c01Exploration_1_1_Interactive_Workbook-4

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Apr 3, 2024

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Exploration 1.1 Can Dogs Understand Human Cues? 1 Note: To ensure full functionality, including saving text in input fields and adding images in image fields, please download and use Adobe Acrobat Reader (free) or any Adobe Acrobat DC product. Student Name: Exploration 1.1 Can Dogs Understand Human Cues? Dogs have been domesticated for about 14,000 years. In that time, have they been able to de- velop an understanding of human gestures such as pointing or glancing? How about similar nonhuman cues? Researchers Udell, Giglio, and Wynne tested a small number of dogs in order to answer these questions. In this exploration, we will first see whether dogs can understand human gestures as well as nonhuman gestures. To test this, the researchers positioned the dogs about 2.5 meters from the experimenter. Two cups were placed, one on each side of the experimenter. The experimenter would perform some sort of gesture (pointing, bowing, looking) toward one of the cups or there would be some other nonhuman gesture (a mechanical arm pointing, a doll pointing, or a stuffed animal looking) toward one of the cups. The researchers would then see whether the dog would go to the cup that was indicated. There were six dogs tested. We will look at one of the dogs in two of his sets of trials. This dog, a four-year-old mixed breed, was named Harley. Each trial involved one gesture and one pair of cups, with a total of 10 trials in a set. We will start out by looking at one set of trials where the experimenter bowed toward one of the cups to see whether Harley would go to that cup. lightpoet/Shutterstock.com STEP 1: State the research question. 1. Based on the description of the study, state the research question. STEP 2: Design a study and collect data. Harley was tested 10 times and 9 of those times he chose the correct cup. 2. What are the observational units? 3. Identify the variable in the study. What are the possible outcomes of this variable? Is this variable quantitative or categorical? Definition The set of observational units on which we collect data is called the sample . The number of observational units in the sample is the sample size . A statistic is a number summarizing the results in the sample. STEP 3: Explore the data. With categorical data, we typically report the number of “suc- cesses” or the proportion of successes as the statistic. 4. What is the number of observational units (sample size) in this study?

2 CHAPTER 1 Significance: How Strong Is the Evidence? 5. Determine the observed statistic and produce a simple bar graph of the data (have one bar for the proportion of times Harley picked the correct cup and another for the proportion of times he picked the wrong cup). 6. If the research conjecture is that Harley can understand what the experimenter means when they bow toward an object, is the statistic in the direction suggested by the research conjecture? 7. Could Harley have gotten 9 out of 10 correct even if he really didn’t understand the human gesture and so was randomly guessing between the two cups? 8. Do you think it is likely Harley would have gotten 9 out of 10 correct if he was just guessing randomly each time? STEP 4: Draw inferences beyond the data. There are two possibilities for why Harley chose the correct cup 9 out of 10 times: • He is merely picking a cup at random and in these 10 trials happened to guess correctly in 9 of them. That is, he got more than half correct just by random chance alone. • He is doing something other than merely guessing and perhaps understands what the experimenters mean when they bow towards the cup. The unknown long-run proportion (i.e., probability) that Harley will choose the correct cup is called a parameter . Definition For a random process, a parameter is a long-run numerical property of the process. We don’t know the value of the parameter, but the two possibilities listed above suggest two different possibilities. 9. What is the value of the parameter if Harley is picking a cup at random? Give a specific value.

Exploration 1.1 Can Dogs Understand Human Cues? 3 10. What is the possible range of values (greater than or less than some value) for the parameter if Harley is not just guessing and instead understands the experimenter? We will show you how statisticians use simulation to make a statement about the strength of evidence for these two possible statements about the parameter’s value. The Chance Model Statisticians often use chance models to generate data from random processes to help them investigate the process. In particular, they can see whether the ob- served statistic is consistent with the values of the statistic simulated by the chance model. If we determine that Harley’s results are not consistent with the results from the chance model, we will consider this to be evidence against the chance model and in favor of the research con- jecture, that he understands the bowing gesture. In this case, we would say Harley’s results are statistically significant , meaning unlikely to have occurred by chance alone. Definition A result is statistically significant if it is unlikely to occur just by random chance. If our observed result appears to be consistent with the chance model, we say that the chance model is plausible or believable. We can’t perform the actual study more times in order to assess the second possibility, but we can simulate the behavior of Harley’s choices if we were to assume the first possibility (that he is simply guessing every time). 11. Explain how you could use a coin toss to represent Harley’s choices if he is guessing between the two cups each time. How many times do you have to flip the coin to represent one set of Harley’s attempts? What does heads represent? 12. If Harley was guessing randomly each time, on average, how many out of the 10 times would you expect him to choose the correct cup? 13. Simulate one repetition of Harley guessing randomly by flipping a coin 10 times (why 10?) and letting heads represent selecting the correct cup (“success”) and tails represent selecting the incorrect cup (“failure”). Count the number of heads in your 10 flips. Combine your results with the rest of the class to create a dotplot of the distribution for the number of heads out of 10 flips of a coin. a. Where does 9 heads fall in the distribution? Would you consider it an unusual outcome or a fairly typical outcome for the number of heads in 10 flips?

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