Chapter Review
16. A(n) __________ variable is one that attempts to explain or is purported to cause (at least partially) differences in a(n) __________ variable.
ANSWERS (RESPECTIVELY): EXPLANATORY; OUTCOME (OR RESPONSE)
6. Describe one of the issues that you would need to think about when deciding how to measure which supermarket is the 'best' one in town.
: WHAT DO WE MEAN BY 'BEST'? WHAT ONE PERSON THINKS OF AS 'BEST' MIGHT NOT MEAN THE SAME THING TO SOMEONE ELSE; DO WE MEASURE IT OVER TIME, OR AT ONE MOMENT IN TIME?
3. The people who are most likely to respond to a volunteer response survey are those who have a strong __________ about the questions being asked.
: OPINION OR EMOTIONAL RESPONSE
7. Explain why even the simplest kind of measurement, such as finding your height, still presents complicated issues.
: THE ACCURACY OF YOUR MEASUREMENT DEPENDS ON YOUR MEASUREMENT TOOL; HOW TALL YOU STAND WHEN YOU MEASURE; WHETHER OR NOT YOU WEAR SHOES, ETC.
4. A histogram of pulse rates of current students in introductory statistics courses at American University is given in the figure below. Students were asked the question, "What is your pulse rate in beats per minute (bpm)" on a survey given in class. Other questions were asked too. a. About how many students have pulse rates between 60 and 80 bpm?
85+92=177 (or about this amount - I would accept 175 and other values close to this)
Study of the relationship between smoking during pregnancy and child's subsequent IQ a few years after birth. Explanatory Variable Response Variable Possible Confounding Variables
: whether or not the mother smoked during pregnancy subsequent IQ of the child •Women who smoke also have poor nutrition, lower levels of education, or lower income. : Mother's nutrition, education, and income.
A poll was based on interviews with 2,000 adults, asking questions about a variety of issues. What is the margin of error for this poll?
A poll was based on interviews with 2,000 adults, asking questions about a variety of issues. What is the margin of error for this poll? = 0.02, or about 2%. One of the statements in the news story was "a margin of error of plus or minus two percentage points means that the 45 percent of Americans for and the 46 percent of Americans against oil exploration in Alaska's Arctic National Wildlife Refuge are in a statistical dead heat."
1. In a statistical study what is the difference between an individual and a variable?
An individual is a member of the population of interest. A variable is an aspect of an individual subject or object being measured.
10. What is the effect of recruiting volunteers to participate in a randomized experiment? a. The results will be more credible because people who really wanted to participate took part in the study. b. The results cannot necessarily be extended to the larger population. c. There will be no effect because the people are always randomly assigned to treatments, eliminating any type of bias. d. Researchers are never allowed to use volunteers to participate in an experiment.
B
4. Using volunteers for a study introduces problems in the form of __________.
BIAS
16. If you weighed yourself using a bathroom scale that always reads five pounds under the actual weight, which of the following aspects of a good measurement would you be violating? a. Validity b. Reliability c. Unbiasedness d. None of the above.
C
19. Why is it important to know how the individuals or objects in a study were selected? a. It is important to know to whom the results can be extended. b. It is important for determining whether or not there is bias in the results. c. Both a) and b) are true. d. It is not important to know how the individuals were selected; only the size of the sample matters.
C
17. One of the major advantages of an experiment over an observational study is that in an experiment, the researcher attempts to control for __________ variables.
CONFOUNDING
20. One of the complications that can arise with observational studies is __________ variables and the implications of causation.
CONFOUNDING
17. Which of the following questions cannot be addressed using statistics? a. What percentage of people in the U.S. are cell phone owners? b. Which of these two medicines has a better success rate at lowering cholesterol? c. Do mothers most often hold their babies in their arms so the baby is on the left side? d. All of the above can be addressed using statistics.
D
5. Suppose you have 20 tomato plants and want to know if fertilizing them will help them produce more fruit. You randomly assign 10 of them to receive fertilizer and remaining 10 to receive non. You otherwise treat the plant in an identical manner. a. Explain whether this would be an observational study or a randomized experiment.
Randomized experiment; plants are randomly assigned to receive the treatments.
12. Which of the following is a potential complication of observational studies? a. Confounding variables b. The improper conclusion of causation c. Improper extension of the results d. All of the above
D
14. Which of the following studies can result in researchers extending the results inappropriately because the sample doesn't represent the intended population? a. Studies involving volunteers (self-selected samples) b. Studies involving convenience samples c. Case-control studies d. All of the above
D
18. If the experimental units as a group do not represent the intended population, the researcher cannot __________ the results from the experiment to the intended population.
