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

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 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.