Fun

  • A cartoon suitable for use in teaching about the variability in estimates (including estimates of the variability of estimates). The cartoon is number 2110 (February, 2019) from the webcomic series at xkcd.com created by Randall Munroe. Free to use in the classroom and on course web sites under a Creative Commons attribution-non-commercial 2.5 license.

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  • A cartoon suitable for use in teaching about risks and the problem with making post hoc comparisons. The cartoon is number 2107 (February, 2019) from the webcomic series at xkcd.com created by Randall Munroe. Free to use in the classroom and on course web sites under a Creative Commons attribution-non-commercial 2.5 license.

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  • A cartoon with an unusual graph suitable for use in teaching about cumulative distribution functions – topics for discussion include how a cdf looks like a step function for a discrete variable and a continuously increasing function over the range of a continuous variable (ask the class if the cartoon gets this correct or not). The cartoon is number 2092 (December, 2018) from the webcomic series at xkcd.com created by Randall Munroe. Free to use in the classroom and on course web sites under a Creative Commons attribution-non-commercial 2.5 license.

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  • A cartoon suitable for use in teaching about perceptions of the size of large numbers and the use of the log scale. The cartoon is number 2091 (December, 2018) from the webcomic series at xkcd.com created by Randall Munroe. Free to use in the classroom and on course web sites under a Creative Commons attribution-non-commercial 2.5 license.

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  • A cartoon suitable for use in teaching about Venn Diagrams and the meaning of mutually exclusive events. The cartoon is number 2090 (December, 2018) from the webcomic series at xkcd.com created by Randall Munroe. Free to use in the classroom and on course web sites under a Creative Commons attribution-non-commercial 2.5 license.

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  • A joke to facilitate discussion of random assignment in an experiment.  The joke was written by Larry Lesser from The University of Texas at El Paso in May, 2020.

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  • An activity to gather data on oranges for use in a unit on descriptive statistics.  The idea was presented at the 2019 USCOTS meeting by Katherine Frey Froslie and is described in her blog at https://www.statistrikk.no/2019/05/19/oranges-are-the-new-statistics/

    Here students measure how long it takes them to peel an orange (an easy to peel variety is recommended for in-class usage), what the orange weighs (possibly with and without the peel), and how many wedges are in the orange.  This creates a data set with both discrete (# of wedges) and continuous variables (time to peel, weight, percentage of orange weight in the peel) to be used for description. Other variables can be added through class discussion depending on student interest. An easy to peel variety of oranges  

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  • Summary: This High School AP activity examines whether students can tell the difference between CokeTM and PepsiTM by taste? During the “tasting part”, data are collected and the class keeps track of how many students can differentiate between Coke and Pepsi. During the “simulation part” of the activity, a simulation is conducted with dice. Finally, students compare their classroom results in the taste test with the simulated results about what would happen when subjects just guess randomly from the three possible choices. The activity is described in F. Bullard, “AP Statistics: Coke Versus Pepsi: An Introductory Activity for Test of Significance: AP Central – The College Board,” 2017 on the AP Central website at https://apcentral.collegeboard.org/courses/ap-statistics/classroom-resources/coke-versus-pepsi-introductory-test-significance

     

    Specifics: The activity is performed in the following steps:

