Bell Work 21 An important part of employee
Bell Work 2/1 An important part of employee compensation is a benefits package the might include health insurance, life insurance, child care, vacation days, retirement plan, bonuses, etc. Suppose you want to conduct a survey of benefit packages available in private businesses in Hawaii. You want a sample of 100. Some sampling techniques are described below. Identify the sampling method for each. a) Assign each business in the Island Business Directory a number, and then use a sequence of random numbers to select businesses to be included in the sample. b) Send a team of five research assistants to Bishop Street in downtown Honolulu. Let each assistant select a block of buildings and interview each individual working in the buildings. c) Use the Island Business Directory. Number all the businesses. Select a random starting point, and then use every 50 th business listed until you get 100. d) Group businesses according to type: medical, shipping, retail, restaurant, manufacturing, financial, construction, other. Then select random samples of 10 businesses from each business type.
Bell Work 2/4 We need to survey a random sample of 300 passengers on a flight from San Francisco to Tokyo. Name each sampling method described below. a) Pick every 10 th passenger as people board b) From the boarding list, randomly choose 5 people flying first class and 25 of the other passengers c) Randomly generate 30 seat numbers and survey the passengers who sit there d) Randomly select a seat position (right, window, right center, right aisle, etc. ) and survey all the passengers in those seats.
Experiments and Observational Studies Objectives Given an observational study, identify as retrospective or prospective, the subjects studied and how they were selected, the variables of interest, and the nature/scope of the conclusion. Recognize the difference between observational studies and randomized comparative experiments
Observational Studies- In an observational study, a researcher observes and measures characteristics of interest of part of a population but does not change existing conditions. Characteristics of observational studies: Retrospective Studies – in a retrospective observational study, researchers identify subjects and then collect data from their past. Prospective studies – in a prospective observational study, researchers identify subjects in advance and collect data as event unfold.
Observational Studies- In an observational study, a researcher observes and measures characteristics of interest of part of a population but does not change existing conditions. Characteristics of observational studies: do not use randomization so they cannot show cause and effect, and they can’t be generalized to the population. At best, they can show that there is a possible relationship between variables. Too many outside variables (lurking variables) that could be giving the appearance that the two variables are associated. Retrospective Studies – in a retrospective observational study, researchers identify subjects and then collect data from their past. Prospective studies – in a prospective observational study, researchers identify subjects in advance and collect data as event unfold.
Observational Studies A study in California showed that students who study a musical instrument have higher GPAs than students who do not, 3. 59 to 2. 91. Of the music students, 16% had all As, compared with only 5% among the students who did not study a musical instrument. Identify The subjects studied The variables of interest The nature and scope of the conclusion of the study
Observational Studies Researchers who examined health records of thousands of males found that men who died of myocardial infarction (heart attack) tended to be shorter than men who did not. Identify whether the study is retrospective or prospective The subjects studied and how they were selected The variables of interest The nature and scope of the conclusion of the study
Observational Studies In 2002 the journal Science reported that a study of women in Finland indicated that having sons shortened the lifespans of mothers by about 34 weeks per son, but that daughters helped to lengthen the mothers’ lives. The data came from church records from the period 1640 to 1870. Identify whether the study is retrospective or prospective The subjects studied The variables of interest The nature and scope of the conclusion of the study
Experiments Experiment - In performing an experiment, a treatment is applied to part of a population and responses are observed. Another part of the population may be used as a control group, in which no treatment is applied. Key words Factors Response Variable Subjects, participants, experimental units Factor Levels Treatments
Experiments Researchers studied the herb black cohosh as a treatment for hot flashes caused by menopause. They randomly assigned 351 women aged 45 to 55 who reported at least two hot flashes a day to one of five groups: (1) black cohosh, (2) a multiherb supplement with black cohosh, (3) the multiherb supplement plus advice to consume more soy foods, (4) estrogen replacement therapy, or (5) receive a placebo. After a year, only the women given estrogen replacement therapy had symptoms different from those of the placebo group. a) Who were the subjects? d) Identify the treatment and response variables. Over a 4 -month period, among 30 people with bipolar disorder, patients who were given a high dose (10 g/day) of omega-3 fats from fish oil improved more than those given a placebo. (Archives of General Psychiatry 56 [1999]: 407) a) Who were the subjects? d) Identify the treatment and response variables.
