Chapter 4 Section 3 day f.notebook. November 10, Honors Statistics

Transcription

1 Chapter 4 Section 3 day f.notebook November 10, 2014 Honors Statistics Monday November 10,

2 Daily Agenda 1. Welcome to class 2. Please take your seat. 3. Check homework C4#10 4. Discuss 4.3 concepts 5. Start group work 6. Finish 4.2 concepts 7. Collect folders 2

3 announced yesterday see next slide add pg MC # 87 to 94 3

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5 HOMEWORK over the weekend C4#10 pg : Multiple Choice #87 to #94 AND Reading and notes Chapter 4 Section 3 pages 266 to 273 5

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7 C4#10 pg : Multiple Choice #87 to #94 Exercise 4.87 MC page 264 Can changing diet reduce high blood pressure? Vegetarian diets and low salt diets are both promising. Men with high blood pressure are assigned at random to four diets: (1) normal diet with unrestricted salt; (2) vegetarian with unrestricted salt; (3) normal with restricted salt; and (4) vegetarian with restricted salt. This experiment has > (a) one factor, the type of diet. > (b) two factors, high blood pressure and type of diet. > (c) two factors, normal/vegetarian diet and unrestricted/restricted salt. > (d) three factors, men, high blood pressure, and type of diet. > (e) four factors, the four diets being compared. C Factor 1 2 levels Vegetarian diet / normal diet Factor 2 2 levels restricted salt / unrestricted salt 7

8 Exercise 4.88 MC page 264 In the experiment of the previous exercise, the subjects were randomly assigned to the different treatments. What is the most important reason for this random assignment? > (a) Random assignment eliminates the effects of other variables such as stress and body weight. > (b) Random assignment is a good way to create groups of subjects that are roughly equivalent at the beginning of the experiment. > (c) Random assignment makes it possible to make a conclusion about all men. > (d) Random assignment reduces the amount of variation in blood pressure. > (e) Random assignment prevents the placebo effect from ruining the results of the study. B Random assignment reduces bias by creating groups of subjects that are roughly equivalent at the beginning of the experiment. Distribute all other possible "confounding" variables between the treatment groups. 8

9 Exercise 4.89 MC page 265 To investigate whether standing up while studying affects performance in an algebra class, a teacher assigns half of the 30 students in his class to stand up while studying and assigns the other half to not stand up while studying. To determine who receives which treatment, the teacher identifies the two students who did best on the last exam and randomly assigns one to stand and one to not stand. The teacher does the same for the next two highest scoring students and continues in this manner until each student is assigned a treatment. Which of the following best describes this plan? (a) This is an observational study. (b) This is an experiment with blocking. (c) This is a completely randomized experiment. (d) This is a stratified random sample. (e) This is a cluster sample. B There is random assignment but the teacher is first creating BLOCKS of students by separating them by exam scores. 9

10 Chapter 4 Section 3 day f.notebook November 10, 2014 Exercise 4.90 MC page 265 A gardener wants to try different combinations of fertilizer (none, 1 cup, 2 cups) and mulch (none, wood chips, pine needles, plastic) to determine which combination produces the highest yield for a variety of green beans. He has 60 green bean plants to use in the experiment. If he wants an equal number of plants to be assigned to each treatment, how many plants will be assigned to each treatment? (a) 1 (b) 3 (c) 4 (d) 5 (e) 12 D 60/12 = 5 plants per treatment Fertilizer amount Mulch Type None none 1 cup 2 cups wood chips pine needles plastic

11 Exercise 4.91 MC page 265 Corn variety 1 yielded 140 bushels per acre last year at a research farm. This year, corn variety 2, planted in the same location, yielded only 110 bushels per acre. Based on these results, is it reasonable to conclude that corn variety 1 is more productive than corn variety 2? (a) Yes, because 140 bushels per acre is greater than 110 bushels per acre. (b) Yes, because the study was done at a research farm. (c) No, because there may be other differences between the two years besides the corn variety. (d) No, because there was no use of a placebo in the experiment. (e) No, because the experiment wasn t double blind. C Too many confounding variable between years... name some... 11