GENERALIZE
9. A survey question that starts out with the phrase "Do you agree that..." is an example of what?
Deliberate bias
10. What motivates a respondent to understate the true response about an undesirable social habit such as smoking?
Desire to please
3. Most statistical studies fall into one of two types, either an observational study or a randomized __________.
Experiment
: Study found that overall left-handed people die at a younger age than right-handed people. What is the Explanatory/ Response
Explanatory = Handedness Response = Age at death
______ is one that may explain or may cause differences in a_______ (or outcome variable).
Explanatory variable, response variable
19. In an experiment to see if a certain new drug can prevent a second heart attack, other drugs that the experimental units may or may not be taking already for heart related illnesses would be considered to be __________ variables.
INTERACTING
27. (5 points) Explain why the ordering of questions on a survey can create bias in the resulting data.
If one question requires respondents to think about something that they may not have otherwise considered, then the order in which questions are presented can change the results.
Is it necessary that "data" consist of numbers? Explain
No, data can be non-numerical information, like ethnicity.
25. The __________ can be applied to any percent reported regarding the sample to find an estimate of the percent of the population that would respond in the same way.
Margin of error
22. The people who are most likely to respond to a volunteer response survey are those who have a strong __________ about the questions being asked.
Opinion or emotional response
Explain why blinding is used in experiments.
Participants are kept blind so they don't alter their behavior or outcome to please the experimenter. Those collecting the measurements are kept blind so they don't inadvertently bias the measurements in the desired direction.
Suppose you wanted to know if men or women students spend more money on clothes. You consider two different plans for carrying out an observational study: Plan 1: Ask the participants how much they spent on clothes during the last 3 months, and then compare the amounts reported by the men and the women. Plan 2: Ask the participants to keep a diary in which they record their clothing expenditures for the next 3 months, and then compare the amounts recorded by the men and the women. Which of these plans is a retrospective study?
Plan 1
A confounding variable is
Related to the explanatory variable, and • affects the response variable.
2. To conduct a good statistical study, you have to be sure that your __________ is representative and large enough.
Sample
26. Random __________ is used to get a representative sample from the population of interest so the results can be extended to that population.
Sampling (digit dialing is also an acceptable response).
23. With a (an) __________ sample, every conceivable group of people of the required size has the same chance of being the selected sample.
Simple random
Explain why it is not always possible to make an experiment double-blind. You may refer to an example in the chapter if it makes it easier to explain.
Some treatments are impossible to hide from the people using them, such as when meditation is compared to exercise for the effect on lowering blood pressure. Obviously, people would know if they have been assigned to meditate or to exercise.
According to Cynthia Crossen†: "It is a poller's business to press for an opinion whether people have one or not. 'Don't knows' are worthless to pollers, whose product is opinion, not ignorance. That's why so many polls do not even offer a 'don't know' alternative." Which of the Seven Critical Components would bring this problem to light?
The lack of "don't know" as a possible response would be uncovered by Component 4.
Is the "experimenter effect" most likely to be present in a double-blind experiment, a single-blind experiment, or an experiment with no blinding? Explain.
The experimenter effect is most likely to be present in an experiment with no blinding, because the experimenter can indicate the favored treatment and the participants can respond to that influence. However, it can also be a problem in a single-blind experiment, because the party who isn't blind to the conditions can try to influence the results.
No. Only those who attended the fitness center that day will have any chance of being included in the sample.
The sample of 5,000. This is a simple random sample. The internet survey represents a convenience sample, which is biased.
In early September, 2003, California's Governor Gray Davis approved a controversial law allowing people who were not legal residents to obtain a California state driver's license. That week the California Field Poll released a survey showing that 59% of registered voters opposed the law and 34% supported it. This part of the survey was based on a random sample of just over 300 people, conducted over the phone. The same week that the Field Poll was released a Web site called SFGate.com† asked visitors to "Click to vote" on their preferred response to "Agree with new law allowing drivers' licenses for illegal immigrants?" The choices and the percent who chose them were "Yes, gesture of respect, makes roads safe" 19%, "No, thwarts immigration law, poses security risk" 79%, and "Oh, great, another messy ballot battle" 2%. The total number of votes shown was 2,900. Which of the following are likely reasons why the percent who supported the law in this poll (19%) differed so much from the percent who supported it in the Field Poll (34%).
There are a couple of possible reasons. First, when interviewed by phone for the field poll, people may have thought the socially acceptable answer was to support the law and thus responded that way even if they didn't support it. Second, who felt strongly about the issue were more likely to oppose the law.
_____ is one or a combination of categories of the explanatory variable(s) assigned by the experimenter.
Treatment
1. What are statistics?
a. Statistics are numbers measured for some purpose. b. Statistics is a collection of procedures for collecting and analyzing data. c. Statistics is a tool to help you make decisions when faced with uncertainty.