Experiments Vs. Observational Studies We are interested in looking at how smoking affects women’s lung capacities in women who have been smoking for a ten year period Observational Study Find 100 women age 30 of which 50 have been smoking a pack a day for 10 years while the other 50 have been smoke free for 10 years. • Measure lung capacity for each of the 100 women. • Analyze, interpret, and draw conclusions from data Experimental Study Find 100 women age 20 who do not currently smoke. • Randomly assign 50 of the 100 women to the smoking treatment and the other 50 to the no smoking treatment. • Those in the smoking group smoke a pack a day for 10 years while those in the control group remain smoke free for 10 years. • Measure lung capacity for each of the 100 women. • Analyze, interpret, and draw conclusions from data
Experiments Vs. Observational Studies Medical researchers followed 6272 Swedish men for 30 years to see if there was any association between the amount of fish in their diet and prostate cancer. Their results suggested that fish consumption could be associated with decreased risk of prostate cancer. (“Fatty Fish Consumption and Risk of Prostate Cancer, ” Lancet, June 2001. ) What kind of study was this? Who were the subjects? What were the variables? Coffee stations in offices often just ask users to leave money in a tray to pay for their coffee, but many people cheat. Researchers at Newcastle University replaced the picture of flowers on the wall behind the coffee station with a picture of staring eyes. They found that the average contribution increased significantly above the well-established standard when people felt they were being watched, even though the eyes were patently not real. What kind of study was this? What were the variables?
Objectives Given a randomized comparative experiment, identify the subjects studied, the factors and levels of each, number of treatments, response variable measured, the design (randomized or blocked), whether it was blind or double blind, and the nature/scope of the conclusion. Identify and explain the four principles of experimental design.
The Four Principles of Experimental Design Control- We control outside sources of variation by making conditions as similar as possible for all treatment groups Randomize. We randomly assign subjects to treatment groups to reduce bias due to uncontrolled sources of variation Replicate - • We apply treatments to number of subjects • We recreate an entire experiment with outside sources of variation at different levels *Block We group similar individuals together and then randomly assign members of blocks to treatments removing much of the variability due to differences among blocks
Experimental Design We are working with a track team of 30 student runners, and we would like to investigate whethere exists a correlation between caffeine and a student’s performance during a race. Control- To reduce possible variability from factors other than caffeine, we keep all athletes on the same diet and ensure each runs the same distance each day before the race Randomize. We randomly assign 15 students to the control group and 15 students to the caffeine group. Ideally, this will evenly distribute individual traits that may influence a person’s performance in a race equalizing the effects of these influences within the two treatment groups. Replicate We replicate the experiment by assigning more than one person to each treatment group, which allows for variability among individual athletes. We could replicate our experiment by using an entirely new set of students from some other part of the country. *Block We divide students into blocks based on their performance in past races(fast, medium, or slow). We then randomly assign students within the blocks to treatment groups.
