Unit notebook May 29, 2015

Transcription

1 S.IC.3 S.IC.6 Objective: Students will recognize the purposes of and differences among sample surveys, experiments, and observational studies; explain how randomization relates to each and evaluate reports based on data. Statistical research takes various forms depending on whether the purpose of the research is : a) to measure a variable in a population, b) to see if there is evidence of an association between two variables, c) or to determine whether one variable actually influences another variable. Example 1 Suppose a graduate school researcher is considering three studies related to math and music. One study involves asking a random sample of high school students in a large school district whether they listen to music while doing math homework. A second study involves asking a random sample of students at a large university whether they are majoring in math and whether they also play a musical instrument or sing. A third study involves a group of adult participants where half will be randomly assigned either to listen to classical music for 15 minutes before taking a logical reasoning test or to listen to white noise for 15 minutes before taking the same test a)which study appears to look for an association between two variables without actively manipulating either one? What are those variables? b)which study appears to be looking for evidence that one variable actually influences another variable? What are those variables, and which one is manipulated to see if it influences the other? c)which study appears to be simply measuring a variable in a population? What is that variable? Think Pair Share Describe the type of result or conclusion the researcher might obtain from each study. A survey measures characteristics of interest about a population using a sample selected from the population. As you saw in a previous lesson, a sample needs to be representative of the population in order for the measurements obtained from the sample to be accurate. Random sampling is generally the best way to ensure representation. Even when random sampling is used, a survey s results can have errors. Some of the sources of errors are: Biased questions: The wording of questions in a survey can influence the way people respond to questions. Survey questions need to be worded in a neutral, unbiased way. Interviewer effect: If an interviewer asks the questions in a survey, the person being interviewed may give inaccurate responses to avoid being embarrassed. Nonresponse: Some people may be difficult to contact, or they may simply refuse to participate once contacted. If nonresponse rates are higher for certain subgroups of a population, then those subgroups will be underrepresented in the survey results.

2 Example 2 Explain why the results of each survey are likely to be inaccurate, and then suggest a way to improve the accuracy of the survey. Example 2 Explain why the results of each survey are likely to be inaccurate, and then suggest a way to improve the accuracy of the survey. a) The owner of a business, conducts interviews with a random sample of employees to have them rate how satisfied they are with their jobs. b)a teacher conducts one on one interviews with a random sample of her students to get feedback on her teaching methods a) The owner of a business, conducts interviews with a random sample of employees to have them rate how satisfied they are with their jobs. Since the interviewer is the owner of the business, the employees may not be completely open about any job dissatisfaction they may have. The employees may feel that their job security is at stake. A better survey would involve a neutral interviewer or allow the employees to respond anonymously b)a teacher conducts one on one interviews with a random sample of her students to get feedback on her teaching methods Since the interviewer is the teacher, students may not be open about any dissatisfaction they may have with her teaching methods. The students may feel that how the teacher grades them will be influenced by their responses. A better survey would allow the students to respond anonymously Vocabulary In an observational study, researchers determine whether an existing condition, called a factor, in a population is related to a characteristic of interest. For instance, an observational study might be used to find the incidence of heart disease among those who smoke. In the study, being a smoker is the factor, and having heart disease is the characteristic of interest. Generally, an experiment is preferred over an observational study because an experiment allows researchers to manipulate one variable to see its effect on another. However, there may be practical or unethical reasons against performing an experiment. For example, it would be unethical to ask people to smoke in order to study the effects of smoking on their health. Instead, an observational study should be performed using people who already smoke In an experiment, researchers create a condition by imposing a treatment on some of the subjects of the experiment. For instance, an experiment might be conducted by having some people with eczema take a vitamin E pill daily, and then observing whether their symptoms improve. In the experiment, taking the vitamin E pill is the treatment, and improvement of symptoms is the characteristic of interest Example 3 Determine whether each research study is an observational study or an experiment. Identify the factor if it is an observational study or the treatment if is an experiment. Also identify the characteristic of interest a) Researchers measure the cholesterol of 50 subjects who report that they eat fish regularly and 50 subjects who report that they do not eat fish regularly Example 3 Determine whether each research study is an observational study or an experiment. Identify the factor if it is an observational study or the treatment if is an experiment. Also identify the characteristic of interest a) Researchers measure the cholesterol of 50 subjects who report that they eat fish regularly and 50 subjects who report that they do not eat fish regularly This research study is an observational study. The factor is whether people eat fish regularly, and the characteristic of interest is cholesterol level b) Researchers have 100 subjects with high cholesterol take fish oil pills daily for two months. They monitor the cholesterol of the subjects during that time. b) Researchers have 100 subjects with high cholesterol take fish oil pills daily for two months. They monitor the cholesterol of the subjects during that time.

