Qualitative and Quantitative Sampling Types of Nonprobability Sampling Nonprobability sampling Typically used by qualitative researchers Rarely determine sample size in advance
Limited knowledge about larger group or population Types Haphazard Quota Purposive Snowball Deviant Case Sequential
Populations and Samples A population is any well-defined set of units of analysis. The population is determined largely by the research question; the population should be consistent through all parts of a research project. A sample is a subset of a population. Samples are drawn through a systematic
procedure called a sampling method. Sample statistics measure characteristics of the sample to estimate the value of population parameters that describe the characteristics of a population. Populations and Samples A population would be the first choice for analysis. Resources and feasibility usually
preclude analysis of population data. Most research uses samples. Haphazard Sampling Cheap and quick Can produce ineffective, highly unrepresentative samples NOT recommended Person-on-the-street interviews
Clip out survey from a newspaper and mail it in Quota Sampling First you identify relevant categories of people Then you figure out how many to sample from each category
Ensures that some differences are in the sample Still haphazard sampling within the category, however Purposive Sampling Expert uses judgment in selecting cases with a specific purpose in mind Especially informative cases
Difficult-to-reach, specialized population Cultural themed magazines Prostitutes Particular types of cases Gamson study in the book Snowball Sampling
Identifying and sampling the cases in a network I find a prostitute to talk to, then ask her for some more prostitutes I could talk to, and it goes on and on and on Deviant Case Sampling Seeks cases that differ from the
dominant pattern or that differ from the predominant characteristics of other cases Selected because they are unusual High school dropouts example Sequential Sampling Researcher uses purposive sampling until the amount of new information or diversity of cases is filled Gather info until the marginal utility of new information levels off
Probability Sampling Saves time and cost Accuracy Sampling element: unit of analysis or case in a population Population is all of the possible elements, specified for unit, geographical location, and temporal boundaries
Probability Sampling Sampling frame is specific list that closely approximates all of the elements in a population Can be extremely difficult because there just arent good lists for some things Frames are almost always inaccurate Parameter v. Statistic
Parameter: characteristic of an entire population Statistic: estimates of population parameters based on sample Literary Digest Poll Mishap
Sampling frame was automobile registrations and telephone directories Accurate predictions in 1920, 24, 28, and 32 Send postcard and respondents send back In 1936, sampled 10 million and predicted massive victory for Landon over FDR Literary Digest Poll Mishap
VERY, VERY wrong Frame did NOT represent the target population (all voters) Excluded as much as 65% of voters, including most of FDRs supporters during the Depression Why Random Sampling? Each element has an equal probability of
selection Can statistically calculate the relationship between sample and the population sampling error Types: Simple Random Systematic Stratified Cluster Simple Random Sample
Number all of the elements in a sampling frame and use a list of random numbers to select elements (or pull from a hat etc.) Pulling marbles out of a jar Random chance can make it so were off on the actual population, but over repeated independent samples, the true number will emerge Simple Random Sample
We will end up with a normal bell curve the more we sample Random sampling does NOT mean that every random sample will perfectly represent the population Confidence intervals are ranges around a specific point used to estimate a parameter
I am 95% certain that the population parameter lies between 2,450 and 2,550 red marbles in the jar Systematic Sampling Simple random sampling with a shortcut for selection Number each element in the sampling frame Calculate a sampling intervaltells researcher how to select elements by
skip pattern Systematic Sampling I want to sample 500 names from a list of 1000 Sampling interval is 2 I select a random starting point and choose every other name to give me 500 Big problem when elements in a sample
are organized in some kind of cycle or pattern Stratified Sampling First divide the population into subpopulations on basis of supplemental info and then do a random sample from each subpopulation Guarantees representation This can allow for oversampling as well
for specific research purposes Cluster Sampling Useful when there is no good sampling frame available All high school basketball players, for example First you random sample clusters of information then draw a random
sample of elements from within the clusters you selected Cluster Sampling Example Want to sample individuals from Cleveland Randomly select city blocks, then
households within blocks, then individuals within households Less expensive, but also less precise Error shows up in each sample drawn How Large Should a Sample Be?
It depends Smaller the population, the bigger your sampling ratio will need to be to be accurate < 1,000 = 30% 10,000 = 10% > 150,000 = 1% > 10,000,000 = .025% How Large Should a Sample Be?
For small samples, small increases in sample size produce big gains in accuracy Decision about best sample size depends on: Degree of accuracy required Degree of variability in population Number of variables measured simultaneously Inference
The goal of statistical inference is to make supportable conclusions about the unknown characteristics, or parameters, of a population based on the known characteristics of a sample measured through sample statistics. Any difference between the value of a population parameter and a sample statistic is bias and can be attributed to sampling error. Inference
On average, a sample statistic will equal the value of the population parameter. Any single sample statistic, however, may not equal the value of the population parameter. Consider the sampling distribution: When the means from an infinite number of samples drawn from a population are plotted on a frequency distribution, the mean of the distribution of means will equal the population parameter. Inference
Inference By calculating the standard error of the estimator (or sample statistic), which indicates the amount of numerical variation in the sample estimate, we can estimate confidence. More variation means less confidence in the estimate. Less variation means more confidence.
Inference One way to increase confidence in an estimate is to collect a larger, rather than a smaller, sample. Measures of variability get smaller with larger samples: But the value of a larger sample may be offset by the increased cost; this is yet
another tradeoff in research design. To reduce sampling error by half, a sample must quadruple in size.
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