A doctor claims to be able to cure migraine headaches. A researcher administers a questionnaire to each of the patients the doctor claims to have cured. Is this study a survey, an experiment, an observational study, or a case study?
case study, because only one doctor is studied in depth
"Graduating is good for your health," according to a headline in The Boston Globe.† The article noted, "According to the Center for Disease Control, college graduates feel better emotionally and physically than do high school dropouts." The headline was based on a study in which a representative sample of over 400,000 adults in the United States was asked a series of questions, including level of education and on how many of the past 30 days they felt physically and emotionally healthy. Explain how each of the "difficulties and disasters in observational studies" applies to this study, if at all.
"Confounding variables and the implications of causation" is a major problem, at least as the study was presented in the newspaper, since it implies that level of education causes people to feel better. There are lots of possible confounding factors, including the reverse explanation that people who are healthier are more likely to finish college. You can probably think of many other possible confounding factors. "Extending the results inappropriately" is not likely to be a problem, since a large representative sample was used. "Using the past as a source of data" could be a problem because people were asked to recall how they felt for the past 30 days rather than to keep a diary for 30 days.
1. Your book lists three major reasons that studies are conducted. Name one of them.
: 1) TO COLLECT DATA IN ORDER TO MAKE A DECISION; 2) TO ASK AND ANSWER QUESTIONS ABOUT THE WORLD AROUND US; OR 3) TO CONVINCE CONSUMERS THAT A CERTAIN PROGRAM OR PRODUCT WORKS BETTER THAN THE COMPETITION.
11. What does randomization mean in terms of experiments? a. Each of the experimental units is randomly selected to participate. b. Each of the experimental units is randomly assigned to a treatment. c. The researchers randomly select which treatments they will include in the experiment. d. None of the above.
A
14. If you tried to measure happiness by using an IQ test, which of the following aspects of a good measurement would you be violating? a. Validity b. Reliability c. Unbiasedness d. None of the above.
A
9. Which of the following describes an experiment? a. Create differences in the explanatory variable and then examine the results. b. Observe differences in the explanatory variable and then notice whether these are related to differences in the response variable. c. Both a) and b) are experiments. d. Neither a) nor b) are experiments
A
=To learn how its employees felt about higher student fees imposed by the legislature, a university divided employees into three categories: staff, faculty, and student employees. A random sample was selected from each group and they were telephoned and asked for their opinions. What type of sampling plan was used? Why might the sampling plan result in a biased sample?
Stratified sampling The sample is unlikely to be biased
1. Suppose a toy company wants to know if certain colors are more appealing and attractive to toddlers than others. They decide to measure this by choosing five colors of blocks and making sets of blocks in each of the five colors. Then they found 30 toddlers to participate in the study, and they randomly assigned each toddler a block color. They observed each toddler separately at the same time of the day, and gave them no other toys to play with. They recorded the length of time each toddler played with the blocks, to see if some colors of blocks were played with longer than other colors. All toddlers in the experiment were the same age (2 years old) and an equal number of girls and boys played with each color of blocks. c. {Toy colors narrative} Name one confounding variable that was controlled for in this study.
ANSWER: ANY OF THE FOLLOWING: AGE; TIME OF DAY; GENDER; OTHER TOYS; INTERACTION WITH OTHER CHILDREN. BOREDOM WITH BLOCKS IS ALSO CONTROLLED FOR BECAUSE EACH TODDLER PLAYED WITH ONE COLOR.
8. This case study examines the relationship between breakfast eating habits and obesity in school kids from low-income families. Researchers compared body mass indices (BMIs) of 625 children to the number of times - out of 9 days - the children reported eating cereal for breakfast. Kids who reported eating breakfast 4 out of 9 days tended to be in the 95th percentile for BMIs, indicating obesity. Kids who reported eating cereal 9 out of 9 days tended to be in the 65th percentile, indicating healthy weights. The study was funded in part by a regional dairy council. Case study 6.2 narrative} What is one possible confounding factor in this experiment?
ANSWER: ANY REASONABLE ANSWER OK. EXAMPLES: OVERALL DIET; EXERCISE; PARENTAL ATTITUDES TOWARDS HEALTH AND FITNESS, ETC.
3. Name two (of the seven) steps involved in evaluating a study
ANSWER: ANY TWO OF THE FOLLOWING OK: DETERMINE WHAT TYPE OF STUDY WAS DONE; CONSIDER THE SEVEN CRITICAL COMPONENTS TO FAMILIARIZE YOURSELF WITH THE RESEARCH; DETERMINE IF ANY OF THE 'DIFFICULTIES AND DISASTERS' APPLY; DETERMINE IF THE INFORMATION IS COMPLETE AND IF NOT, TRY TO GET THE MISSING INFORMATION; ASK IF THE RESULTS MAKE SENSE IN THE LARGER SCOPE OF THINGS; ASK YOURSELF IF THERE IS ANY ALTERNATIVE EXPLANATION FOR THE RESULTS; DETERMINE IF THE RESULTS ARE MEANINGFUL ENOUGH TO CHANGE YOUR LIFESTYLE, ATTITUDES, OR BELIEFS.
