Lecture Unit 3PowerPoint PresentationLecture Unit 3 ObjectivesBeyond 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 9Slide 10Example: hospital employee drug useExample (cont.)BiasIdea 2: RandomizeIdea 2: Randomize (cont.)Slide 16Hospital example (cont.)01 NCSU 02 UNC 03 Duke 04 Wake F 05 BC 06 UM 07 Maryl. 08 Clem 09 UVA 10 VaTech 11 GaTech 12 FSU 13 OSU 14 ILL 15 IN 16 PUR 17 IOWA 18 MSU 19 Mich 20 PennS 21 NorthW 22 MN 23 WISC 96927 19931 36089 74192 77567 88741 48409 41903 The first 3 schools in a random sample selected from the ACC and Big Ten using the above random numbers are:Idea 3: It’s the Sample Size!!ExampleSlide 21Does 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 293.2 Simple Random SamplesSlide 31Simple Random SamplesSimple Random Samples (cont.)Sampling FrameWarning!Example: simple random sampleSolutionSampling VariabilitySlide 39Slide 40Stratified Random SamplingSlide 42Slide 43Cluster SamplingCluster Sampling Useful When…Mean length of sentences in our course textCluster sampling - not the same as stratified sampling!!Multistage SamplingMean length of sentences in our course text, cont.Slide 50Systematic SamplingSystematic Sampling-exampleSummary: What have we learned?Summary: What have we learned? (cont.)Slide 55End of Lecture Unit 3Lecture Unit 3Sample 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 45Lecture Unit 3 Objectives1. Given a survey sample, determine whether the sample is a simple random sample, a stratified sample, a cluster sample, or a systematic sample.2. Choose a simple random sample, stratified random sample, cluster sample, and systematic random sample in a variety of situations.3. Explain the affect of sample size when determining whether a sample is representative of the population.Beyond 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.”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