    1. The Tasting part:
      1. First, two students will label three cup positions “A,” “B,” and “C.” Then they will roll a die and pour drinks into the cups such that all combinations of two of one drink and one of the other are represented, and the die roll makes each combination equally likely and keep track of the treatment.
      2. Students will be called out into the hall one by one to taste the three drinks and decide which cup contains the different drink. They do not need to identify the drinks as Coke or Pepsi, they only have to identify the cup containing the different soda, either A, B, or C.
    2. The Simulation part:
      1. The next stage of the discussion is to ask the students how many correct identifications they need before they can conclude that people were not just randomly guessing: “11 out of 30 is more than a third, but not enough more to be convincing, right?” Students will probably volunteer different dividing lines, but they will not be good at defending them. At the point when all the students understand the question but are unsure of how to answer it, the dice should be introduced into the activity.
      2. The students can suggest a simulation in which two die outcomes (say, 1 and 2) are considered a correct cup identification, and the other four die outcomes (say, 3, 4, 5, and 6) are considered incorrect cup identifications. Demonstrate by rolling a set of dice or one die many times. You should have as many die rolls as there are subjects in the study. Count the 1s and 2s. Suppose there are 8 out of 30 that “guessed correctly.” On your number line at the blackboard, make an X over the number 8. The students or group of students should do five or 10 simulations each (it’s good to have about 100—200 simulations) and then come to the blackboard and stack their Xs over the appropriate integers, making a histogram of the distribution of “number of correct cup identifications if everyone is randomly guessing.”
    3. Conclusion:
      1. Upon the conclusion of the tasting, the number of correct identifications is then counted. At this point, if the number is unusually high (say, 18 out of 30), then most students are prepared to conclude (correctly) that there is evidence that at least some people can tell the difference between Coke and Pepsi.
      2. Some statement like this would be great: “If everyone were randomly guessing, we would almost never see 18 students get it right by luck, because we did that 100 times with dice, and the highest we ever got was 16, and that was only once.”
      3. In the author’s experience, usually, about half or a little more will identify the correct drink. When the author, did this activity with a class: 13 out of 21 students correctly identified the different drinks.

    (Resource photo illustration by Barbara Cohen, 2020; this summary compiled by Bibek Aryal)

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  • Summary: This article describes the capture-recapture method of estimating the size of a population of fish in a pond and illustrates it with both a “hands-on” classroom activity using Pepperidge Farm GoldfiishTM crackers and a computer simulation that investigates two different estimators of the population size.  The activity was described in R. W. Johnson, “How many fish are in the pond?,”Teaching Statistics, 18 (1) (1996), 2-5

    https://onlinelibrary.wiley.com/doi/abs/10.1111/j.1467-9639.1996.tb00882.x

    Specifics: To illustrate the capture-recapture method in the classroom, two different varieties of Pepperidge Farm GoldfishTM crackers are used. The instructor places all of the Goldfish from a full bag of the original variety in a bowl to correspond to the initial state of the pond (the instructor should have previously counted the true number from the bag, which turned out to be 323 in the paper’s example). Students then captured c = 50 of these fish and replaced them with 50 Goldfish of a flavored variety of different color. After mixing the contents of the bowl, t=6 ‘tagged’ fish - fish of the flavored variety were found in a recaptured sample size of r = 41, giving the estimate cr/t= 341. This used the maximum likelihood (ML method. To examine the behavior of the MLE the capture-recapture ML  method is repeated 1000 times using a computer simulation. The distribution of the results will be heavily skewed since the MLE is quite biased (in fact, since there is positive probability that t = 0, the MLE has an infinite expectation). The simulation is then redone using Seber’s biased-corrected estimate = [(c+1)(r+1)/(t+1)] – 1.  After the true value of the population size is revealed by the instructor, students see that the average of the 1000 new simulations show that the biased-corrected version is indeed closer to the truth (and also that the new estimate has less variability).

    (Resource photo illustration by Barbara Cohen, 2020; this summary compiled by Bibek Aryal)

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  • Summary: Through generating, collecting, displaying, and analyzing data, students are given the opportunity to explore a variety of descriptive statistical techniques and develop an understanding of the distinction between theoretical, subjective, and empirical (or experimental) probabilities. These concepts are developed with activities using Hershey KissesTM and may be extended to introduce the sampling distribution of a sample proportion. The activities are described in M. Richardson and S. Haller. (2002), “What is the Probability of a Kiss? (It's Not What You Think),” Journal of Statistics Education, 10(3), https://www.tandfonline.com/doi/full/10.1080/10691898.2002.11910683

    Specifics: The main activity uses Hershey’s Kisses to explore the concept of probability. Three specific sub-activities are performed such as: 

    1. Students explore the empirical probability that a plain Hershey’s Kiss will land on its flat base when spilled from a cup. 
    2. Students make predictions about the probability of an almond Hershey’s Kisses landing on its base when spilled from a cup, after having experimented with the plain Kisses.
    3. Students explore the properties of the distribution of a sample proportion to see whether the percentages of base landings have a specified distribution and whether they think that the number of Kisses tossed affects the shape or the mean and standard deviation of this distribution.

    (Resource photo illustration by Barbara Cohen, 2020; this summary compiled by Bibek Aryal)

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