12 Exercise 4.92 MC page 265 A report in a medical journal notes that the risk of developing Alzheimer s disease among subjects who regularly opted to take the drug ibuprofen was about half the risk among those who did not. Is this good evidence that ibuprofen is effective in preventing Alzheimer s disease? > (a) Yes, because the study was a randomized, comparative experiment. > (b) No, because the effect of ibuprofen is confounded with the placebo effect. > (c) Yes, because the results were published in a reputable professional journal. > (d) No, because this is an observational study. An experiment would be needed to confirm (or not confirm) the observed effect. > (e) Yes, because a 50% reduction can t happen just by chance. D There was no assigned treatment 12

13 Chapter 4 Section 3 day f.notebook November 10, 2014 Exercise 4.93 MC page 265 A farmer is conducting an experiment to determine which variety of apple tree, Fuji or Gala, will produce more fruit in his orchard. The orchard is divided into 20 equally sized square plots. He has 10 trees of each variety and randomly assigns each tree to a separate plot in the orchard. What are the experimental unit(s) in this study? > (a) The trees > (b) The plots > (c) The apples > (d) The farmer > (e) The orchard B The farmer is experimenting with his farmland plots not "doing things to the trees". 13

14 Exercise 4.94 MC page 265 Two essential features of all statistically designed experiments are > (a) compare several treatments; use the double blind method. > (b) compare several treatments; use chance to assign subjects to treatments. > (c) always have a placebo group; use the double blind method. > (d) use a block design; use chance to assign subjects to treatments. > (e) use enough subjects; always have a control group. COMPARE, RANDOMIZE, CONTROL, REPLICATE B Compare and randomization 14

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18 Foster care versus orphanages Do abandoned children placed in foster homes do better than similar children placed in an institution? The Bucharest Early Intervention Project found that the answer is a clear Yes. The subjects were 136 young children abandoned at birth and living in orphanages in Bucharest, Romania. Half of the children, chosen at random, were placed in foster homes. The other half remained in the orphanages. 55 (Foster care was not easily available in Romania at the time and so was paid for by the study.) What conclusion can we draw from this study? Explain. Random assignment This allows us to conclude (infer) that children placed in foster care "do better". Bad experimental design... so... 18

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20 Exercise Frozen batteries page 273 Frozen batteries Will storing batteries in a freezer make them last longer? To find out, a company that produces batteries takes a random sample of 100 AA batteries from its warehouse. The company statistician randomly assigns 50 batteries to be stored in the freezer and the other 50 to be stored at room temperature for 3 years. At the end of that time period, each battery s charge is tested. Result: Batteries stored in the freezer had a higher average charge, and the difference between the groups was statistically significant. What conclusion can we draw from this study? Explain. Random assignment This allows us to conclude (infer) that placing batteries in the freezer causes them to last longer. Random selection This allows us to (infer) that the experiment results will generalize to the population of batteries at the warehouse. 20

21 Exercise Who talks more? page 274 Who talks more women or men? According to pg 267 Louann Brizendine, author of The Female Brain, women say nearly three times as many words per day as men. Skeptical researchers devised a study to test this claim. They used electronic devices to record the talking patterns of 396 university students who volunteered to participate in the study. The device was programmed to record 30 seconds of sound every 12.5 minutes without the carrier s knowledge. According to a published report of the study in Scientific American, Men showed a slightly wider variability in words uttered. But in the end, the sexes came out just about even in the daily averages: women at 16,215 words and men at 15, This difference was not statistically significant. What conclusion can we draw from this study? Explain. Random assignment There was no random assignment and no actual treatment. This was an observational study. Random selection There was no random selection... volunteers agreed to wear the electronic devices. 21

22 Exercise Attend church, live longer? page 274 Attend church, live longer? One of the better studies of the effect of regular attendance at religious services gathered data from a random sample of 3617 adults. The researchers then measured lots of variables, not just the explanatory variable (religious activities) and the response variable (length of life). A news article said: Churchgoers were more likely to be nonsmokers, physically active, and at their right weight. But even after health behaviors were taken into account, those not attending religious services regularly still were about 25% more likely to have died. 57 What conclusion can we draw from this study? Explain. Random assignment This was not an experiment. No random assignment so no cause and effect can be inferred. Random selection This allows us to (infer) that the result (longer life) will generalize to the population adults from which the sample was selected. 22

