Sampling Why Sample Why not study everyone Debate about Census vs sampling Problems in Sampling What problems do you know about What issues are you aware of What questions do you have Key Sampling Concepts Copyright 2002 William M K Trochim All Rights Reserved Sampling Process Units of Analysis people Target Population Population of Interest Actual Population to Which Generalizations Are Made Defined Listed by Sampling Frame Generalization Sample The people actually studied Target Sample Response Rate List or Procedure Sampling Frame List or Rule Defining the Population Method of selection List of Target Sample Key Ideas Distinction between the population of interest and the actual population defined by the sampling frame Generalizations can be made only to the actual population Understand crucial role of the sampling frame Sampling Frame The list or procedure defining the POPULATION From which the sample will be drawn Distinguish sampling frame from sample Examples Telephone book Voter list Random digit dialing Essential for probability sampling but can be defined for nonprobability sampling Types of Samples Simple Random Probability Systematic Random Stratified Random Random Cluster Stratified Cluster Complex Multi stage Random various kinds Non Probability Convenience Quota Purposive Probability Samples A probability sample is one in which each element of the population has a known non zero probability of selection Not a probability sample of some elements of population cannot be selected have zero probability Not a probability sample if probabilities of selection are not known Probability Sampling Cannot guarantee representativeness on all traits of interest A sampling plan with known statistical properties Permits statements like The probability is 99 that the true population correlation falls between 46 and 56 Sampling Frame is Crucial in Probability Sampling If the sampling frame is a poor fit to the population of interest random sampling from that frame cannot fix the problem The sampling frame is non randomly chosen Elements not in the sampling frame have zero probability of selection Generalizations can be made ONLY to the actual population defined by the sampling frame Types of Probability Samples Simple Random Systematic Random Stratified Random Random Cluster Stratified Cluster Complex Multi stage Random various kinds Simple Random Sampling Each element in the population has an equal probability of selection AND each combination of elements has an equal probability of selection Names drawn out of a hat Random numbers to select elements from an ordered list Stratified Random Sampling 1 Divide population into groups that differ in important ways Basis for grouping must be known before sampling Select random sample from within each group Stratified Random Sampling 2 For a given sample size reduces error compared to simple random sampling IF the groups are different from each other Tradeoff between the cost of doing the stratification and smaller sample size needed for same error Probabilities of selection may be different for different groups as long as they are known Oversampling small groups improves intergroup comparisons Systematic Random Sampling 1 Each element has an equal probability of selection but combinations of elements have different probabilities Population size N desired sample size n sampling interval k N n Randomly select a number j between 1 and k sample element j and then every kth element thereafter j k j 2k etc Example N 64 n 8 k 64 8 8 Random j 3 Systematic Random Sampling 2 Has same error rate as simple random sample if the list is in random or haphazard order Provides the benefits of implicit stratification if the list is grouped Systematic Random Sampling 3 Runs the risk of error if periodicity in the list matches the sampling interval This is rare In this example every 4th element is red and red never gets sampled If j had been 4 or 8 ONLY reds would be sampled Random Cluster Sampling 1 Done correctly this is a form of random sampling Population is divided into groups usually geographic or organizational Some of the groups are randomly chosen In pure cluster sampling whole cluster is sampled In simple multistage cluster there is random sampling within each randomly chosen cluster Random Cluster Sampling 2 Population is divided into groups Some of the groups are randomly selected For given sample size a cluster sample has more error than a simple random sample Cost savings of clustering may permit larger sample Error is smaller if the clusters are similar to each other Random Cluster Samplng 3 Cluster sampling has very high error if the clusters are different from each other Cluster sampling is NOT desirable if the clusters are different It IS random sampling you randomly choose the clusters But you will tend to omit some kinds of subjects Stratified Cluster Sampling Reduce the error in cluster sampling by creating strata of clusters Sample one cluster from each stratum The cost savings of clustering with the error reduction of stratification Strata Stratification vs Clustering Stratification Clustering Divide population into groups different from each other sexes races ages Sample randomly from each group Less error compared to simple random More expensive to obtain stratification information before sampling Divide population into comparable groups schools cities Randomly sample some of the groups More error compared to simple random Reduces costs to sample only some areas or organizations Stratified Cluster Sampling Combines elements of stratification and clustering First you define the clusters Then you group the clusters into strata of clusters putting similar clusters together in a stratum Then you randomly pick one or more cluster from each of the strata of clusters Then you sample the subjects within the sampled clusters either all the subjects or a simple random sample of them Multi stage Probability Samples 1 Large national probability samples involve several stages of stratified cluster sampling The whole country is divided into geographic clusters metropolitan and rural Some large metropolitan areas are selected with certainty certainty is a non zero probability Other areas are formed into strata of areas e g middle sized cities rural counties clusters are selected randomly from these strata Multi stage Probability Samples 2 Within each sampled area the clusters are defined and the process is repeated perhaps several times until
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