7. Suppose you wanted to find out what percentage of all Americans approve of the job the president is doing and you mailed questionnaires to 2,000 readers of The Wall Street Journal and compiled the results. This is a(n) __________ sample of all-American voters.
ANSWER: BIASED (NONRANDOM OR NONREPRESENTATIVE)
1. Suppose a toy company wants to know if certain colors are more appealing and attractive to toddlers than others. They decide to measure this by choosing five colors of blocks and making sets of blocks in each of the five colors. Then they found 30 toddlers to participate in the study, and they randomly assigned each toddler a block color. They observed each toddler separately at the same time of the day, and gave them no other toys to play with. They recorded the length of time each toddler played with the blocks, to see if some colors of blocks were played with longer than other colors. All toddlers in the experiment were the same age (2 years old) and an equal number of girls and boys played with each color of blocks. b. {Toy colors narrative} Is this study an observational study or an experiment?
ANSWER: EXPERIMENT
2. Explain why it is important to find out not only who conducted a study, but also who funded the study.
ANSWER: IF THE STUDY WAS FUNDED BY AN ORGANIZATION THAT WOULD LIKELY HAVE A STRONG PREFERENCE FOR A CERTAIN OUTCOME, THERE MAY BE A CONFLICT OF INTEREST THAT COMPROMISES THE RESULTS. YOU MUST BE SURE PROPER SCIENTIFIC PROCEDURES WERE CONDUCTED.
11. Suppose you want to set up a survey involving only closed questions. Why is it important to first conduct a pilot survey involving open questions?
ANSWER: IF YOU DON'T OFFER THE MOST POPULAR POSSIBLE ANSWERS TO YOUR CLOSED QUESTION, EVEN IF YOU INCLUDE AN ALTERNATIVE OF 'OTHER', THE RESULTS OF YOUR SURVEY COULD CHANGE DRAMATICALLY, COMPARED TO THE RESULTS OF A SURVEY WITH ONLY OPEN QUESTIONS.
13. Why do IQ tests continue to be surrounded by controversy as a measure of intelligence?
ANSWER: IT IS VERY DIFFICULT TO DEFINE WHAT IS MEANT BY INTELLIGENCE. IT IS DIFFICULT TO MEASURE SOMETHING IF YOU CAN'T EVEN AGREE ON WHAT IT IS YOU ARE TRYING TO MEASURE.
8. This case study examines the relationship between breakfast eating habits and obesity in school kids from low-income families. Researchers compared body mass indices (BMIs) of 625 children to the number of times - out of 9 days - the children reported eating cereal for breakfast. Kids who reported eating breakfast 4 out of 9 days tended to be in the 95th percentile for BMIs, indicating obesity. Kids who reported eating cereal 9 out of 9 days tended to be in the 65th percentile, indicating healthy weights. The study was funded in part by a regional dairy council. b. {Case study 6.2 narrative} Based on this study, can a cause and effect relationship between cereal consumption and obesity be made?
ANSWER: NO; THIS WAS AN OBSERVATIONAL STUDY; SUBJECTS WERE NOT RANDOMLY ASSIGNED TO EITHER CONSUME CEREAL OR NOT; POTENTIAL CONFOUNDING VARIABLES ARE UINCONTROLLED.
6. The conclusions that can be drawn from an observational study are not as strong as the conclusions that can be drawn from a(n) __________.
ANSWER: RANDOMIZED (OR CONTROLLED) EXPERIMENT
12. Name one of the major problems with offering open questions on a survey.
ANSWER: THE BIGGEST PROBLEM WITH OPEN QUESTIONS IS THAT THE RESULTS CAN BE DIFFICULT TO SUMMARIZE, CATEGORIZE, OR QUANTIFY.
2. What is the final question you should ask when you read the results of research that involves statistical studies?
ANSWER: WHETHER YOU WILL MAKE ANY CHANGES IN YOUR LIFESTYLE OR BELIEFS AS A RESULT OF THE RESEARCH.
1. Suppose a toy company wants to know if certain colors are more appealing and attractive to toddlers than others. They decide to measure this by choosing five colors of blocks and making sets of blocks in each of the five colors. Then they found 30 toddlers to participate in the study, and they randomly assigned each toddler a block color. They observed each toddler separately at the same time of the day, and gave them no other toys to play with. They recorded the length of time each toddler played with the blocks, to see if some colors of blocks were played with longer than other colors. All toddlers in the experiment were the same age (2 years old) and an equal number of girls and boys played with each color of blocks. a. {Toy colors narrative} What is the explanatory variable and what is the response variable?
ANSWERS (RESPECTIVELY): BLOCK COLOR AND PLAYING TIME.
Explain what is meant by this statement. "a margin of error of plus or minus two percentage points means that the 45 percent of Americans for and the 46 percent of Americans against oil exploration in Alaska's Arctic National Wildlife Refuge are in a statistical dead heat."
