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NCSU ST 511 - Ssampling

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SamplingSlide 2Beyond the Data at Hand to the World at Large3 Key Ideas That Enable Us to Make the StretchIdea 1: Examine a Part of the WholeExamplesSlide 8Slide 9Response BiasExample: hospital employee drug useExample (cont.)BiasIdea 2: RandomizeIdea 2: Randomize (cont.)Slide 16Hospital example (cont.)Idea 3: It’s the Sample Size!!ExampleSlide 20Does a Census Make Sense?Does a Census Make Sense? (cont.)Population versus sampleSample Statistics Estimate ParametersWe typically use Greek letters to denote parameters and Latin letters to denote statistics.Various claims are often made for surveys. Why are each of the following claims not correct?Survey claims (cont.)Slide 28Simple Random SampleSimple Random Samples (cont.)Warning!Example: simple random sampleSolutionSampling VariabilitySlide 35Slide 36Stratified Random SamplingSlide 38Slide 39Cluster SamplingCluster Sampling Useful When…Mean length of sentences in a statistics textCluster sampling - not the same as stratified sampling!!Multistage SamplingMean length of sentences in our course text, cont.Slide 46Systematic SamplingSystematic Sampling-exampleEnd of SamplingSamplingSample SurveysProducing Valid Data“If you don’t believe in random sampling, the next time you have a blood test tell the doctor to take it all.”The election of 1948 The PredictionsThe Candidates Crossley Gallup Roper The ResultsTruman 45 44 38 50Dewey 50 50 53 45Beyond the Data at Hand to the World at LargeWe have learned ways to display, describe, and summarize data, but have been limited to examining the particular batch of data we have.We’d like (and often need) to stretch beyond the data at hand to the world at large.Let’s investigate three major ideas that will allow us to make this stretch…3 Key Ideas That Enable Us to Make the StretchIdea 1: Examine a Part of the WholeThe first idea is to draw a sample. –We’d like to know about an entire population of individuals, but examining all of them is usually impractical, if not impossible. –We settle for examining a smaller group of individuals—a sample—selected from the population.Examples1. Think about sampling something you are cooking—you taste (examine) a small part of what you’re cooking to get an idea about the dish as a whole.2. Opinion polls are examples of sample surveys, designed to ask questions of a small group of people in the hope of learning something about the entire population.Convenience sampling: Just ask whoever is around. –Example: “Man on the street” survey (cheap, convenient, often quite opinionated or emotional => now very popular with TV “journalism”)Which men, and on which street?–Ask about gun control or legalizing marijuana “on the street” in Berkeley or in some small town in Idaho and you would probably get totally different answers. –Even within an area, answers would probably differ if you did the survey outside a high school or a country western bar. Bias: Opinions limited to individuals present.Sampling methodsVoluntary Response Sampling: Individuals choose to be involved. These samples are very susceptible to being biased because different people are motivated to respond or not. Often called “public opinion polls.” These are not considered valid or scientific.Bias: Sample design systematically favors a particular outcome.Ann Landers summarizing responses of readers70% of (10,000) parents wrote in to say that having kids was not worth it—if they had to do it over again, they wouldn’t. Bias: Most letters to newspapers are written by disgruntled people. A random sample showed that 91% of parents WOULD have kids again.CNN on-line surveys:Bias: People have to care enough about an issue to bother replying. This sample is probably a combination of people who hate “wasting the taxpayers money” and “animal lovers.”10Response BiasWork hard to avoid influencing responses.–Response bias refers to anything in the survey design that influences the responses. –For example, the wording of a question can influence the responses:Example: hospital employee drug use•Why might this result in a biased sample?•Dept. might not represent full range of employee types, experiences, stress levels, or the hospital’s drug supplyAdministrators at a hospital are concerned about the possibility of drug abuse by people who work there. They decide to check on the extent of the problem by having a random sample of the employees undergo a drug test. The administrators randomly select a department (say, radiology) and test all the people who work in that department – doctors, nurses, technicians, clerks, custodians, etc.Example (cont.)Name the kind of bias that might be present if the administration decides that instead of subjecting people to random testing they’ll just…•a. interview employees about possible drug abuse.•Response bias: people will feel threatened, won’t answer truthfully•b. ask people to volunteer to be tested.Voluntary response bias; only those who are “clean” would volunteerBias•Bias is the bane of sampling—the one thing above all to avoid.•There is usually no way to fix a biased sample and no way to salvage useful information from it.•The best way to avoid bias is to select individuals for the sample at random. •The value of deliberately introducing randomness is one of the great insights of Statistics – Idea 2Idea 2: Randomize•Randomization can protect you against factors that you know are in the data. –It can also help protect against factors you are not even aware of.•Randomizing protects us from the influences of all the features of our population, even ones that we may not have thought about. –Randomizing makes sure that on the average the sample looks like the rest of the populationIdea 2: Randomize (cont.)Individuals are randomly selected. No one group should be over-represented.Sampling randomly gets rid of bias.Random samples rely on the absolute objectivity of random numbers. There are tables and books of random digits available for random sampling. Statistical software cangenerate random digits (e.g., Excel “=random()”,ran# button oncalculator).Idea 2: Randomize (cont.)Not only does randomizing protect us from bias, it actually makes it possible for us to draw inferences about the population when we see only a sample.Hospital example (cont.)Listed in the table are the names of the 20 pharmacists on

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