Significance Testing Principles

  • Oops! ... I Picked the Wrong Test is a 4 minute, 12 second video that provides a fun review of common mistakes made in conducting hypothesis tests. The video was first sung for students in a Psychology class at the University of Oregon. The singer is Jennifer Simonds, Ph.D. of Westminster College in Salt Lake City Utah (where the video was filmed). The song is a parody of "Oops ... I did it again" by Britney Spears (2000). Characters: Britney Spearman - Jennifer Simonds, Chuck - Chuck Tate, Frustrated Professor - Bill Bynum, Dancers - Cressa Perloff (dance captain), Kathleen Ware, and Mariah Mercer. Credits: Lyrics, vocals, directions, and production by Jennifer Simonds; Recording and Sound Engineering by Ted Sablay; Final Cut Consulting by Zelda Randazzo; Audio Sync Assistance by Lizzie Randazzo; Camera Work and Props by Amy Fairchild. This video won the overall Grand Prize in the 2009 CAUSE A-Mu-sing contest.

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  • These three haikus were written as part of an activity in Paul Roback's introductory statistics class at St. Olaf College in February, 2009 ("World of chaos" by Carolyn Raitt; "Reality bites" by Hannah Johnson; "Is it you or me" by Nicole Villa). As a collection, the haikus won first place in the poetry category of the 2009 A-Mu-sing competition. The entire class is shown in this picture: http://www.causeweb.org/resources/fun/pics/Roback_class.jpg

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  • This is my take on the ubiquitous M&Ms counting activity. Each student records the color proportions in a fun-size bag of M&Ms. We pool the class data and run a Chi-Square goodness-of-fit test to determine whether or not the color proportions match those claimed on the manufacturer's website. We consistently find that the proportions do not match. The blue M&Ms, in particular, are underrepresented. This activity also includes a review of the 1-proportion z confidence interval.

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  • Song about the need to show a significant result in order to have a manuscript published. May be sung to the tune of Robert Feldman, Gerald Goldstein and Richard Gottehrer's 1963 song "My Boyfriend's Back," popularized by The Angels. Lyrics by Marc Coram and Matthew Finkelman (December, 2003). This song is part of the "Stanford Statistics Songbook" found at www.bscb.cornell.edu/~hooker/StanfordStatisticsSongbook.pdf Free to use for non-commercial educational purposes. Contact author to use in publications or for commercial purposes. Musical accompaniment realization and vocals are by Joshua Lintz from University of Texas at El Paso.

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  • Outliers is a triangular shaped poem written in 2008 by Jacqueline Shaffer (1980 - ) of California State University, East Bay. The poem focuses on the issue that outliers should not be removed from a data set without a reason.

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  • Probability is a 2 minute 14 second video that can be used in discussing the probability of rare events (e.g. how many consecutive times must a coin land heads before you question whether it is a fair coin?). The video was written, shot, and edited by Sam Rapien in 2007. The music is by Brett Musil and Sam Rapien and the single cast member is Jon Anderson. Mr. Rapien made this video while a graduate student in the Department of Art and Art History at the University of Nebraska, Lincoln.

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  • In this activity, students explore calculations with simple rates and proportions, and basic time series data, in the context of news coverage of an important statistical study. From 1973 to 1995, a total of 4578 US death penalty cases went through the full course of appeals, with the result that 68% of the sentences were overturned! Reports of the study in various newspapers and magazines fueled public debate about capital punishment.
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  • In this activity, students learn the true nature of the chi-square and F distributions in lecture notes (PowerPoint file) and an Excel simulation. This leads to a discussion of the properties of the two distributions. Once the sum of squares aspect is understood, it is only a short logical step to explain why a sample variance has a chi-square distribution and a ratio of two variances has an F-distribution. In a subsequent activity, instances of when the chi-square and F-distributions are related to the normal or t-distributions (e.g. Chi-square = z2, F = t2) will be illustrated. Finally, the activity will conclude with a brief overview of important applications of chi-square and F distributions, such as goodness-of-fit tests and analysis of variance.
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  • This group activity illustrates the concepts of size and power of a test through simulation. Students simulate binomial data by repeatedly rolling a ten-sided die, and they use their simulated data to estimate the size of a binomial test. They carry out further simulations to estimate the power of the test. After pooling their data with that of other groups, they construct a power curve. A theoretical power curve is also constructed, and the students discuss why there are differences between the expected and estimated curves. Key words: Power, size, hypothesis testing, binomial distribution
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  • This activity allows students to explore the relationship between sample size and the variability of the sampling distribution of the mean. Students use a Java applet to specify the shape of the "parent" distribution and two sample sizes. The simulation then samples from the parent distribution to approximate the sampling distributions for the two sample sizes. Students can see both sampling distributions at the same time making them easy to compare. The activity also allows students to determine the probability of extreme sample means for the different sample sizes so that they can discover that small sample sizes are much more likely than large samples to produce extreme values. Keywords: sampling distribution, sample size, simulation
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