Chapter 7: Survey Sampling and InferenceSurvey Terminology•The population is the group of people or objects we wish to study. •A parameter is a numerical value that characterizes some aspect of the population.•A census is a survey in which every member of the population is measured.•The sample is a collection of people or objects taken from the population.•A statistic is a number that estimates a population parameter derived from the samplePopulation vs Sample•Population is the collection of ALL data values•Population size is usually very large, often unknown, and usually impossible to obtain all values.• Measures that come from the population are parameters•Sample is a subset of the population and we can measure characteristics.•Sample size is the number of observations in a sample, n.• Measures that come from the sample are statistics.Notation•Typically, we use Greek letters to represent population parameters and Latin letters to represent sample statistics.Example•Are the values from the Gallup poll below parameters or statistics?Census•Wouldn’t it be better just to include everyone and sample the entire population?•Such a special sample is called a census•There are problems with taking a census:•It can be difficult to complete a census•Populations rarely stand still•It may be more complex than taking a sampleSampling is Natural•Sampling is a natural thing to do.•Think about sampling something you are cooking - you taste (examine) a small part of what you are cooking to get an idea about the dish as a whole•If you walk into a clothing store that you’ve never heard of before, in order to decide if the store affordable you wouldn’t check every tag of every single item in the store. You would instead try to check out the price of a variety of items (a representative sample) and based on what you see decide if you think the store overall is overpriced or not.Explanatory Analysis to Inference•When you taste a spoonful and decide it doesn’t taste salty enough, that’s exploratory analysis•If you generalize and conclude that your soup needs salt, thats an inference•For your inference to be valid the spoonful you tasted (the sample) needs to be representative of the entire pot (the population)•If your spoonful comes only from the surface and the salt is collected at the bottom of the pot, what you tasted is probably not representative of the whole pot.•If you first stir the soup thoroughly before you taste, your spoonful will more likely be representative of the whole pot.Statistical Inference•Statistical Inference is the art and science of drawing conclusions about a population on the basis of observing only a small subset of that population (i.e. a sample).•Statistical Inference always involves uncertainty, so an important component of this science is measuring our uncertainty.Sample Surveys•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.•Professional pollsters try to ensure that the sample they take is representative of the population•If not, the sample can give misleading information about the populationLandon vs. FDRIn 1936, Landon sought the presidential nomination, as a Republican, opposing the re-election of FDR.The Literary Digest Poll•The Literary Digest polled about 10 million Americans, and got responses from about 2.4 million.•The poll showed that Landon would likely be the overwhelming winner and FDR would get only 43% of the votes.•Election result: FDR won, with 62% of the votes. •The magazine was completely discredited because of the poll and was soon discontinued.The Literary Digest Poll - What Went Wrong?•The magazine had surveyed:•Its own readers•Registered automobile owners•Registered telephone users•These groups had incomes well above the national average of the day (it was the Great Depression era) which resulted in lists of voters far more likely to support Republicans than a truly typical voter of the time, i.e. the sample was not representative of the American population at the timeBias•A method is biased if it has a tendency to produce an untrue value•Sampling bias results from taking a sample that is not representative of the population.•Convenience sampling •Voluntary response sampling•Measurement bias comes from asking questions that do no produce a true answer.•Confusing wording, misleading questions.Voluntary Samples are Problematic•In a voluntary response sample a large group of individuals are invited to respond, and all who do respond are counted.•Voluntary response samples are almost always biased, and so conclusions drawn from them are almost always wrong.•Voluntary response samples are often biased toward those with strong opinions or those who are strongly motivated.•Since the sample is not representative, the resulting voluntary response bias invalidates the survey.Convenience Samples Are Not So Convenient…•In convenience sampling we simply include the individuals who are convenient.•Unfortunately, this group may not be representative of the population.•For example, if you are strongly against smoking chances are none of your close friends are smokers, so your friends wouldn't make a good sample to ask about anti-smoking laws.•Convenience sampling is not only a problem for students or other beginning samplers.•In fact, it is a widespread problem in the business world - the easiest people for a company to sample are its own customers.Non-response•A common and serious potential source of bias for most surveys is nonresponse bias.•No survey succeeds in getting responses from everyone.•The problem is that those who don't respond may differ from those who do.•And they may differ on just the variables we care about.•Non-response error occurs when those who respond may differ from whose who do not•For example, surveys sent home with students may show that parents have no trouble sparing time to spend with their children. But which parents return the surveys?Design of Survey Questions•Surveys that are too long are more likely to be refused, reducing the response rate and biasing all the results.•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