Randomized Experiment 15 runners caffeine 30 runners compare 15 runners Randomized Block Experiment Block A 6 Fast 30 runners 6 Fast 18 Medium 6 Slow Block B 18 Medium Block C 6 Slow no caffeine Group 1 3 runners caffeine Group 2 3 students no caffeine Group 3 9 runners caffeine Group 4 9 runners no caffeine compare Group 5 3 runners caffeine Group 6 3 runners no caffeine compare
Bell Work 2/5 Among a group of disabled women aged 65 and older who were tracked for several years, those who had a vitamin B 12 deficiency were twice as likely to suffer severe depression as those who did not. (American Journal of Psychiatry 157 [2000]: 715) Identify Whether the study is an observational study or an experiment Who were the subjects The variables of interest The nature and scope of the conclusion the study can reach
Blinding- Anyone who can affect the outcome of the experiment is kept from knowing which subjects have been assigned to which treatments Two classes of people who can effect the outcome: Single blind – Double blind - Placebos
Experiments a) the subjects studied. b) the factor(s) in the experiment and the number of levels for each. c) the number of treatments. d) the response variable measured. e) the design (completely randomized, blocked) f) whether it was blind (or doubleblind). g) the nature and scope of the conclusion the experiment can reach Some people claim they can get relief from migraine headache pain by drinking a large glass of ice water. Researchers plan to enlist several people who suffer from migraines in a test. When a participant experiences a migraine headache, he or she will take a pill that may be a standard pain reliever or a placebo. Half of each group will also drink ice water. Participants will then report the level of pain relief they experience.
Experiments a) the subjects studied. b) the factor(s) in the experiment and the number of levels for each. c) the number of treatments. d) the response variable measured. e) the design (completely randomized, blocked) f) whether it was blind (or doubleblind). g) the nature and scope of the conclusion the experiment can reach A dog food company wants to compare a new lower-calorie food with their standard dog food to see if it’s effective in helping inactive dogs maintain a healthy weight. They have found several dog owners willing to participate in the trial. The dogs have been classified as small, medium, or large breeds, and the company will supply some owners of each size of dog with one of the two foods. The owners have agreed not to feed their dogs anything else for a period of 6 months, after which the dogs’ weights will be checked.
Bell Work 2/6 1) Researchers identified 242 children in the Cleveland area who had been born prematurely (at about 29 weeks). They examined these children at age 8 and again at age 20, comparing them to another group of 233 children not born prematurely. Their report, published in the New England Journal of Medicine, said the “preemies” engaged in significantly less risky behavior than the others. a) Is this an observational study or an experiment b) Who were the subjects c) What were the variables 2) It’s a common belief that people behave strangely when there’s a full moon and that as a result police and emergency rooms are busier than usual. Design a way you could find out whethere is any merit to this belief. Will you use an observational study or an experiment? Why?
Objectives Given a randomized comparative experiment, identify the subjects studied, the factors and levels of each, number of treatments, response variable measured, the design (randomized or blocked), whether it was blind or double blind, and the nature/scope of the conclusion. Identify and explain the four principles of experimental design.
Experiments a) the subjects studied. b) the factor(s) in the experiment and the number of levels for each. c) the number of treatments. d) the response variable measured. e) the design (completely randomized, blocked) f) whether it was blind (or doubleblind). g) the nature and scope of the conclusion the experiment can reach Athletes who had suffered hamstring injuries were randomly assigned to one of two exercise programs. Those who engaged in static stretching returned to sports activity in a mean of 15. 2 days faster than those assigned to a program of agility and trunk stabilization exercises. ( Journal of Orthopaedic & Sports Physical Therapy 34 [March 2004]: 3)
Experiments a) the subjects studied. b) the factor(s) in the experiment and the number of levels for each. c) the number of treatments. d) the response variable measured. e) the design (completely randomized, blocked) f) whether it was blind (or doubleblind). g) the nature and scope of the conclusion the experiment can reach After menopause, some women take supplemental estrogen. There is some concern that if these women also drink alcohol, their estrogen levels will rise too high. Twelve volunteers who were receiving supplemental estrogen were randomly divided into two groups, as were 12 other volunteers not on estrogen. In each case, one group drank an alcoholic beverage, the other a nonalcoholic beverage. An hour later, everyone’s estrogen level was checked. Only those on supplemental estrogen who drank alcohol showed a marked increase.