23 Exercise Daytime running lights page 274 Daytime running lights Canada and the European Union require that cars be equipped with daytime running lights, headlights that automatically come on at a low level when the car is started. Many manufacturers are now equipping cars sold in the United States with running lights. Will running lights reduce accidents by making cars more visible? An experiment conducted in a driving simulator suggests that the answer may be Yes. What concerns would you have about generalizing the results of such an experiment? A driving simulator may lack realism and may help the driver to pay closer attention. Like a contest... Perhaps the next slides will help... Once everyone has them it may not be so exceptional to see. 23

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29 Random sampling versus random assignment Explain the difference between the types of inference that can be made as a result of random sampling and random assignment. Random sampling Random assignment 29

30 Observation versus experimentation Explain the difference between the types of inference than can usually be made from an observational study and an experiment. Observational Study Experiment Study 30

31 HOMEWORK From THURSDAY Night A Skips 70, 74 C4#9 pg : 70, 71, 72, 74, 76, 79, 81, 86 LABEL YOUR A SKIPS... 31

32 Exercise 4.70 Pain relief study page 262 (a) Why should Fizz not simply administer the drug and record the patients' responses? If a control group is not formed there will be nothing to compare the new medication with. The fact that the patients are in a study and receive pain relief could then be attributed to the "placebo effect". (b) Should the patients be told with drug they are receiving? How would this knowledge probably affect their reactions? The patients must not be told which pain medication they are receiving. If a person knows they are receiving the placebo, they will most likely not experience any pain relief. There will be no "placebo effect". No chance for the person's mind to do the pain relief. EXTRAS (c) Outline the design of an experiment to compare the drug's effectiveness with that of aspirin and a placebo. Group 1: 20 subjects Treatment 1: received new pain medication 60 patient suffering from arthritis Group 2: 20 subjects Treatment 2: received aspirin compare pain relief Random Assignment Group 3: 20 subjects Treatment 3: received placebo (d) If patients are not told which treatment they are receiving, the experiment is single blind. Should this experiment be double blind? All experiments should be double blind if it is possible to do so. A double blind experiment adds credibility to the results. Those administering the medication cannot inadvertently bias the results because they will not know which person is receiving the new pain relief medication. 32

33 Exercise 4.71 Meditation for anxiety page 262 Big LACK OF EXPERIMENTAL CONTROL Lack of BLINDING... The same person "experimenter" that ranked the subjects anxiety levels at the beginning of the study also taught the meditation techniques and then did the final rating. There should have been a different person doing the ratings (one who is not told which treatments the subjects were given) There is too much pressure to provide successful results when you are designing, rating and implementing the experiment. 33

34 Exercise 4.72 Testosterone for older men page 262 Too much testosterone? Double Blind means that neither the patients who were taking the medicine nor the doctors evaluating the patients knew what type of medicine was selected for each patient. A third party would be needed to keep track of the medicines and treatment groups. Randomized. This refers to the practice of selecting the patients for the treatment groups by a method that involves chance. This will provide for roughly equivalent treatment groups that will distribute the other possible confounding variables throughout the treatment groups. Placebo Controlled. This refers to the practice of providing all patients and treatment groups with a "treatment". Everyone involved in the experiment got something to take. This will separate the placebo effect from the active treatment medicine. The factor involved when a person takes a pill has an expectation for healing to occur because of begin given a treatment. 34

35 Exercise 4.74 Acupuncture and pregnancy page 262 Acupuncture and pregnancy A study sought to determine whether the ancient Chinese art of acupuncture could help infertile women become pregnant.43 One hundred sixty healthy women undergoing assisted reproductive therapy were recruited for the study. Half of the subjects were randomly assigned to receive acupuncture treatment 25 minutes before embryo transfer and again 25 minutes after the transfer. The remaining 80 subjects were instructed to lie still for 25 minutes after the embryo transfer. Results: In the acupuncture group, 34 women became pregnant. In the control group, 21 women became pregnant. (a) Why did researchers randomly assign the subjects to the two treatments? Randomization reduces bias and creates roughly equivalent treatment groups. This provides for all other possible confounding variables to be distributed throughout the treatment groups before treatment begins. (b) The difference in the percent of women who became pregnant in the two groups is statistically significant. Explain what this means to someone who knows little statistics. The treatment results were so largely different that they would not have happened very often by just chance alone. We consider the result to "mean" that the treatment worked. The acupuncture provided a positive outcome, that of becoming pregnant. (c) Explain why the design of the study prevents us from concluding that acupuncture caused the difference in pregnancy rates. While there was a comparison group, this group did not receive any "treatment" so it is hard to conclude a cause and effect relationship in this study. Perhaps the placebo effect occured because the first group of women received an actual treatment. 35

