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Chapter 2 – Data, Reality and Problem SolvingHow data is gathered is as important as what we do with it once we have it.The characteristic(s) recorded about each individual are called variables.Order Number NameStateUnit PriceZip CodeGift?23432Meg HSC10.9929672YObservational Study versus Designed ExperimentObservational studies come about by measuring “what is”. With observational studies cause and effect cannot be determined but an association may be present. There is no attempt to manipulate the subjects being studied.In an observational study, we observe individuals and measure variables of interest but do not attempt to influence the responses.Cause and effect cannot be determined but an association may be present.The variables correspond to the data you are observing.Designed Experiments measure the response of one variable to changes in another variable. The researcher attempts to control the environment of the experiment so that the effect of one variable on another can be isolated and measured. At least one explanatory variable and a response variable ?are involved….the explanatory-response relationship is measuredExample 1: Flu VaccinesDetermine whether each of the following describes an observational study or an experiment.a.To determine the effectiveness of this season’s flu vaccine, medical researchers recruit 100 participants for a study. At the start of the flu season, the researchers randomly select 50 of the participants to receive the flu vaccine and 50 to not receive the vaccine. At the end of flu season, the proportion of participants in each treatment group who contracted the flu is compared.Designed Experimentb.To determine the effectiveness of this flu season’s vaccine at the end of the season, medical researchers compare the proportion of individuals who contracted the flu among a group of 50 randomly chosen individuals who chose to receive the flu vaccine and 50 randomly chosen individuals who chose not to receive the vaccine.Observational StudyWhat is the response variable and what is the explanatory variable for the experiment?Response variable:Status of receiving flu vaccine (yes/no)Explanatory variable:Whether or not patient contracted the flu (yes/no)3 Basic Principles of Experimental DesignControl – A comparison of several treatments in the same environment is the simplest form of control. A control group (no treatment) may be utilized.Replication – There will be natural variability among experimental units so we must replicate our results (use many subjects).Randomization – Subjects should be randomly assigned to treatments. Randomization is utilized to control the effects of variables not under study and in order for cause and effect conclusions to be madeExample 2: Stress ReliefBecause of concerns about employee stress, a large company is conducting a study to compare two programs (tai chi or yoga) that may help employees reduce their stress levels. Tai chi is a 1200-year-old practice, originating in China, that consists of slow, fluid movements. Yoga is a practice, originating in India, that consists of breathing exercises and movements designed to stretch and relax muscles. The company has assembled a group of volunteer employees to participate in the study during the first half of their lunch hour each day for a 10-week period. Each volunteer will be assigned at random to one of the two programs. Volunteers will have their stress levels measured just before the beginning of the program and 10 weeks later at the completion of it. Identify the three components of this experiment.Control:? Two treatments are to be comparedReplication:? More that just a few employees will be involved in the studyRandomization:? Employees will be randomly assigned to either the yoga or tai chi group A group of volunteers who work together ask to be assigned to the same program so that they may participate in that program together. Give an example of a problem that might arise if this is permitted. Explain to this volunteer why random assignment to the two programs will address this problem. ?Volunteers who work together may be under the same amount of stress due to an upcoming deadline or other work factors. This will confuse (confound) the results of the experiment (Is it yoga, tai chi or other factors that change stress levels?)?Someone proposes that a control group be included in the design as well. The stress level would be measured for each volunteer assigned to the control group at the start of the study and again 10 weeks later. What additional information, if any, would this provide about the effectiveness of the program?A control group that doesn’t participate in the yoga or tai chi will provide a baseline for comparison – perhaps stress levels will change due to other work-related factors.A confounding variable is a variable that was not controlled or accounted for by the researcher and thus damaged the integrity of the experiment.Example 3: Stress Relief (revisited)Refer to Example 2, part b. Describe several confounding variables that may affect the results of the study if the employees are allowed to choose their treatment group along with their friends.Variables might include work factors that friends who work in the same department experience that could affect stress levels.Or friend may tend to have similar interests that affect stress levels – tend to exercise to reduce stress, socialize to reduce stress Example 4: Effect of PropagandaIn 1940, a psychologist conducted an experiment to study the effect of propaganda on attitude toward a foreign government. He administered a test of attitude toward the German government to a group of American students. After the students read the German propaganda for several months, he tested them again to see if their attitudes had changed. Unfortunately, Germany attacked and conquered France while the experiment was