Experiments A medical researcher suspects that giving post-surgical patients large doses of vitamin E will speed their recovery times by helping their incisions heal more quickly. Design an experiment to test this conjecture. Be sure to identify the factors, levels, treatments, response variable, and the role of randomization. Determine how you would blind the experiment.
Experiments Hoping to learn how to control crop damage by a certain species of beetle, a researcher plans to test two different pesticides in small plots of corn. A few days after application of the chemicals, he’ll check the number of beetle larvae found on each plant. The researcher wants to know whether either pesticide works and whethere is a significant difference in effectiveness between them. Design an appropriate experiment. Be sure to identify the factors, levels, treatments, response variable, and the role of randomization. Determine how you would blind this experiment and how you would control outside sources of variation.
This experiment has 1 factor (pesticide), at 3 levels (pesticide A, pesticide B, no pesticide), resulting in 3 treatments. The response variable is the number of beetle larvae found on each plant. Randomly select a third of the plots to be sprayed with pesticide A, a third with pesticide B, and a third to be sprayed with no pesticide (since the researcher also wants to know whether the pesticides even work at all). To control the experiment, the plots of land should be as similar as possible, with regard to amount of sunlight, water, proximity to other plants, etc. If not, plots with similar characteristics should be blocked together. If possible, use some inert substance as a placebo pesticide on the control group, and do not tell the counters of the beetle larvae which plants have been treated with pesticides. After a given period of time, count the number of beetle larvae on each plant and compare the results.
Experiments Do cars get better gas mileage with premium instead of regular unleaded gasoline? It might be possible to test some engines in a laboratory, but we’d rather use real cars and real drivers in real day-to-day driving, so we get 20 volunteers. Design the experiment. Be sure to identify the factors, levels, treatments, response variable, and the role of randomization
Answers may vary. This experiment has 1 factor (type of gasoline), at 2 levels (premium and regular), resulting in two treatments. The response variable is gas mileage. An experiment diagram for a simple design appears above. Randomly assign each of the 20 volunteers to the premium or regular groups. Ask them to keep driving logs (the number of miles driven and the gallons of gasoline) for one month. Compare the differences in the fuel economy for the two groups. Stronger designs would control for several variables that may have an effect on fuel economy, such as size of engine, type of driving (for example, city or highway), and driving style (for example, if the is driver aggressive, or if the driver exceeds the speed limit).
Bell Work 2/7 Can makeup damage fetal development? Many cosmetics contain a class of chemicals called phthalates. Studies that exposed some laboratory animals to these chemicals found a heightened incidence of damage to male reproductive systems. Since traces of phthalates are found in the urine of women who use beauty products, there is growing concern that they may present a risk to male fetuses. (Science News, July 20, 2002) Identify whether this is an experiment or an observational study? Who were the subjects of this study? What were the variables of interest?
Identify variables as categorical or quantitative Unit 1 Objectives Identify population parameters and statistics in descriptions of populations and samples. Identify sampling techniques as simple random, stratified, cluster, systematic, convenience, or voluntary response Identify the sampling frame, sample and any potential biases Perform a simulation and interpret the results. Identify a study as observational or experimental. Given an observational study, identify as retrospective or prospective, the subjects studied and how they were selected, the parameter of interest, and the nature/scope of the conclusion. Given an experimental study, identify the subjects studied, the factors and levels of each, number of treatments, response variable measured, the design (randomized, blocked, or matched), whether it was blind or double blind, and the nature/scope of the conclusion. Identify and explain the four principles of experimental design
Identify variables as categorical or quantitative Indicate which of the following variables are quantitative and which are categorical. a. Number of persons in a family e. Time to commute from home to work b. Colors of cars f. Number of errors in a person’s credit report c. Marital status of people g. Student ID numbers d. Social Security Number
Identify population parameters and statistics in descriptions of populations and samples.