Adding and subtracting the margin of error of 2% to each of the two figures given, 45% and 46%, produces intervals that overlap. These intervals are likely to cover the true population values for and against oil exploration, so it's possible that the percentages are very similar. Since these figures are based on the same survey, another way to think about this is to assume that the percent who didn't answer for or against stays the same (at about 9% based on these results). Adding the margin of error to the 45% for oil exploration means that the true percent for oil exploration could be as high as 47%, in which case there would be only 44% against, after accounting for the 9% undecided.
13. What type of study often results in problems related to using the past as a source of data? a. Case-control study b. Retrospective study c. Prospective study d. Before vs. after matched-pairs experiment
B
15. If you used a 12-inch ruler to measure the distance across a large pond, which of the following aspects of a good measurement would you be violating? a. Validity b. Reliability c. Unbiasedness d. None of the above.
B
18. Suppose you want to determine how Americans feel about reality TV. Which of the following samples contains the least amount of bias? a. All the people who phone in their opinion on reality TV to a CBS Evening News call-in poll. b. All those who were randomly selected to receive a reality TV survey in the mail. c. People who call the networks during reality TV programs to voice their opinion. d. People who respond to an Internet survey at www.realitytv.com.
B
4. Explain Why the relationship shown in table below concerning use of aspirin and heart attack rates, can be used as evidence that aspirin prevent heart attacks? Group 1: took ordinary aspirin tablet every other day. Group 2: took placebo (looked like aspirin but no active ingredients).
Because the men were randomly assigned to the two conditions (i.e., because it was a randomized experiment), the only substantial difference between the two groups should have been whether they took aspirin or a placebo. Therefore, the observed reduction in heart attack rates for those taking aspirin can be attributed to the difference in treatments.
20. Which of the following is a well worded survey question for determining a voter's opinion on a tax increase for education? a. Would you be willing to agree to a small tax increase that would help the education of our children? b. Do you agree with a tax increase for education? c. How do you feel about a tax increase for education (agree, disagree, neutral)? d. All of the above are well worded questions.
C
21. Suppose a recent election exit pollster reports that "Forty-eight percent of the voters polled said they voted for Candidate A. The margin of error for this survey is plus or minus 2.5 percentage points." Assume the exit poll was designed and conducted correctly. What can be concluded about Candidate A? a. 48% of all voters will vote for Candidate A. b. We are confident that between 45.5% and 50.5% of all voters will vote for Candidate A. This means he/she will win the election, because 50.5% is more than half of the votes. c. We are confident that between 45.5% and 50.5% of the voters will vote for Candidate A. The election is 'too close to call' at this point. It could go either way. d. None of the above
C
To survey the opinions of its customers, an airline company made a list of all its flights and randomly selected 25 flights. All of the passengers on those flights were asked to fill out a survey. What type of sampling plan was used? Why might the sampling plan result in a biased sample?
Cluster sampling the sample is unlikely to be biased
Suppose an observational study finds that people who use public transportation to get to work have better knowledge of current affairs than those who drive to work, but that the relationship is weaker for well-educated people. What term from this chapter applies to each of the following variables? c. level of education:
interacting variable. Interacting variable is a second variable that interacts with the explanatory variable but result reported without taking that interaction into account. Solution: the researcher should measure and report variables that may interact with explanatory variable.
15. An observational study based on a sample of students in introductory psychology classes at a university in the Midwestern U.S. compared drinking behavior and hangover symptoms in men and women. To what group can the results of this study definitely be extended? a. All men and women b. All men and women of the same age group as those in the study c. All college students in the Midwestern U.S. d. None of the above
D
Patients who visit a clinic to help them stop smoking are given a choice of two treatments: undergoing hypnosis or applying nicotine patches. The percentages who quit smoking are compared for the two methods. Is this study a survey, an experiment, an observational study, or a case study?
observational study, because patients were allowed to choose their method of treatment rather than having it randomly assigned
Suppose an observational study finds that people who use public transportation to get to work have better knowledge of current affairs than those who drive to work, but that the relationship is weaker for well-educated people. What term from this chapter applies to each of the following variables? b. knowledge of current affairs:
response variable
4. A histogram of pulse rates of current students in introductory statistics courses at American University is given in the figure below. Students were asked the question, "What is your pulse rate in beats per minute (bpm)" on a survey given in class. Other questions were asked too. c. Suggest improvements to the study design to avoid the issues you highlighted in part (c) above.
Ideally, for any measure of interest, we would select a sample of students randomly from all students. Ideally, we would sample from a list of all students and reach out to those selected to participate. In reality, we may not be able to get such a list so we would be better off sampling different classes and then students within classes in an effort to approximate a random sample and to guarantee everyone an opportunity to participate. With regards to the measure, it would be best to have a professional measure the pulse rate of each individual using a standard protocol.