36 Exercise 4.76 Comparing cancer treatments page 262 Comparing cancer treatments The progress of a type of cancer differs in women and men. Researchers want to design an experiment to compare three therapies for this cancer. They recruit 500 male and 300 female patients who are willing to serve as subjects. (a) Which are the blocks in this experiment: the cancer therapies or the two sexes? Why? The blocks will be male and female. They are the variable that causes a different type of progression in the cancer. You cannot randomly choose a person to be male or female. (b) What are the advantages of a randomized block design over a completely randomized design using these 800 subjects? The advantage is that the results should have less variability between the men's and women's treatment groups. This will allow results to show significance if there is a true difference between how women and men react to the three therapies. If only a completely randomized design is used, gender difference will cause more variation in the results and confound the experiment hiding a possible working treatment for men and/or women. (c) Suppose the researchers had 800 male and no female subjects available for the study. What advantage would this offer? What disadvantage? If only male subjects were available a completely randomized design would be acceptable for the study. This would have the advantage of stronger replication for the treatment groups and less variability in the study results. The disadvantage is that the study results and conclusions would only then apply to males. The results should not be applied to the female population 36

37 Exercise 4.79 Aw Rats! page 263 Aw, rats! A nutrition experimenter intends to compare the weight gain of newly weaned male rats fed Diet A with that of rats fed Diet B. To do this, she will feed each diet to 10 rats. She has available 10 rats from one litter and 10 rats from a second litter. Rats in the first litter appear to be slightly healthier. (a) If the 10 rats from Litter 1 were fed Diet A, the effects of genetics and diet would be confounded, and the experiment would be biased. Explain this statement carefully. Because the rats from litter 1 are healthier (have better genetics) this fact alone may be the reason that they gain weight more easily than the other rats. The weight gain would have nothing to do with the treatment. We would make conclusions based on the wrong explanatory variable (health vs. treatment diet A). (b) Describe a better design for this experiment. we should block on litter because we have NO control over the genetics of the litters. weigh all rats before experiment begins 20 rats from 2 different litters 10 from litter 1 and 10 from litter 2 Block 1: 10 rats litter 1 Block 2: 10 rats litter 2 Group 1: 5 rats Group 2: 5 rats Group 1: 5 rats Treatment 1: diet A Treatment 2: diet B Treatment 1: diet A measure weight gain measure weight gain Examine differences in results between the 2 litters Random Assignment Group 2: 5 rats Treatment 2: diet B Randomize by labeling all rats from litter 1 with single digits 1 to 0 where 0 = 10. Use the random digit table to select 5 different single digits from 1 to 0. These rats will be fed diet A. The remaining 5 rats will be fed diet B. Repeat this process for litter 2 to randomly distribute the rats to the treatment groups. 37

38 Exercise 4.81 Look, Ma no hands! page 263 Look, Ma, no hands! Does talking on a hands free cell phone distract drivers? Researchers recruit 40 student subjects for an experiment to investigate this question. They have a driving simulator equipped with a hands free phone for use in the study. Each subject will complete two sessions in the simulator: one while talking on the hands free phone and the other while just driving. The order of the two sessions for each subject will be determined at random. The route, driving conditions, and traffic flow will be the same in both sessions. (a) What type of design did the researchers use in their study? The researchers used a matched pairs design. (b) Explain why the researchers chose this design instead of a completely randomized design. There are many confounding factors when trying to compare people and driving habits. By using each subject compared to themselves the researchers do not have to try and match people and then randomly assign them to treatment groups. Using matched pairs reduces variability and reduces confounding variables. (c) Why is it important to randomly assign the order of the treatments? The first time through the experiment subjects will have a "learning curve" the next time the subjects repeat the experiment this "learning curve" will not exist. To reduce this effect it is wise to randomly assign the order of the treatments. Without this randomization we would have treatment order confounded with "learning from ones' mistakes" (d) Explain how and why researchers controlled for other variables in this experiment. The other methods of control were... All subjects were students, all subjects completed the task on a driving simulator, all used the same hands free device. The route, driving conditions, and traffic flow were the same in both sessions. This reduces possible confounding variables and thus reduces variability in the experiment results. 38