in progress. Explain clearly why confounding makes it impossible to determine the effect of reading the propaganda. We can never know how much the change in attitude was due to the explanatory variable (reading propaganda) and how much was due to the historical events of the time.PlaceboSometimes in designed experiments it is necessary to have a baseline with no treatment. When studying humans, patients can respond to any treatment (or lack of) simply by knowing they are not getting the actual treatment and therefore it may be necessary to include a fake treatment called a placebo.Since the placebo effect is prevalent in medical studies, sometimes a double blind study is used to counteract this effect. In a double blind study, the subjects and study administrators are not told whether the subjects are part of the control group or treatment group.Example 5: Migraines and ChocolateLondon scientists conducted a study to determine if chocolate can trigger migraines. Twelve migraine-prone subjects were given a peppermint-laced chocolate candy and eight migraine-prone subjects were given a peppermint-laced placebo made of carob, peppermint, and vegetable fat. Five subjects from the group given chocolate developed a migraine headache within one day. No one from the group given the placebo developed a migraine in the same time period. a.Identify the variables in this study (explanatory, response, confounding).Explanatory: consumption of chocolate? Response: number of migraine headaches,?? Confounding:? peppermint – could it react with the other ingredients to affect the number of headaches.b. Is this a controlled experiment or an observational study?ExperimentExample 6: New CavitiesThe dentists in a dental clinic would like to determine if there is a difference between the number of new cavities in people who eat an apple a day and in people who eat less than one apple a week. They are going to conduct a study with 50 people in each group. Fifty clinic patients who report that they routinely eat an apple a day and 50 clinic patients who report that they eat less than one apple a week will be identified. The dentists will examine the patients and their records to determine the number of new cavities the patients have had over the past two years. They will then compare the number of new cavities in the two groups. a.Is the above an observational study or a designed experiment? Explain. Observational study – no treatment is imposed upon the subjectsb.Describe any confounding variables that could affect the results of this study.More health conscious individuals may be more prone to eat apples and have healthier teeth because they take care of themselves.More about Experimental Design and SamplingThe methods of approximation and decision making which you will learn later in this course are dependent upon a simple random sample being taken from a population and/or treatments to be randomly assigned to subject. Whether a random sample is taken or random assignment is performed will determine the what conclusions can be made about the inference procedure.When a study is an observational study, a random sample needs to be taken. If the study is experimental, it is ideal to have both a random sample and random allocation, but valid conclusions may be drawn with only random allocation.Random AssignmentNo Random AssignmentRandom SamplingCausation that is generalized to the entire populationAssociation generalized to the entire populationInference generalized to the entire populationNo Random SamplingCausation – it is reasonable to generalize to those similar to those in the studyAssociation – it is reasonable to generalize to those used in the studyMay not make inference to the entire populationCausationAssociationThe goal in sampling is to choose a representative sample with low bias and low error.Simple Random SamplesA simple random sample of size n is selected from a population in such a way that each individual in the sample has an equally likely chance of being chosen. In addition, the sample is selected so that each possible sample of size n has an equally likely chance of being selected. The goal is to choose a representative sample with low bias and low error.Steps to obtain a random sample:Step 1: Obtain a list of observations (frame) for the entire population (this can be a list of phone numbers, names, addresses, etc.)? Step 2: Label each observation with a number.Step 3: Obtain random numbers (random numbers may be generated using computer programs, calculator functions, by using a random number table, or by selecting numbers from a hat). Step 4: The first n unique numbers that are selected are the numbers of the observations select.? No duplicates may be selected; if a duplicate number is obtained skip it and obtain a new random number. There are additional methods for obtaining random samples which do not result in a simple random sample. These methods are commonly used in experimental design. If these methods are utilized, the inference procedures that are used in this course may not be appropriate. Stratified Random Samples – obtained by dividing the population into non-overlapping groups called strata then randomly selecting from each strata.Data may be classified according to several characteristics.Examples:? A school may be divided according to grade, a state may be divided into zip code areas.? Advantage:? The sample is representative of each strataCaution:? The number of subjects drawn from each strata should be reflect the size of the strata relative to the population Cluster Sample – obtained by dividing the population into non-overlapping groups called clusters then randomly selecting an entire cluster.Advantage:? Easier, cheaper alternative to SRSCaution:? May not represent the entire populationSystematic Sample – obtained by choosing the ith element from a list of units in the population and every kth unit afterward (the