4. A histogram of pulse rates of current students in introductory statistics courses at American University is given in the figure below. Students were asked the question, "What is your pulse rate in beats per minute (bpm)" on a survey given in class. Other questions were asked too. Suppose we are interested the population of all undergraduate students at American University. Discuss at least two concerns about using this survey design and sample for learning about this population of interest. Use terminology from the units covered in your discussion.
If we are interested in learning about all undergraduate students at AU then this sample might be biased because it is not a random sample but a convenience sample of those students who enroll in introductory statistics courses with this Professor. Of more concern, this is not a reliable measure because pulse rate was self-reported with no instructions provided on how to measure it! others.
Give two reasons why we must sometimes use an observational study instead of an experiment.
It is unethical or impossible in certain situations to assign people to receive a specific "treatment" (such as smoking). Certain explanatory variables such as left vs. right handedness, are inherent traits and cannot be randomly assigned. Another option, we might not be interested in cause-effect relationships and thus an experiment is not necessary.
According to Cynthia Crossen†: "It is a poller's business to press for an opinion whether people have one or not. 'Don't knows' are worthless to pollers, whose product is opinion, not ignorance. That's why so many polls do not even offer a 'don't know' alternative." Many research organizations give their interviewers an exact script to follow when conducting interviews to measure opinions on controversial issues. Why do you think they do so?
Many research organizations give their interviewers an exact script to follow so that the interviewers don't change the wording slightly to encourage answers that support their own opinions.
5. Suppose you want to find out what percentage of students at your university would pay extra fees for the use of a new fitness center, and you want a simple random sample of 100 students. Suppose you go to the current fitness center and ask every 10th student who comes in the door to participate in your survey, until you have 100 people. Does this method of sampling give you a probability sample of all university students? Explain your answer.
No. Only those who attended the fitness center that day will have any chance of being included in the sample.
Suppose you want to find out what percentage of students at your university would pay extra fees for the use of a new fitness center, and you want a simple random sample of 100 students. Suppose you go to the current fitness center and ask every 10th student who comes in the door to participate in your survey, until you have 100 people. Does this method of sampling give you a probability sample of all university students? Explain your answer.
No. Only those who attended the fitness center that day will have any chance of being included in the sample.
______observe differences in the explanatory variable and notice whether these are related to differences in the response variable
Observational study:
A pollster interested in opinions on gun control divided a city into city blocks, then surveyed the third house to the west of the southeast corner of each block. If the house was divided into apartments, the westernmost ground floor apartment was selected. The pollster conducted the survey during the day, but left a notice for those who were not at home to phone her so she could interview them. What type of sampling plan was used? Why might the sampling plan result in a biased sample?
systematic sampling the sample is likely to be biased for a number of reasons: For instance, groundfloor residents may be more susceptible to crime and thus have more extreme views. Those at home during the day may differ from those not at home, and leaving a notice for the others to call would introduce bias because only those with strong opinions would be likely to do so.
According to Cynthia Crossen†: "It is a poller's business to press for an opinion whether people have one or not. 'Don't knows' are worthless to pollers, whose product is opinion, not ignorance. That's why so many polls do not even offer a 'don't know' alternative." Explain how this problem might lead to bias in a survey.
People who would prefer to answer that they don't know, but are forced to choose an answer, will use something other than an informed opinion to do so. For example, if a person is asked, "Do you support the new tax bill in Congress?" and he is unfamiliar with the bill but is forced to answer, his answer would probably be more of a reflection of how he feels about taxes or about the current Congress.
Suppose you wanted to know if men or women students spend more money on clothes. You consider two different plans for carrying out an observational study: Plan 1: Ask the participants how much they spent on clothes during the last 3 months, and then compare the amounts reported by the men and the women. Plan 2: Ask the participants to keep a diary in which they record their clothing expenditures for the next 3 months, and then compare the amounts recorded by the men and the women. Give one disadvantage of each plan
Plan 1 has the disadvantage that participants may not remember how much they spent. Plan 2 has the disadvantage that participants might change their normal spending behavior, knowing that they were part of a study.
Suppose you wanted to know if men or women students spend more money on clothes. You consider two different plans for carrying out an observational study: Plan 1: Ask the participants how much they spent on clothes during the last 3 months, and then compare the amounts reported by the men and the women. Plan 2: Ask the participants to keep a diary in which they record their clothing expenditures for the next 3 months, and then compare the amounts recorded by the men and the women. Which of these plans is a prospective study?
Plan 2
4. A histogram of pulse rates of current students in introductory statistics courses at American University is given in the figure below. Students were asked the question, "What is your pulse rate in beats per minute (bpm)" on a survey given in class. Other questions were asked too. How would you characterize the distribution of pulse rates?
Pulse rates fall between 30 and 150bpm with "most" being between 60 and 80 bpm and a few outside of that range. The shape has a single maximum (called unimodal) although some might notice there is a slight skewness I would describe this as mostly symmetric about 70bpm. There are outliers at 140-150bpm.