39 Exercise 4.86 Close shave page 264 Close shave: Which of two brands (X or Y) of electric razor shaves closer? Researchers want to design and carry out an experiment to answer this question using 50 adult male volunteers. Here s one idea: Have all 50 subjects shave the left sides of their faces with the Brand X razor and shave the right sides of their faces with the Brand Y razor. Then have each man decide which razor gave the closer shave and compile the results. (a) Identify any flaws you see in the proposed design for this experiment. Confounding variable of Left and Right shaves will exist in this design. Perhaps men (who are mostly right handed) can more skillfully shave one side of their face. This would cause bias in the results. (b) Describe how you would design the experiment. Explain how your design addresses each of the problems you identified in part (a). Use a matched pairs design still but randomly determine which razor brand shaves which face side. See the flow chart below. 50 adult male volunteers Group 1: 25 men Treatment 1: Razor brand X on left Razor brand Y on right rate shaving closeness on each side of face Group 2: 25 men Treatment 2: Razor brand X on right Razor brand Y on left Random Assignment Randomization: label the men 1 to 50. Using technology randomly generate 25 different numbers between 1 and 50. (Use RANDINT(1,50,1)). The men corresponding to these first 25 selected number receive treatment 1, the rest of the men receive treatment 2. 39

40 Blocking Block Design A BLOCK is a group of experimental units or subjects that are known before the experiment to be similar in some way that is expected to systematically affect the response to the treatments. In a BLOCK DESIGN, the random assignment of units to treatments is carried out separately within each block.! A wise experimenter will form blocks based on the most important, unavoidable sources of variability among the experimental units. 40

41 Does calcium reduce blood pressure? (a) Outline an appropriate design for the experiment. 40 middle aged men with high blood pressure (measure blood pressure) Group 1: 20 men Group 2: 20 men Treatment 1: received calcium supplement Treatment 2: received placebo measure blood pressure Random Assignment (c) Modify the design in (a) to account for differences between black men and white men. 40 middle aged men with high blood pressure (measure blood pressure) Block 1: black men Block 2: white men Random Assignment Group 1: half of the black men Group 2: half of the black men Group 1: half of the white men Group 2: half of the white men Treatment 1: received calcium Treatment 2: received placebo Treatment 1: received calcium Treatment 2: received placebo measure blood pressure measure blood pressure Examine differences in results 41

42 Examine differences in results random assignment 42

43 Exercise 4.75 Doctors and nurses? page 262 a) The blocks are the diagnoses... we can not randomly assign chronic health conditions to patients... b) A randomized block design is preferable because we seek to determine if nurse practitioners are a capable as doctors in treating the patients. Perhaps the care of certain chronic conditions require more expertise than others. If we think that the type of health condition makes a difference in the type of health care needed we should "control" for this factor in our experiment before we begin to decrease the variability in the results. C) Single blind, double blind or no blind? D) Create flowchart for experiment. Block 1: asthma patients Group 1: half of the asthma Group 2: half of the asthma Treatment 1: received doctor Treatment 2: received nurse practitioner measure patient health and satisfaction 1316 patients with asthma, diabetes, or high blood pressure Block 2: diabetes patients Group 1: half of the diabetes Group 2: half of the diabetes Treatment 1: received doctor Treatment 2: received nurse practitioner measure patient health and satisfaction Block 3: high blood pressure patients Group 1: half of the high blood pressure Group 2: half of the high blood pressure Treatment 1: received doctor Treatment 2: received nurse practitioner measure patient health and satisfaction Random Assignment Examine differences in results 43

44 Exercise 4.85 Got deodorant? page

45 MATCHED PAIRS Matching the subjects in various ways can produce more precise results than simple randomization. The simplest use of matching is a MATCHED PAIRS DESIGN. This design compares just two treatments. The subjects are matched in pairs or a subject is compared to itself (often with a pre and post test). 45