3 think pair share Suppose the researchers in Part A find that considerably more people who eat fish regularly have normal cholesterol levels than those who do not eat fish regularly. Is it reasonable to conclude that eating fish regularly has an effect on cholesterol? Explain. Whether a study is observational or experimental, it should be comparative in order to establish a connection between the factor or treatment and the characteristic of interest. For instance, determining the rate of car accidents among people who talk on cell phones while driving is not instructive unless you compare it with the rate of car accidents among people who don t talk on cell phones while driving and find that it is significantly different. It is not reasonable to make that conclusion because there may be other factors that the people who eat fish regularly have in common, such as a better diet or regular exercise, and it may be those factors that have an effect on cholesterol. think pair share An experiment involves testing the effectiveness of a new drug. Why does giving the subjects in the control group a pill that does not contain the drug make the results more valid than if the subjects in the control group did not take any pill at all? While a comparative observational study can suggest a relationship between two variables, such as cell phone use while driving and car accidents, it cannot establish a cause and effect relationship because there can be confounding variables (also called lurking variables) that influence the results. For instance, perhaps people who talk on cell phones while driving are more likely to drive aggressively, so it is the aggressive driving (not the cell phone use) that leads to a higher rate of car accidents Possible answer: If subjects in the control group did not take a pill, then the placebo effect (in the treatment group) could make it difficult to interpret the results of the experiment. If the treatment group had different outcomes from the control group, researchers could not tell whether the result was due to the drug in the pill or merely to the effect of taking a pill. In an experiment, randomization can remove the problem of a confounding variable by distributing the variable among the groups being compared so that its influence on the groups is more or less equal. Therefore, the best way to establish a cause and effect relationship between two variables is through a randomized comparative experiment where subjects are randomly divided into two groups: the treatment group, which is given the treatment, and the control group, which is not Example 4 To see whether zinc has an effect on the duration of a cold, researchers have half of the subjects take tablets containing zinc at the onset of cold symptoms and the other half take tablets without any zinc. The durations of the colds are then recorded.

4 Example 4 To see whether zinc has an effect on the duration of a cold, researchers have half of the subjects take tablets containing zinc at the onset of cold symptoms and the other half take tablets without any zinc. The durations of the colds are then recorded. Example 5 To see whether regular moderate exercise has an effect on blood pressure, researchers have half of the subjects set aside 30 minutes daily for walking and the other half not do any walking beyond their normal daily routines. The subjects also take and record their blood pressure at the same time each day The treatment is having subjects take tablets that contain zinc at the onset of cold symptoms. The characteristic of interest is the duration of the cold. The control group consists of subjects who took tablets without zinc. The treatment group consists of subjects who took tablets containing zinc Example 5 Example 6 To see whether regular moderate exercise has an effect on blood pressure, researchers have half of the subjects set aside 30 minutes daily for walking and the other half not do any walking beyond their normal daily routines. The subjects also take and record their blood pressure at the same time each day To see whether reviewing for a test with a classmate improves scores, researchers ask half of the subjects to study with a classmate and the other half to study alone. The test scores are then recorded. Example 6 To see whether reviewing for a test with a classmate improves scores, researchers ask half of the subjects to study with a classmate and the other half to study alone. The test scores are then recorded. The treatment is studying for the test with a classmate. The characteristic of interest is the student s test score. The control group consists of subjects who study for the test alone. The treatment group consists of subjects who study for the test with a classmate When you encounter media reports of statistical research in your daily life, you should judge any reported conclusions on the basis of how the research was conducted. Among the questions you should consider are the following: Is the research a survey, an observational study, or an experiment? In broad terms, a survey simply measures variables, an observational study attempts to find an association between variables, and an experiment attempts to establish a cause and effect relationship between variables. Was randomization used in conducting the research? As you know, random sampling is considered the best way to obtain a representative sample from a population and therefore get accurate results. Randomization also helps to dilute the effects of confounding variables. Does the report include the details of the research, such as sample size, statistics, and margins of error? The details help you judge how much confidence to have in the results of the research or how much importance to place on the results.

5 Evaluate the article by answering the following questions. This study is an experiment because treatments were imposed on two groups of patients: those who had a standard interaction with a doctor and those who had an enhanced interaction with a doctor. Randomization was used by randomly assigning subjects to a control group or one of two treatment groups. The report includes the number of subjects but no statistics, such as measures of cold duration or severity. Evaluate the article by answering the following questions. Think Pair Share What conclusion do you draw from the report in Part A? How much confidence do you have in that conclusion? Why A doctor should be empathetic because empathy causes a patient s cold to be shorter and milder. My confidence about the conclusion of the research is relatively high because it seems that the research was a comparative randomized experiment and involved a substantial number of subjects