21. One of the complications that can arise with observational studies is using the past as a source of data. This type of study is called a __________ study.
RETROSPECTIVE
24. Experiments use __________ to reduce the effects of confounding variables and other sources of bias that are naturally present in observational studies.
Randomization
_______create differences in the explanatory variable and examine results (response variable).
Randomized experiment:
The experimenter effect is most likely to be present in an experiment with no blinding, because the experimenter can indicate the favored treatment and the participants can respond to that influence. However, it can also be a problem in a single-blind experiment, because the party who isn't blind to the conditions can try to influence the results.
Retrospective: The outcome has already happened; consequently, it can only be observational. People have already have cancer. Prospective: The participants do not have cancer but we will watch them over the year. It can be observational or Experimental.
7. Briefly explain at least one aspect that is wrong with each of the following study scenarios: a. You want to study student opinions about a proposed change in procedures for changing majors. You and three research assistants each choose one classroom on campus and then you each hand out questionnaires to the first 25 students as they arrive at your chosen classroom at 8:10am.
Students who take 8:10am classes might be different from other students. Also not all students have an opportunity to be in your sample.
Briefly explain at least one aspect that is wrong with each of the following study scenarios: a. You want to study student opinions about a proposed change in procedures for changing majors. You and three research assistants each choose one classroom on campus and then you each hand out questionnaires to the first 25 students as they arrive at your chosen classroom at 8:10am.
Students who take 8:10am classes might be different from other students. Also not all students have an opportunity to be in your sample.
5. Explain why even the simplest kind of measurement, such as finding your height, still presents complicated issues.
THE ACCURACY OF YOUR MEASUREMENT DEPENDS ON YOUR MEASUREMENT TOOL; HOW TALL YOU STAND WHEN YOU MEASURE; WHETHER OR NOT YOU WEAR SHOES, ETC.
7. Briefly explain at least one aspect that is wrong with each of the following study scenarios: b. An experiment will assign 40 rats to four different treatment conditions. The rats arrive from the supplier in batches of 10 and the treatment lasts two weeks. Rats are then provided similar cages and diets and followed for the remainder of their lifetimes. The survival time of each rate after treatment will be compared between the four different treatment groups to assess the impact of treatment on lifetime. Because rats arrive in batches, the researcher decides to as the first batch of all 10 rats randomly to one of the four treatments, and data for these rats are collected. After a one-week, another batch of 10 rats arrives and is assigned to one of the three remaining treatments. The process continues until the last batch of rats is given the treatment that has not been assigned to the three previous batches.
The experimental unit is batch - that is, batches of rats are randomized to treatments as opposed to individual rats. This is an issue because the rats from the same batch may be more alike than rats from different batches. For example, if all rats from the same batch are from the same litter, then they might react to a treatment in a similar way because of some genetic component. Likewise, even if they are not related to each other within a batch, if they lived under the same environmental conditions that would make the rats "more alike" than between batches (say one of the shipments required more travel time than the others, then those rats have been exposed to less optimal environment for longer than other rats and that could impact the results.) If individual rats were randomly assigned to a treatment upon arrival, these factors would be "averaged out" over the different treatment groups
Briefly explain at least one aspect that is wrong with each of the following study scenarios: b. An experiment will assign 40 rats to four different treatment conditions. The rats arrive from the supplier in batches of 10 and the treatment lasts two weeks. Rats are then provided similar cages and diets and followed for the remainder of their lifetimes. The survival time of each rate after treatment will be compared between the four different treatment groups to assess the impact of treatment on lifetime. Because rats arrive in batches, the researcher decides to as the first batch of all 10 rats randomly to one of the four treatments, and data for these rats are collected. After a one-week, another batch of 10 rats arrives and is assigned to one of the three remaining treatments. The process continues until the last batch of rats is given the treatment that has not been assigned to the three previous batches.
The experimental unit is batch - that is, batches of rats are randomized to treatments as opposed to individual rats. This is an issue because the rats from the same batch may be more alike than rats from different batches. For example, if all rats from the same batch are from the same litter, then they might react to a treatment in a similar way because of some genetic component. Likewise, even if they are not related to each other within a batch, if they lived under the same environmental conditions that would make the rats "more alike" than between batches (say one of the shipments required more travel time than the others, then those rats have been exposed to less optimal environment for longer than other rats and that could impact the results.) If individual rats were randomly assigned to a treatment upon arrival, these factors would be "averaged out" over the different treatment groups.
In early September, 2003, California's Governor Gray Davis approved a controversial law allowing people who were not legal residents to obtain a California state driver's license. That week the California Field Poll released a survey showing that 59% of registered voters opposed the law and 34% supported it. This part of the survey was based on a random sample of just over 300 people, conducted over the phone. The same week that the Field Poll was released a Web site called SFGate.com† asked visitors to "Click to vote" on their preferred response to "Agree with new law allowing drivers' licenses for illegal immigrants?" The choices and the percent who chose them were "Yes, gesture of respect, makes roads safe" 19%, "No, thwarts immigration law, poses security risk" 79%, and "Oh, great, another messy ballot battle" 2%. The total number of votes shown was 2,900. What type of sample was used for this poll?