Identifying Sampling Methods A quality control engineer selects every 10, 000 th M&M plain candy that is produced ABC News conducts an election day poll by randomly selecting voting precincts in New York, then interviewing all voters as they leave those precincts. NBC News polled reactions to the last presidential election by surveying adults who were approached by a reporter at a location in New York City. In order to test for a gender gap in the way that citizens view the current President, the Tomkins Company polls exactly 500 men and 500 women by grouping voters according to gender and then taking a random sample from each group.
Identifying Sampling Methods Administrators at a high school are concerned about the possibility of drug abuse by students. They decide to check on the extent of the problem by searching a sample of students. Several plans for choosing the sample are proposed. Name the sampling strategy in each. a. Organize students into groups according to grade level (Freshmen, Sophomores, Juniors, and Seniors). Randomly select 25 students from each grade level. b. Each student has a 4 -digit ID number. Randomly choose 100 numbers. c. At the start of each day, choose every tenth person who arrives to school. d. Randomly select a classrooms and search every student that within the classrooms.
Sampling Methods Administrators at a high school are concerned about the possibility of drug abuse by students. They decide to check on the extent of the problem by searching a sample of students. A small sampling frame is given in the box. Perform an SRS with a sample size of 5 using the sampling frame and the sequence of random numbers. Jamie Jonathan Ernesto Donavan Erick Jeremy Terrell Gabriella Vincent Danicia Julia Meredith Latisha Joy Jordan Frank Tony Robert 04905 83852 29350 91309 19994 65142 05087 11232 Our Sample: Terrell, Tony, Gabriella, Vincent
Simulations: Perform a simulation and interpret the results A certain bowler can bowl a strike 70% of the time. What’s the likelihood that she goes three consecutive frames in a game without a strike? Trial # Sequence of Random Numbers Trial Outcome 1 99154 22477 2 60171 21130 3 42641 52714 4 64532 14714 5 81928 93143 6 31876 68521 7 90990 41937 8 51374 70179 9 60017 76297 10 94186 42968
Simulations: Perform a simulation and interpret the results As a promotional offer, the manufactures of Pepsi are placing winning symbols under the caps of 10% of all Pepsi bottles. You buy a six-pack. What is the likelihood that you win something? Trial # Sequence of Random Numbers Trial Outcome 1 68791 57929 2 05211 70057 3 59133 08509 4 81828 81405 5 81612 51681 6 26716 47337 7 35749 89688 8 67112 21040 9 13623 26987 10 99066 82136
Simulations: Perform a simulation and interpret the results When taking bets on sporting events, bookmakers often include a “point spread” that awards the weaker team extra points. In theory this makes the outcome of the bet a toss-up (50 – 50). Suppose a gambler places a $10 bet and picks the winners of five games. If he’s right about fewer than three of the games, he loses. If he gets three, four, or all five correct, he’s paid $10, $20, and $50, respectively. Estimate the amount such a bettor might expect to lose over many weeks of gambling. Trial Sequence of Random Trial Outcome # Numbers 1 86581 62171 2 12229 78162 3 67384 57042 4 32306 80771 5 85796 05849 6 88435 86296 7 72372 85856 8 38921 62691 9 70858 75258 10 65320 05119
Simulations: Perform a simulation and interpret the results A new electronics store holds a contest to attract shoppers. Once an hour someone in the store is chosen at random to play the Music Game. Here’s how it works: An ace and four other cards are shuffled and placed face down on a table. The customer gets to turn cards over one at a time, looking for the ace. The person wins $100 worth of free CDs or DVDs if the ace is the first card, $50 if it is the second card, and $20, $10, or $5 if it is the third, fourth, or fifth card chosen. What is the average dollar amount of music the store will give away? Trial # Sequence of Random Numbers Trial Outcome 1 11442 31320 20342 2 20234 31302 20140 3 00314 32430 41121 4 22444 32222 11021 5 23113 10042 23220 6 34431 24020 20231 7 03303 10302 12133 8 41214 40132 11424 9 03441 13141 30103 10 23202 24101 02422
Bell Work 2/8 An artisan wants to create pottery that has the appearance of age. He prepares several samples of clay with four different glazes and test fires them in a kiln at three different temperature settings. Is this an experiment or an observational study Identify the factors and the levels of each How many treatments are there? What is the response variable?
