Statistics Lab 4.4 PDF

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Stat lab 4.4 - use for reference...

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LAB 4.4 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 analyzed a simplified version of their data. Assume that 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. 1. What are the correct null and alternative hypotheses? H0: versus Ha: Let group 1 be the mortality treatment and group 2 be the dental pain treatment. 2. 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! X bar = 2.77 3. Use StatKey to calculate the p-value for this hypothesis test. P value 0.101 4. What is the generic conclusion for this test? insufficient 5. What is the conclusion in context? Cannot reject the null 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.

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LAB 4.4 6. 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? Type 2

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? Say that the drug is effective when it really isnt b. What does it mean in context to make a type II error in this situation? Find that the drug is not effective when it really is c. Which error do you think is worse? Type 1 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? The vitamins each day have benefits when they really dont b. What does it mean in context to make a type II error in this situation? the vitamins each day don’t have benefits when they really do c. Which error do you think is worse? Type 2 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? 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 3/11/19

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LAB 4.4 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 H0: 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 evidence for a biased coin (Yes or No) Situation

^ =0.60 p ^p=0.60 ^p=0.60 ^p=0.70 ^p=0.53 ^p=0.53 ^p=0.51

(12 heads in 20 flips) (30 heads in 50 flips) (60 heads in 100 flips) (35 heads in 50 flips) (53 heads in 100 flips) (530 heads in 1000 flips) (510 heads in 1000 flips)

Biased? (1st step) yes yes yes yes no no no

p-value (2nd step) .254, .237 .094, .096 .025, .0026, .0046 .314, .317 .025 .271, .268

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 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 2. The sample proportion 3. The number of simulated samples in the randomization distribution Activity 4: Parental misperception of youngest child size2 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. 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. When considering a hypothesis test for H 0: μd = 0 vs Ha: μd > 0, where μ is the estimated error, the p-value is 0.00. A corresponding 95% confidence interval for μd is (2.10 to 4.00) inches. 1.

In this instance, has statistical significance been found? Include a reason.

Yes because the 0 is not in the 95% confidence interval and 0 < 0.05 2. Do you have some support for practical significance? How do you make that determination? If the 95% confidence interval for μd was instead (0.2 to 0.5) inches would you change your answer? Yes because 0 isnt in the confidence interval but 0.2 to 0.5 wouldn’t bc the value of 0 is too close 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

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