies, a famous probability "teaser," and some applications to everyday life.

By now, the student should be curious about what a random sequence of 100 flips should look like, and they get an opportunity to find out in the second section of the exercise. They either flip a real coin themselves, or they have the computer generate 100 "random" flips. The random number generator is not very good and frequently fails at least one of the randomness tests. This should increase skepticism about computer output and increase appreciation for how hard it is to create anything that acts randomly. If students want to explore a high-quality random number generator, they can then link to a site using radioactive decay to generate "real" random numbers.

After comparing the coin/computer results with their imaginary results, students read brief descriptions of the research on people's problems with behaving randomly, and students are asked to generate some reasons why randomness is so hard for us grasp [a number of reasons are provided latter]

In the last part of the exercise, students can test their new insights by repeating the coin flip exercises (imagine, real, or computer generated) . Each time they repeat the coin flip exercise, their results are stored in a table so they can see whether practice leads to closer approximation of randomness. They can also take an interactive multiple choice and short answer quiz. They can ask for hints if they are unsure of an answer; after they pick an answer, they find out if it is correct; they can read justifications/explanations for the correct answer, and they can link to relevant sections of the exercise which they can review to solidify their learning. Finally, students complete a brief evaluation of the exercise.

Right now, the program will not send student responses to any data file, but it can be easily set up to do so by adding a POSTURL or MAILTO command.

Go to the webtutorial exercise        Chris Wetzel's homepage