46 Is the right hand generally stronger than the left in right handed people? You can crudely measure hand strength by placing a bathroom scale on a shelf with the end protruding and then squeezing the scale between the thumb below and the four fingers above. The reading of the scale shows the force exerted. (1) It is an experiment because we have a treatment. Squeezing the scale (2) What is/are the explanatory variable(s)? What "handedness" you are, right handed people are stronger with their right hand. (3) What is the response variable? Force exerted when squeezing the scale. (4) You have recruited 10 right handed people to serve as subjects. Carefully describe the design of a matched pairs experiment to compare the strength of the right and left hands, using these subjects. Be specific and draw a flowchart. (5) Use line 139 in Table B to do the required randomization and report your results So the subjects selected for group 1 are # 5,8,9,4,0 46

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49 Experiment Mantra... Control what you can, Block on what you can't control, and Randomize the rest. 49

50 EXPERIMENT MANTRA: Control what you can,block on what you can't control,and randomize the rest. Control what you can,block on what you can't control,and randomize the rest. Control what you can,block on what you can't control,and randomize the rest. Control what you can,block on what you can't control,and randomize the rest. Control what you can,block on what you can't control,and randomize the rest. Control what you can,block on what you can't control,and randomize the rest. Control what you can,block on what you can't control,and randomize the rest. Control what you can,block on what you can't control,and randomize the rest. Control what you can,block on what you can't control,and randomize the rest. Control what you can,block on what you can't control,and randomize the rest. Control what you can,block on what you can't control,and randomize the rest. Control what you can,block on what you can't control,and randomize the rest. 50

51 HOMEWORK A Skips 4.3 C4#11 pg : Chapter Review Exerciese 4.1 to Design flowchart and random technique are needed... 51

52 Exercise R4.1 Ontario Health Survey page 278 R4.1. Ontario Health Survey The Ministry of Health in the province of Ontario, Canada, wants to know whether the national health care system is achieving its goals in the province. Much information about health care comes from patient records, but that source doesn t allow us to compare people who use health services with those who don t. So the Ministry of Health conducted the Ontario Health Survey, which interviewed a random sample of 61,239 people who live in the province of Ontario. (a) What is the population for this sample survey? What is the sample? People who live in Ontario, people who live in Ontario (b) The survey found that 76% of males and 86% of females in the sample had visited a general practitioner at least once in the past year. If a census were conducted, do you think that the percentages would be the same as in the sample? Explain. Because this is a sample, sampling variability tells us the due to the sample size the results should be very close to the census but most likely not exactly equal. 52

53 Exercise R4.2 Bad Sampling page 278 R4.2. Bad sampling A large high school wants to gather student opinion about parking for students on campus. It isn t practical to contact all students. (a) Give an example of a way to choose a voluntary response sample of students. Explain how this method could lead to bias. During the video announcements make an announcement about a twitter account where students can express their opinions about the parking. This will lead to bias for a few reasons. Voluntary response those who feel strongly will most likely respond. Undercoverage only those with twitter accounts can quickly send in their opinions. (b) Give an example of a way to choose a convenience sample of students. Explain how this method could lead to bias. When a student receives a parking ticket on campus, ask them to fill out a quick survey about their opinions about parking for students on campus. Bias will result because we are undercovering those students who have not received parking tickets. We will get strong negative opinions with only asking students who are probably "perturbed" that they received a ticket. 53

54 Exercise R4.3 Drug Testing page 278 R4.3. Drug testing A baseball team regularly conducts random drug tests on its players. The 25 members of the team are listed below. 01 Agarwal 06 Chen 11 Healy 16 Moser 21Roberts 02 Andrews 07 Frank 12 Hixon 17 Musselman 22Shen 03 Baer 08 Fuest 13 Lee 18 Pavnica 23Smith 04 Berger 09 Fuhrmann 14 Lynch 19 Petrucelli 24Sundheim 05 Brockman 10 Garcia 15 Milhalko 20 Reda 25Wilson (a) Explain how you would use the line of random digits below to select an SRS of 3 team members for a random drug test. LABEL: Label the team using 2 digit numbers from 01 to 25 TABLE: below STOPPING PROCEDURE: Continue until 3 DIFFERENT 2 digit numbers from 01 to 25 have been selected. (b) Use your method from part (a) to choose the SRS using the digits below. Show your work IDENTIFY: Musselman, Fuhrmann, Smith will be taking the drug test this time. 54