Identify a study as observational or experimental. The journal Circulation reported that among 1900 people who had heart attacks, those who drank an average of 19 cups of tea a week were 44% more likely than nondrinkers to survive at least 3 years after the attack. Can long-term exposure to strong electromagnetic fields cause cancer? Researchers in Italy tracked down 13 years of medical records for people living near Vatican Radio’s powerful broadcast antennas. A disproportionate share of the leukemia cases occurred among men and children who lived within 6 kilometers of the antennas. (Science News, July 20, 2002) Researchers at the Purina Pet Institute studied Labrador retrievers for evidence of a relationship between diet and longevity. At 8 weeks of age, 2 puppies of the same sex and weight were randomly assigned to one of two groups—a total of 48 dogs in all. One group was allowed to eat all they wanted, while the other group was fed a diet about 25% lower in calories. The median lifespan of dogs fed the restricted diet was 22 months longer than that of other dogs. (Science News 161, no. 19)
Given an observational study, identify as retrospective or prospective, the subjects studied and how they were selected, the parameter of interest, and the nature/scope of the conclusion. In the journal Science, a research team reported that plants in southern England are flowering earlier in the spring. Records of the first flowering dates for 385 species over a period of 47 years indicate that flowering has advanced an average of 15 days per decade, an indication of climate warming, according to the authors. Can long-term exposure to strong electromagnetic fields cause cancer? Researchers in Italy tracked down 13 years of medical records for people living near Vatican Radio’s powerful broadcast antennas. A disproportionate share of the leukemia cases occurred among men and children who lived within 6 kilometers of the antennas. (Science News, July 20, 2002) Physically fit people seem less likely to die of cancer. A report in the May 2002 issue of Medicine and Science in Sports and Exercise followed 25, 892 men aged 30 to 87 for 10 years. The most physically fit men had a 55% lower risk of death from cancer than the least fit group.
Given an experimental study, identify the subjects studied, the factors and levels of each, number of treatments, response variable measured, the design (randomized, blocked, or matched), whether it was blind or double blind, and the nature/scope of the conclusion. Tests of gene therapy on laboratory rats have raised hopes of stopping the degeneration of tissue that characterizes chronic heart failure. Researchers at the University of California, San Diego, used hamsters with cardiac disease, randomly assigning 30 to receive the gene therapy and leaving the other 28 untreated. Five weeks after treatment the gene therapy group’s heart muscles stabilized, while those of the untreated hamsters continued to weaken. (Science News, July 27, 2002) An article in a local newspaper reported that dogs kept as pets tend to be overweight. Veterinarians say that diet and exercise will help these chubby dogs get in shape. The veterinarians propose two different diets (Diet A and Diet B) and two different exercise programs (Plan 1 and Plan 2). Diet A: owners control the portions of dog food and dog treats; Diet B: a mixture of fresh vegetables with the dog food and substitute regular dog treats with baby carrots. Plan 1: three 30 -minute walks a week; Plan 2: 20 -minute walks daily. Sixty dog owners volunteer to take part in an experiment to help their chubby dogs lose weight.
Identify and explain the four principles of experimental design Does the use of computer software in Introductory Statistics classes lead to better understanding of the concepts? A professor teaching two sections of Statistics decides to investigate. She teaches both sections using the same lectures and assignments, but gives one class statistics software to help them with their homework. The classes take the same final exam, and graders do not know which students used computers during the semester. The professor is also concerned that students who have had calculus may perform differently from those who have not, so she plans to compare software vs. no-software scores separately for these two groups of students.
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