Chapter 3 Surveys Sampling 1 Three Ideas of Sampling a Examine a Part of the Whole i It is impractical to examine the population at large so instead examine a sample of the 1 Sample Survey Ask questions of a small group of people in the hope of learning something about the entire population population b Randomize i Randomization protects us from the influences of all the features of our population by ensuring each individual is given a fair random chance of selection ii Sampling Error The variability of responses from sample to sample even if both are random 1 No actual error has occurred c Sample Size Matters i Sample Size is the number of individuals in a sample ii SIZE OF THE SAMPLE DETERMINES WHAT WE CAN CONLCUDE ABOUT DATA REGARDLESS OF THE SIZE OF THE POPULATION 2 Statistical Sampling Methods a Census An attempt to collect data on the entire population of interest i Difficult to complete some individuals are hard to locate or hard to measure not cost effective can be impractical population may change requires a large team to complete b Simple Random Sample SRS Each combination of individuals has an equal chance of being selected i Sampling Frame List of Individuals from which the sample will be drawn 1 Does not work as effectively when a larger sample is given c Stratified Sampling Slice the population into homogeneous groups called strata and use SRS within each stratum Combine the results at the end to form a larger group i Reduces Sampling Variability when a sampling method restricts by strata additional samples are more like one another therefore statistics calculated for the sampled values will vary less from sample to sample d Cluster Sampling Split the population into heterogeneous parts or clusters that each represent the population and then select one or a few clusters at random and perform a census within each of them e Systematic Sampling Select individuals systematically maybe by selecting every nth person f Multistage Sampling Sample schemes that combine several methods 3 Non Statistical Sampling Methods a Voluntary Response Sample A large group of individuals is invited to respond and all who respond are counted Bias almost always occurs i Voluntary Response Bias Individuals with strong feelings on either side of an issue are more likely to respond those who do not care may not bother b Convenience Sampling Limited to those who are conveniently available 4 Populations Parameters a Population The entire group of individuals or instances about whom we hope to learn b Population Parameter A numerically valued attribute of a model for a population we rarely expect to know the value of a parameter but we do hope to estimate it from sampled data 1 When the sample reflects the population parameter then the sample is considered Representative c Sample A subset of the population examined in the hope of learning about the population as a whole d Sampling Frame A list of individuals from which the sample is drawn i Individuals in the population of interest but who are not in the sampling frame cannot be included in any sample e Sample Statistic A value calculated for sampled data particularly one that corresponds to and thus estimates a population parameter population 5 Biases Any systematic failure of a sampling method that over or under estimates characteristics of the a Nonresponse Bias A large fraction of those sampled fail to respond b Response Bias Anything in a survey design that influences specific responses c Undercoverage Some portion of the population is not sampled at all or has a small representation in the sample than it has in the population d Measurement Errors Inaccurate responses whether unintentional or intentional i Cut down on these errors by performing a Pilot Test Draw a small sample from the sampling frame and administer a draft of the survey
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