55 Exercise R4.4 Polling the faculty page 278 R4.4. Polling the faculty A researcher wants to study the attitudes of college faculty members about the work habits of entering freshmen. These attitudes appear to differ depending on the type of college. The American Association of University Professors classifies colleges as follows: Class I: Offer doctorate degrees and award at least 15 per year. Class IIA: Award degrees above the bachelor s but are not in Class I. Class IIB: Award no degrees beyond the bachelor s. Class III: Two year colleges. The researcher would like to survey about 200 faculty members. Would you recommend a simple random sample, stratified random sample, or cluster sample? Justify your answer. I would use a stratified random sample (with additional grouping for professors who teach freshmen classes). This is necessary because the prompt seems to suggest that freshmen work habits are influenced by the "class" of the university/college that they are attending. 55

56 Exercise R4.5 Been to the movies? page 278 R4.5. Been to the movies? An opinion poll calls 2000 randomly chosen residential telephone numbers, then asks to speak with an adult member of the household. The interviewer asks, How many movies have you watched in a movie theater in the past 12 months? In all, 1131 people responded. The researchers used the responses to estimate the mean number of movies adults have watched in a movie theater in the past 12 months. (a) Describe a potential source of bias related to the wording of the question. Suggest a change that would help fix this problem. The question implies that you have seen some movies in a theater, could have response bias. If you have been to many movies perhaps a year is too long to remember how many movies you have seen. (b) Describe how using only residential phone numbers might lead to bias and how this will affect the estimate. There are people who do not have land line phones any more or use them. This would lead to undercoverage (particularly youth). Also depending on what time the calls are made, people may not be home (non response), they could be at the movies!!! (c) Describe how nonresponse might lead to bias and how this will affect the estimate. As discussed in the above question. Non response could be due to the fact that people are at the movies and not at home to get the call. This results in underestimating the number of movies people have seen in the last 12 months. 56

57 Exercise R4.6 Are anesthetics safe? page 278 R4.6. Are anesthetics safe? The National Halothane Study was a major investigation of the safety of anesthetics used in surgery. Records of over 850,000 operations performed in 34 major hospitals showed the following death rates for four common anesthetics: There seems to be a clear association between the anesthetic used and the death rate of patients. Anesthetic C appears to be more dangerous. (a) Explain why we call the National Halothane Study an observational study rather than an experiment, even though it compared the results of using different anesthetics in actual surgery. There is no random assignment to the different treatments. Only the records were reviewed to determine if there is an association between treatment and death rates. (b) When the study looked at other variables that are related to a doctor s choice of anesthetic, it found that Anesthetic C was not causing extra deaths. Explain the concept of confounding in this context and identify a variable that might be confounded with the doctor s choice of anesthetic. Doctors would choose the least "risky" treatment for those patients that are in the "worst" shape. The elderly, those that are physically weak from other medical conditions (in a car accident), etc. 57

58 Exercise R4.7 Ugly fries page 279 R4.7. Ugly fries Few people want to eat discolored french fries. Potatoes are kept refrigerated before being cut for french fries to prevent spoiling and preserve flavor. But immediate processing of cold potatoes causes discoloring due to complex chemical reactions. The potatoes must therefore be brought to room temperature before processing. Researchers want to design an experiment in which tasters will rate the color and flavor of french fries prepared from several groups of potatoes. The potatoes will be freshly picked or stored for a month at room temperature or stored for a month refrigerated. They will then be sliced and cooked either immediately or after an hour at room temperature. (a) Identify the experimental units, the explanatory and response variables, and the treatments. Experimental Unit Potatoes, Explanatory variable Potato freshness and storage conditions Response variable the customer rating of color and flavor of the fries Wait time before cooking Treatments 6 in total see treatment table below Storage treatment Freshly picked Stored at room temp (b) The researchers plan to use a completely randomized design. Describe how they should assign treatments to the experimental units if there are 300 potatoes available for the experiment. Use equal sizes of 300 pieces of paper. Number the papers from 1 to 6 (each number 50 times). Place the papers into a container and mix well. Each time fries are to be prepared pick a number and follow the treatment directions for that specific number. See treatment table above. (c) The researchers decided to do a follow up experiment using sweet potatoes as well as regular potatoes. Describe how they should change the design of the experiment to account for the addition of sweet potatoes. A blocked experiment should now be implemented. The potatoes should be blocked by potato type. Stored in frige sliced & cooked hour at room temp

