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

So Talk 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 Sampling Small 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 Lexingtonians Statistic ◦ 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 sample The 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 samples In 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 samples Convenience sample (also called ‘haphazard’ or ‘accidental’ sample) Volunteer sample Purposive sample Quota sample Network sample

Convenience sample Respondents 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 sample Subjects 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 samples Simple random sample Systematic random sample Stratified random sample Cluster 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 sample A 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 sampling Larger groupings of individual sample elements are chosen, then the elements are measured ◦ Usually geographic areas

Cluster sampling Advantages: ◦ Only part of the population needs to be enumerated ◦ Costs reduced ◦ Cluster estimates can be compared to population numbers

Cluster sampling Disadvantages ◦ 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 sampling Sample large groups/clusters, then sample smaller units within the groups, and so on ◦ metropolitan area ◦ county ◦ block ◦ residence ◦ individual

Sample Size Generally 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 size There 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 error Two 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%.

So We 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