Qualitative and Quantitative Sampling

Types of 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 Cultural themed magazines Difficult-to-reach, specialized population 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 aren’t 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 FDR’s 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 we’re 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 interval—tells 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 Less expensive, but also less precise 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.