59 Exercise R4.8 Don't catch a cold page 279 R4.8. Don t catch a cold! A recent study of 1000 students at the University of Michigan investigated how to prevent catching the common cold. The students were randomly assigned to three different cold prevention methods for 6 weeks. Some wore masks, some wore masks and used hand sanitizer, and others took no precautions. The two groups who used masks reported 10 50% fewer cold symptoms than those who did not wear a mask. (a) Does this study allow for inference about a population? Explain. We do not know if the students were selected from the population of students at the University at random or if they were volunteers. So we will not be able to generalize the results of the study to anyone. (b) Does this study allow for inference about cause and effect? Explain. Because the students were randomly assigned to treatment groups. We say that for the students in the study, the masks seem reduce the cold symptoms. 59

60 Exercise R4.9 An herb for depression? page 279 R4.9. An herb for depression? Does the herb Saint John s wort relieve major depression? Here is an excerpt from the report of a study of this issue: Design: Randomized, Double Blind, Placebo Controlled Clinical Trial. The study concluded that the difference in effectiveness of Saint John s wort and a placebo was not statistically significant. (a) How did the design of this experiment account for the placebo effect? There were two treatment groups, one of which received a "dummy" pill that hopefully matched the design and look of the other pilll. (b) Explain the purpose of the random assignment. The purpose of random assignment is to reduce BIAS by creating roughly equivalent treatment groups.l (c) Why is a double blind design a good idea in this setting? To aviod "researcher" bias, neither the subjects nor the person giving the pills to the subjects should know which bottle is the REAL study and which is an inactive ingredient. (d) Explain what not statistically significant means in this context. A result occurred that we not expect to see very often. The random chance of the result occurring is very low... Under 5%. So we can conclude that the effectiveness of the treatment is in fact caused by the treatment its self! 60

61 Exercise R4.10 How long did I work? page How long did I work? A psychologist wants to know if the difficulty of a task influences our estimate of how long we spend working at it. She designs two sets of mazes that subjects can work through on a computer. One set has easy mazes and the other has difficult mazes. Subjects work until told to stop (after 6 minutes, but subjects do not know this). They are then asked to estimate how long they worked. The psychologist has 30 students available to serve as subjects. (a) Describe an experiment using a completely randomized design to learn the effect of difficulty on estimated time. Flowchart and random technique please. 30 students Group 1: 15 students Treatment 1: received easy mazes measure work time estimates Group 2: 15 students Treatment 2: received difficult mazes Random Assignment Label students 1 to 30. Use a random number generator to generate 15 different numbers between 1 and 30. These 15 numbers identify with the 15 students who receive treatment 1. (b) Describe a matched pairs experimental design using the same 30 subjects. 30 students Random Assignment Group 1: 15 students Group 2: 15 students Treatment 1: received easy mazes and then difficult mazes Treatment 2: received difficult mazes and then easy mazes measure work time estimates and the differences between the two treatments (c) Which design would be more likely to detect a difference in the effects of the treatments? Explain. I think this is a hard call because there would be a quick and influential learning curve after the first set of mazes is completed. Theoretically the matched pairs should have a more effective data collection because students differ greatly on their maze enthusiasm and skill. (there is great variability between students and maze skills). 61

62 Exercise 4.11 Deceiving subjects. page 279 R4.11. *Deceiving subjects Students sign up to be subjects in a psychology experiment. When they arrive, they are told that interviews are running late and are taken to a waiting room. The experimenters then stage a theft of a valuable object left in the waiting room. Some subjects are alone with the thief, and others are in pairs these are the treatments being compared. Will the subject report the theft? (a) The students had agreed to take part in an unspecified study, and the true nature of the experiment is explained to them afterward. Does this meet the requirement of informed consent? Explain. This does not meet the requirement of informed consent. Informed consent means that the terms and study design will be explained before the experiment is to begin. (b) What two other ethical principles should be followed in this study? The experiment and design should be approved by a review board before being implemented. The subjects and results of the experiment should be kept confidential. 62

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