This is a volunteer (self-selected) sample.
8. Describe one of the issues that you would need to think about when deciding how to measure which supermarket is the 'best' one in town.
WHAT DO WE MEAN BY 'BEST'? WHAT ONE PERSON THINKS OF AS 'BEST' MIGHT NOT MEAN THE SAME THING TO SOMEONE ELSE; DO WE MEASURE IT OVER TIME, OR AT ONE MOMENT IN TIME?
Researchers interested in the mechanisms of (dis)honesty designed a study to examine the impact of a "moral standard reminder" on subsequent (dis)honesty. Two hundred seven students participated in the study which consisted of completing a task involving solving a sequence of arithmetic puzzles that they could easily verify were correct or not. Each participant was given a test sheet with the puzzles and an answer sheet to self-report the number of correctly solved puzzles after five minutes of testing. They would be paid 50 cents for each correct puzzle solved in a five minute testing period. Prior to completing the task, students were randomly assigned to one of three "moral standard reminder" groups: (1) the control group, for which at the end of the five minutes participants handed their test solution and answer sheets to the researcher who verified their answers and paid them for each correct solution, (2) the recycle group in which the participants indicated the total number of correctly solved puzzles on the answer sheet, folded the original test sheet, and placed it in their belongings (to recycle later), thus providing them an opportunity to cheat, and (3) the recycle and honor code group which was the same as (2) except that at the top of the test sheet, there was an additional statement that read "I understand that this short survey falls under [the] honor system." Participants printed and signed their names below the statement. Thus, the honor code statement appeared on the same sheet as the puzzles, and this sheet was recycled before participants submitted their answer sheets, so there was still the opportunity to cheat. The researchers reported that an average of 3.4 puzzles were solved under the control condition, an average of 6.1 under the recycle only condition, and an average of 3.1 under the recycle plus honor code reminder condition. They concluded that the recycle plus honor code condition "eliminated cheating" to the extent that this condition was undistinguishable from the control condition, where students did not have the opportunity to cheat, but significantly different from the recycle only condition, where they did. a. Is this an observational study or a randomized experiment? b. Identify the response variable. c. Identify the explanatory variable. d. Is the response variable quantitative (i.e. numeric) or qualitative (i.e. categorical)? e. Is the explanatory variable quantitative (i.e. numeric) or qualitative (i.e. categorical)? f. Did the researchers measure any confounding variables? g. Are you convinced by their conclusions? Is there other information you would want?
a. Randomized experiment b. Number of puzzles solved c. Moral reminder condition (control, recycle, recycle plus honor code) d. Quantitative (numerical) e. Qualitative (categorical) f. None mentioned g. Answers will vary.
5. Suppose you have 20 tomato plants and want to know if fertilizing them will help them produce more fruit. You randomly assign 10 of them to receive fertilizer and remaining 10 to receive non. You otherwise treat the plant in an identical manner. b. If the fertilized plants produce 30% more fruit than unfertilized plants, can you conclude that the fertilizer caused the plants to produce more? Explain
b. If the fertilized plants produce 30% more fruit than unfertilized plants, can you conclude that the fertilizer caused the plants to produce more? Explain
Suppose an observational study finds that people who use public transportation to get to work have better knowledge of current affairs than those who drive to work, but that the relationship is weaker for well-educated people. What term from this chapter applies to each of the following variables? d. whether the participant reads a daily newspaper:
confounding variable. For instance, maybe those taking public transportation used the time to read a daily newspaper, and that might have caused the difference in the response variable. Solution: Randomaziation
A large store wanted to know if consumers would be willing to pay slightly higher prices to have computers available throughout the store to help them locate items. The store posted an interviewer at the door and told her to collect a sample of 100 opinions by asking the next person who came in the door each time she had finished an interview. What type of sampling plan was used? Why might the sampling plan result in a biased sample?
convenience or haphazard sample The sample is likely to be biased for a number of reasons The most obvious is that the people who looked approachable and had time to answer questions would be the ones chosen. Since this survey only occurred during one day, only people who came to the store that day and around the time the survey began were able to give their opinions.
A large company wants to compare two incentive plans for increasing sales. The company randomly assigns a number of its sales staff to receive each kind of incentive and compares the average change in sales of the employees under the two plans. Is this study a survey, an experiment, an observational study, or a case study?
experiment, because the incentive methods are randomly assigned
Suppose an observational study finds that people who use public transportation to get to work have better knowledge of current affairs than those who drive to work, but that the relationship is weaker for well-educated people. What term from this chapter applies to each of the following variables? a. method of getting to work:
explanatory variable
