Section #04.4 shared lab

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Pennsylvania State University *

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200

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Statistics

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Apr 3, 2024

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LAB 4.4 – A CLOSER LOOK AT TESTING Statistics 200: Lab Activity for Section 4.4 A closer look at testing- Learning objectives:  Interpret Type I and Type II errors in hypothesis tests  Recognize a significance level as measuring the tolerable chance of making a Type I error  Explain the potential problem with significant results when doing multiple tests  Recognize the value of replicating a study that shows significant results  Recognize that statistical significance is not always the same as practical significance  Recognize that larger sample sizes make it easier to achieve statistical significance if the alternative hypothesis is true Activity 1: Warm up with a hypothesis test! Reproducing the results of statistically significant experiments is an important part of performing good science. A psychology experiment in 2008 showed that young adults demonstrated an increased preference for their parents after completing an exercise about death as compared to an exercise about dental pain. 1 In the study, participants were asked to allocate phone minutes to talk to a parent after completing a randomly assigned activity about either death or dental pain. A significant result was found with a p-value of 0.03. Another group of researchers replicated the experiment to see if the results could be reproduced. In this activity we will analyze a simplified version of their data. Research Question : Our goal is to show that young adults want to spend more minutes talking with their parents when they are thinking about mortality as opposed to dental pain. *Let group 1 be the mortality treatment and group 2 be the dental pain treatment. Understanding the Research 1. What is the parameter of interest? Difference in mean of talking about death or dental pain Analysis 2. What are the correct null and alternative hypotheses? H 0 : mu1 = mu2 versus H a : mu 1 > mu2 3. The simplified data set (preference for parents) is available on Canvas. Load it into StatKey for analysis. What is the sample statistic? Use correct notation! Mu1 – mu2 4. Use StatKey to calculate the p-value for this hypothesis test. 1 Cox, C.R., Arndt, J., Pyszczynski, T., Greenberg, J., Abdollahi, A., & Solomon, S. (2008). Terror management and adults' attachment to their parents: The safe haven remains. Journal of Personality and Social Psychology, 94 (4), 696-717. 3/11/19 © - Pennsylvania State University

LAB 4.4 – A CLOSER LOOK AT TESTING .100 5. What is the formal conclusion for this test? Fail to Reject null 6. What is the conclusion in context? Young adults want to talk more with parents about death than dental pain 7. The experiment we just used to perform a hypothesis test was designed to mimic the experiment from the original study, yet the original study yielded significant results while this study did not. If young adults really do want to talk more with their parents after thinking about mortality, did our analysis make a Type I error, a Type II error, or no error at all? In this case, our analysis did not make a Type I error (rejecting a true null hypothesis), but rather a Type II error (failing to reject a false null hypothesis). Activity 2: Which is worse, type I or type II error? 1. We are testing a new drug with potentially dangerous side effects to see if it is significantly better than the drug currently in use. If it is found to be more effective, it will be prescribed to millions of people. a. What does it mean in context to make a type I error in this situation? making a Type I error would mean incorrectly rejecting the null hypothesis. The null hypothesis usually assumes that the new drug is not significantly better than the current drug. Making a Type I error would imply that you conclude the new drug is significantly better when it is not. b. What does it mean in context to make a type II error in this situation? Making a Type II error would mean failing to reject the null hypothesis when it's false. In this case, it would mean not detecting that the new drug is actually significantly better than the existing one. c. Which error do you think is worse? Generally, in the context of pharmaceuticals, making a Type I error (approving a drug that is not significantly better) is often considered more serious because it may expose patients to unnecessary risks. It could lead to adverse health outcomes and can have legal and ethical ramifications. 3/11/19 © - Pennsylvania State University

LAB 4.4 – A CLOSER LOOK AT TESTING 2. Now we are testing to see whether taking a vitamin supplement each day has significant health benefits. There are no (known) harmful side effects of the supplement. a. What does it mean in context to make a type I error in this situation? Type 1 error: This occurs when the null hypothesis is incorrectly rejected when it is true. In the context of the vitamin supplement study, it would mean concluding that the supplement has a significant health benefit when, in reality, it does not. In other words, it's a mistake to believe there is an effect when there isn't. b. What does it mean in context to make a type II error in this situation? Type 2 error: This occurs when the null hypothesis is not rejected when it is false. In the context of the vitamin supplement study, it would mean failing to detect a significant health benefit when, in reality, the supplement does have benefits. In other words, it's a mistake to believe there is no effect when there is one. c. Which error do you think is worse? Type II 3. For a given situation, what should you do if you think that committing a type I error is much worse than committing a type II error? (Choose the best answer from the following) A. Increase the significance level. B. Decrease the significance level. C. Nothing, just be careful to take a good sample. Activity 3: Developing Intuition about Significance: Fair Coins If we are flipping a coin, how large a proportion of heads do we need to get in order to claim evidence that the coin is biased to give more heads than tails? If the coin is fair, the proportion of heads should be 0.5, so our null and alternative hypotheses are H 0 : p = 0.5 vs Ha: p > 0.5, where p is the proportion of heads. First For each situation below, make a guess about whether or not you think that sample outcome would give convincing evidence for a biased coin (Yes or No) Situation Biased? (Your guess) (1 st step) p-value (2 nd step) ^ p = 0.60 (12 heads in 20 flips) yes .267 ^ p = 0.60 (30 heads in 50 flips) yes .106 ^ p = 0.60 (60 heads in 100 flips) yes .025 3/11/19 © - Pennsylvania State University

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LAB 4.4 – A CLOSER LOOK AT TESTING ^ p = 0.70 (35 heads in 50 flips) no .0024 ^ p = 0.53 (53 heads in 100 flips) no .308 ^ p = 0.53 (530 heads in 1000 flips) no .025 ^ p = 0.51 (510 heads in 1000 flips) no .290 Second Now using StatKey (using at least 5,000 simulated samples) find the p-value in each case above and indicate whether (at a 5% level) there is convincing evidence that the coin is biased. If you are working in a group, consider divide and conquer, before discussing results. Examine the results from the p-values. Consider each of the factors below. Decide whether or not each has an impact on whether or not a sample proportion shows significance. 1. The sample size yes 2. The sample proportion yes 3. The number of simulated samples in the randomization distribution yes Activity 4: Parental misperception of youngest child size 2 After the birth of a second child many parents report that their first child appears to grow suddenly and substantially larger. One possible explanation is the biopsychological phenomenon called ‘baby illusion’, under which they routinely misperceive their youngest child as smaller than he/she really is. Research Question : Do parents report that their first child appears to grow suddenly and substantially larger after the birth of their second child? To answer this question, a researcher conducted a study where 39 mothers first estimated the height of their youngest children (aged 2–6 years) by marking a featureless wall in the presence of an investigator. The actual height was then obtained. An estimated error was calculated for each child when looking at the difference of (actual height and estimated height), in inches. Analysis When considering a hypothesis test for H 0 : μ = 0 vs Ha: μ > 0, where μ is the estimated error, the p-value is 0.00. A corresponding 95% confidence interval for μ is (2.10 to 4.00) inches. 1. In this instance, has statistical significance been found? Include a reason. No, not in parameter 2. Do you have some support for practical significance? How do you make that determination? If the 95% confidence interval for μ was instead (0.2 to 0.5) inches would you change your answer? yes 2 Kaufman, J., Tarasuik, J., Dafner, L., Russell, J., Marshall, S., and Meyer, D. (2013). Parental misperception of youngest child size, Current Biology, Vol. 26(24) 1085–1086. 3/11/19 © - Pennsylvania State University

Section #04.4 shared lab

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