1Class 15The Logic of SamplingMini Project • No restriction on the topic, methodology, or data.• 2 Options - with a team or by yourself. A team may contain up to 2 people if secondary data analysis is used, or 4 people if the team collects original data.• Research proposal due on November 7. Members of a team need to submit their own proposals (and papers). • You may collect data using any method discussed class. If you decide to conduct a secondary analysis, you might want to use a data set from http://sda.berkeley.edu:7502/archive.htmComponents of a Research Proposal • Introduction to the research problem• Literature review• Methodological plan• Budget• Ethics statement• Statement of limitations2Probability and Nonprobability SamplingProbability Sampling• Each element in the population has a known probability of selection.• A sampling frame is used.• Avoids researcher’s biases in element selection. Nonprobability Sampling• The probability of selection is unknown.• Typically no sampling frame is used.• The selection process may be biased.Sample RepresentationTheoretical populationPopulation represented by the sampling frameActual sampleWho do you want to generalize to?Who can you get access to?Who’s in your study?Non-responseElements not captured by sampling frameTarget sampleSample Size, Population Homogeneity, and Representativeness• The larger the sample, the more confidence we can have in the sample’s representativeness.• The more homogeneous the population, the more confidence we can have in the representativeness of a sample of any particular size.• The fraction of the total population that a sample contains does not affect the sample’s representativeness.3Simple Random Sampling (SRS)Steps:1. Assign a unique number to each element in the sampling frame. 2. Use random numbers to select elements into the sample until the desired number of cases is obtained.– Use a table of random numbers– Use computers to generate random numbers.Systematic SamplingSteps:1. Calculate the sampling interval as the ratio between population size and sample size, I = N/n. 2. Arrange all elements in the population in an order. 3. Select an element in the first interval randomly. 4. Select every Ithelement from this point.Systematic Sampling• Systematic sampling is easier than simple random sampling (SRS).• But there is a potential danger. What is it?I1st element israndomly chosenII II I4Stratified SamplingSteps1. Divide the population into subpopulations (called strata), say, males and females. 2. Among males, we select cases randomly using SRS or systematic sampling; among females, we also select cases randomly.3. The resulting sample will guarantee the desired numbers of males and females.We could use any other characteristics, such as region, ethnicity, age, or education to define the strata. Stratified sampling guarantees representativeness in these characteristics.Stratified SamplingSRS SRSPopulationSampleStratum 1 Stratum 2Advantage and Disadvantage of Stratified Sampling• Stratified sampling ensures representativeness in the stratifying variables by decreasing the probable sampling error. Gains in efficiency.• Stratified sampling is advantageous when strata are vastly different from each other for the variables of interest.• It requires some knowledge about the elements in the sampling frame, which may be unavailable. E.g., in order to stratify the sample by education, we must know the education of each individual in the sampling frame.5Stratified Sampling: Oversample• Oversampling increases the representation of a particular group in a sample.SRSSRSPopulationSampleStratum 1 Stratum 2Multistage Cluster Sampling• A cluster is a natural aggregate of elements of the population. • Steps1. List all clusters.2. Draw a random sample of clusters.3. List all elements in the selected clusters.4. Draw a random sample of elements from each cluster.• Multistage cluster sampling:– states Æ citiesÆ schools Æ studentsMultistage Cluster SamplingSelected clusters6Advantage and Disadvantage of Cluster Sampling• Cluster sampling is desirable from an economic point of view.• It saves money but lowers the quality (representativeness) of data. Loss of efficiency.• Cluster sampling is not a good sampling choice if the clusters are very different from each other.• The trade-off between the number of clusters and the number of elements selected within clusters.Probability Proportionate to Size• A type of cluster sampling where a cluster's probability of being selected is proportional to its size. That is, the larger a cluster, the higher its probability of being selected. • Within each cluster, a fixed number of cases is selected. For element i in cluster j (by the rule of conditional probability):• Equal probability for each elementP(ij) = P(i | j)*P(j) =1nj⋅njn=1nNonprobability Sampling1. Reliance on available subjects• Only justified if less risky sampling methods are not possible. • Researchers must exercise great caution in generalizing from their data when this method is used.7Nonprobability Sampling2. Purposive or judgmental sampling• Selecting a sample on the basis of knowledge of a population, its elements, and the purpose of the study.• Often used when field researchers are interested in studying cases that don’t fit into regular patterns of attitudes and behaviorsNonprobability Sampling3. Snowball sampling• Appropriate when members of a population are difficult to locate (homeless, migrant workers, prostitutes).• Researcher collects data on members she can locate, then asks those individuals to help locate other members of that population. Nonprobability Sampling4. Quota sampling• Begins with a matrix of the target population.• Data is collected from people with the characteristics of a given cell. • Each group is assigned a weight appropriate to their portion of the total population.• With proper weighting, a quota sample may be representative in characteristics where the quotas are set, but we don’t know if it is representative in term of other characteristics or
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