Sampling

Representing populations

Let’s say you wanted to know whether people over 60 used the Internet for medical information

You could save a bundle on providing medical information by putting up a web page with the necessary information rather than contacting people directly or having them call their doctors for it

But how could you determine whether they would use it?Track them all down and ask

them?◦Practically impossible◦Prohibitively expensive◦Not really necessary

SoTalk to some of them and

estimate what the rest would say

But which ones should be talked to?

Sampling theory guides us in the choice of people to measure as well as estimating what the entire population would have answered

Samples and Sampling

A sample is a subgroup drawn from a larger population that is meant to represent all members

Sampling refers to the actions taken to draw a sample from a population

Examples of SamplingSmall portions of food are given away in

supermarkets in order to get you to buy the product (I made it through grad school this way)

Geologists drill out deep cylinders of rock to determine whether to drill for oil

Farmers pick ears of corn from many parts of the field to check for insects

Short portions of songs are downloaded from the Internet by prospective buyers

Sampling frame◦A list of the units of the population used to draw the sample

◦A sampling frame must closely reflect population (e.g., telephone books, voter

registration lists)

Parameters and statistics

Parameter◦A true characteristic of a population

Average age of LexingtoniansStatistic

◦A numeric summary of a variable in a sample Mean age of a sample of Lexingtonians

◦Sample statistics are computed in order to estimate population parameters.

Random sampleThe best method for

representing the entire population with a sample is to use a random sample

In a random sample, each person in the population of interest has an equal and known chance of being selected◦allows researchers to calculate

sampling error

Nonrandom samplesIn nonrandom samples, the

likelihood of inclusion of any individual elements from the population into the sample is not known◦Means that many of the advantages

of statistical analyses are lost

The researcher may choose a nonrandom sample for several reasons:

◦Purpose of the study explore variable relationships (experiment) exploratory research

◦Cost versus value probability sample may be too expensive

Low incidence of preferred respondents black lawyers

Willingness to participate focus groups

◦Time constraints◦Exploratory study

Types of nonrandom samplesConvenience sample (also called

‘haphazard’ or ‘accidental’ sample)

Volunteer samplePurposive sampleQuota sampleNetwork sample

Convenience sampleRespondents are included

based on availability◦students in introductory courses◦mall intercepts◦movie studio tours

Volunteer sample

Respondents choose to participate in the study◦clinical trials◦consumer juries◦extra-credit psych experiments

Volunteers are different:◦higher educational status◦higher occupational status◦greater need for approval◦higher IQ◦ lower authoritarianism◦more sociable◦more ‘arousal-seeking’◦ less conventional◦tend to be first children◦younger

Purposive sampleSubjects selected on the basis of

specific characteristics or qualities◦users of a particular brand◦young mothers with small children◦doctors◦members of a fan club◦target market members

Quota sample“respondents are selected

nonrandomly according on the basis of their known proportion in a population” (Frey et al., 2000)◦Large/medium/small hospitals◦Caucasian/Black/Asian◦Heavy/medium/light users

Responses may be weighted according to population proportion

Network sample‘Snowball’ sample

◦ask respondents to recommend additional sources/respondents cheaper helps identify people with certain

characteristics aids in respondent compliance identify networks of people

Random samplesSimple random sampleSystematic random sampleStratified random sampleCluster sample

Simple random sample (SRS)

The simple random sample is a case where each element has an equal chance of being selected into the sample◦Lottery◦Random number table◦Roulette wheel◦Random digit dialing

Statistics often assume a “SRS”

Systematic random sampling“A random sample that chooses every

nth person/text from a complete list of a population after starting at a random point.” (Frey et al., 2000)

For example, if you have a sampling frame of 600 elements and you need a sample of 100, then you would have to pick every 6th name. You randomly choose the first name--it turns out to be the 4th element. You then choose the 4th, 10th, 16th, 22nd, etc.

Stratified random sampleA sample developed by first

splitting the population based on some important characteristic and sampling randomly from within categories◦e.g. age, gender, race, income

random samples are taken from within each of the subpopulations

Cluster samplingLarger groupings of individual

sample elements are chosen, then the elements are measured◦Usually geographic areas

Cluster samplingAdvantages:

◦Only part of the population needs to be enumerated

◦Costs reduced◦Cluster estimates can be

compared to population numbers

Cluster samplingDisadvantages

◦Sampling errors are likely◦Clusters may not be

representative of the population Number and size of clusters is

important◦Each subject or unit must be

assigned to a specific cluster

Multi-stage samplingSample large groups/clusters,

then sample smaller units within the groups, and so on◦metropolitan area◦county◦block◦residence◦individual

Sample SizeGenerally speaking, the larger

the better◦But quality is most important◦Though people find it hard to

believe, you can make some pretty good estimates of very large populations from rather small samples National polls can be pretty accurate

with 600 respondents

Sample sizeThere is a law of diminishing

returns:◦additional units add less and

less precision The first respondent is the most

valuable, the second is second-most, etc.

Will often be determined by time and cost considerations

Sampling error“A number that expresses how

much the characteristics of a sample probably differ from the characteristics of its population” (Frey et al., 2000)

Sampling error can be estimated for random samples

this is nonsystematic error variance

Sampling errorTwo key components of sampling error

estimates are confidence levels and confidence intervals

“We express the accuracy of our sample statistics in terms of a level of confidence that the statistics fall within a specified interval from the parameter.” (Babbie)◦tradeoff between confidence level and

confidence interval

Example:Research finds that 45% of males

say that they have broken the speed limit by 15 mph in the last two months.◦The researcher is 99% confident that the

actual percent is between 42% and 48%.◦That is, if the researcher took 100

samples, she would expect that in 99 of them the estimate of the % of males speeding by 15 mph would fall between 42% & 48%.

SoWe use samples to estimate

population parameters because our estimates can be pretty close while drastically reducing the costs of carrying out the research

Samples are either random or nonrandom

Random samples allow us to estimate the sampling error attached to statistics describing the sample

Nonrandom samples are used when random samples are too expensive or impractical◦They employ methods other than

randomization meant to increase their representativeness

A number of different types of random and nonrandom sampling can be used to reduce costs or improve sample quality