Matched Pairs Test A special type of t-inference Matched Pairs вЂ“ two forms вЂў Pair individuals by certain characteristics вЂў Randomly select treatment for individual A вЂў Individual B is assigned to other treatment вЂў Assignment of B is dependent on assignment of A вЂў Individual persons or items receive both treatments вЂў Order of treatments are randomly assigned or before & after measurements are taken вЂў The two measures are dependent on the individual Is this an example of matched pairs? 1)A college wants to see if thereвЂ™s a difference in time it took last yearвЂ™s class to find a job after graduation and the time it took the class from five years ago to find work after graduation. Researchers take a random sample from both classes and measure the number of days between graduation and first day of employment No, there is no pairing of individuals, you have two independent samples Is this an example of matched pairs? 2) In a taste test, a researcher asks people in a random sample to taste a certain brand of spring water and rate it. Another random sample of people is asked to taste a different brand of water and rate it. The researcher wants to compare these samples No, there is no pairing of individuals, you have two independent samples вЂ“ If you would have the same people taste both brands in random order, then it would be an example of matched pairs. Is this an example of matched pairs? 3) A pharmaceutical company wants to test its new weight-loss drug. Before giving the drug to a random sample, company researchers take a weight measurement on each person. After a month of using the drug, each personвЂ™s weight is measured again. Yes, you have two measurements that are dependent on each individual. A whale-watching company noticed that many customers wanted to know whether it was better to book an excursion in the morning or the afternoon. To test this question, the You may subtract either company thewhen following data on 15 way вЂ“ collected just be careful writing Hadays over the past randomly selected month. (Note: days were not consecutive.) Day 1 2 Morning 8 9 3 4 5 6 7 8 9 10 11 12 13 14 15 7 9 10 13 10 8 2 5 7 7 6 8 7 After8 10 9 8 9 11 8 noon Since you have two values for 10 4 7 8 9 6 6 9 First, you must find the differences for each day. each day, they are dependent on the day вЂ“ making this data matched pairs Day 1 2 3 Morning 8 9 7 9 10 13 10 Afternoon 8 10 4 5 9 8 9 6 7 8 9 10 11 12 13 14 15 8 2 5 7 7 6 8 7 11 8 10 4 7 8 9 6 6 9 I subtracted: Differenc 0 -1 -2 1 1 Morning 2 2 вЂ“ -2 -2 -2 -1 -2 0 2 -2 afternoon es You could subtract the other way! вЂў Have an SRS of days for whale-watching You need to state assumptions using the вЂў s unknown differences! Assumptions: вЂўSince the normal probability plot is approximately linear, the distribution of difference is approximately Notice the granularity in this normal. plot, it is still displays a nice linear relationship! Differences 0 -1 -2 1 1 2 2 -2 -2 -2 -1 -2 0 2 Is there sufficient evidence that more whales are sighted in the afternoon? H0: mD = 0 Ha: mD < 0 Be careful writing your Ha! Think about how youвЂ“ If you subtract afternoon subtracted: M-A Hdifferences mD>0should Notice morning; we mthen a:more D foris Ifused afternoon & it equals since the nullbeshould the0 differences + or -? be that there NOat difference. DonвЂ™t islook numbers!!!! Where mD is the true mean difference in whale sightings from morning minus afternoon -2 0 Differences -1 -2 1 1 2 2 -2 finishing the hypothesis test: t пЂЅ x пЂ m s n пЂЅ пЂ .4 пЂ 0 1 . 639 пЂЅ пЂ . 945 15 p пЂЅ . 1803 df пЂЅ 14 a пЂЅ . 05 -2 -2 -1 -2 0 2 In your calculator, perform t-test Notice athat if the youusing subtracted differences (L3) A-M, then your test statistic t = + .945, but pvalue would be the same Since p-value > a, I fail to reject H0. There is How could I insufficient evidence to suggest that more whales increase theare sighted in the afternoon than in the morning. power of this test? -2

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