ith element would be chosen, next the ith +kth element, ith+2kth etc.).WARNINGConvenience Sampling is not random sampling!Examples:? Select the first six students to enter a room.? Ask for volunteers? A website polls those who use the websiteExample 7: SamplingWhich of the following sampling methods produce a random sample from a class of 36 students? If the sample is random, state what type of sampling was utilized.Select the first six students to enter a room. CONVENIENCE SAMPLE – not random, may not be representative of the classSelect those students whose phone numbers end with the digit 4. CLUSTER SAMPLE – the entire cluster of numbers ending with 4 were chosen, random provided phone numbers are randomly assignedSuppose that the class has 18 boys and 18 girls.? Select a sample of 6 students by using a random number table to choose 1 of the 18 boys, then 1 of the 18 girls, then a boy, then a girl, and so on until you have chosen 6 students. STRATIFIED SAMPLE – population divided by genderSuppose that the classroom has six rows of chairs with six chairs in each row.? Assign the rows the digits 1 through 6.? Throw a die and place all the students in the row corresponding to the number on the die in the sample. CLUSTER SAMPLE – the chosen row is a clusterAssign each student a number from 1 to 36.? The girls get the number 1 to 18 and the boys the numbers from 19 to 36, choose 6 numbers at random.SIMPLE RANDOM SAMPLETypes of DataQualitative versus QuantitativeQualitative (categorical): data consists of labels or descriptions and do not have naturally occurring numerical valuesQuantitative (numerical measurements): data can be measured using a naturally occurring numerical scaleAll of these variables are qualitative except ______Unit Price___________.Order Number NameStateUnit PriceZip CodeGift?23432Meg HSC10.9929672YDiscrete versus ContinuousDiscrete data is quantitative data that are restricted to a set of values that possesses gaps (such as 0, 1, 2, 3, 4,).Continuous data are quantitative data that can take on any value within some interval (such as measurements).Example 8: Classify the following variables as discrete or continuous. A. The number of doctors who wash their hands between patient visits.DiscreteB. Amount of water consumed by the average American each day.ContinuousC. The time it takes to react to a stimulus.ContinuousD. The number of S.C. voters who favored a particular candidate.DiscreteLevels of MeasurementNominal – data that represent whether a variable possesses some characteristic Ordinal – data that represent categories that have some associated orderInterval – data that can be ordered and the arithmetic difference is meaningfulRatio – data that can be ordered and arithmetic difference is meaningful AND there is a meaningful zero point (at which zero means “none”), i.e. it make sense to make a ratioExample 9: – Determine the level of measurementSAT scoreIntervalRating from 1 to 5 of quality of service in a restaurantOrdinalMake and model of a vehicleNominalThe number of students with a business majorRatioPractice Exercise for Chapter 21.Identify the following as qualitative/quantitative, discrete/continuous/neither, nominal/ordinal/interval/ratio.A.A researcher records whether a sample of Clemson students attend the football games or not.Qualitative, neither, nominalB. A bar owner records the number of vodka drinks that a sample of patrons order per dayQuantitative, discrete, ratioC.An advisor records the number of credit hours her advisees attempt per semester.Quantitative, discrete, ratioD.A dorm RA records whether each of his resident drinks/drank while underageQualitative, neither, nominalE.A housing officer at a university records a student’s class status (Fr, So, Jr, Sr)Qualitative, neither, ordinalG.An instructor records the responses to a satisfaction evaluation (Very Satisfied, Satisfied, Neutral, Slightly Unsatisfied, Very Unsatisfied)Qualitative, neither, ordinalH.A student records the amount of sleep per night she gets during a semesterQuantitative, continuous, ratio2.Chantix is a prescription pill used to help smokers who want to quit. However, some doctors are concerned about the potential negative side effects of the drug including nausea, abnormal dreams, insomnia, and headache. A study of the safety and effectiveness of Chantix included 1,493 smokers wanting to quit who volunteered to participate in a clinical trial of the drug. Of the 751 smokers randomly assigned to take Chantix over a 24-week period, 28 experienced serious side effects. Of the 742 smokers randomly assigned to take a placebo over the same period, 16 experienced serious side effects. Researchers were interested in whether the data provide convincing statistical evidence that taking Chantix would increase the risk of serious side effects among all smokers similar to the volunteers.A. Does this study represent an experiment or observational study?ObservationalB. Define the explanatory and response variables.The explanatory variable is the administration of the drug Chantix.?The response variable is the incidence of side effects from the drug.?C. What is the unknown parameter of interest in this study?The parameter of interest is the true proportion of Chantix users who experience negative side effects.3. If a sample of 20 adults ends up containing only men, two explanations are possible.? The first is that the sampling procedure wasn't random; the second is that the sampling procedure was random but that a non-representative sample resulted.? Which explanation would you be more inclined to believe?? Explain. What if the sample of size 20 had 13 men? I am more inclined to believe that the sampling procedure wasn’t random since it is rather unlikely to get a sample that only contained men.It would be reasonable to get 13 men in the sample as 13/20 is nearly half. ................
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