Sampling

Chapter 5

Introduction

Sampling The process of drawing a number of individual cases

from a larger population A way to learn about a larger population by obtaining

information from a subset of a larger population Example

Presidential polls are based upon samples of the population that might vote in an election

Introduction

Why Sample? To learn something about a large group

without having to study every member of that group

Time and cost Studying every single instance of a thing is

impractical or too expensive Example

Census

Introduction

Why Sample? Improve data quality

Obtain in-depth information about each subject rather than superficial data on all

Introduction

Why Sample? We want to minimize the number of things we

examine or maximize the quality of our examination of those things we do examine.

Introduction

Why Sample? When is sampling unnecessary?

The number of things we want to sample is small Data is easily accessible Data quality is unaffected by the number of things

we look at Example

You are interested in the relationship between team batting average and winning percentage of major league baseball teams

There are only 30 major league teams Data on team batting averages and winning

percentages are readily available

Introduction

Why Sample? Elements

A kind of thing the researcher wants to look at

Quiz – Question 1

If you were interested in understanding the relationship between level of education and lifetime earnings what elements would you sample?

Introduction

Why Sample? Population

The group of elements from which a researcher samples and to which she or he might like to generalize

Quiz – Question 2

In the case of presidential elections in the United States the population is ________ and the elements of this population are _________.

Introduction

Why Sample? Sample

A number of individual cases drawn from a larger population

Introduction

Sampling Frames, Probability versus Nonprobability Samples Target population

A population of theoretical interest

Introduction

Sampling Frames, Probability versus Nonprobability Samples Sampling frame or study population

The group of elements from which a sample is actually selected

Quiz – Question 3

The local television station conducted a study of TV viewers in the local viewing region. A list of all residential customers who subscribed to cable TV was obtained from the cable company. The list had 200,000 households as subscribers. The TV station samples every 40th household on the subscriber list. An interviewer visited each household and conducted the survey on viewing habits of household members.

What is the sampling frame of the study?

Introduction

Sampling Frames, Probability versus Nonprobability Samples Nonprobability Samples

A sample that has been drawn in a way that doesn’t give every member of the population a known chance of being selected

Introduction

Sampling Frames, Probability versus Nonprobability Samples Probability

A sample drawn in a way to give every member of the population a known (nonzero) chance of inclusion

Probability samples are usually more representative than nonprobability samples of the populations from which they are drawn

Introduction

Sampling Frames, Probability versus Nonprobability Samples Biased Samples

A sample that is not representative from the population which it is drawn

Probability samples are LESS likely to be biased samples

Introduction

Sampling Frames, Probability versus Nonprobability Samples Generalizability

The ability to apply the results of a study to groups or situations beyond those actually studied

A probability sample tends to be more generalizable because it increases the chances that samples are representative of the populations from which they are drawn.

Introduction

STOP AND THINK Can you think why researchers haven’t used

cell phone numbers in polling until recently? What problem may result from only using

landline numbers?

Focal Research

“Calling Cell Phones in ’08 Pre-Election Polls” Examines the hypothesis than Barack Obama

fared better in probability samples including landline- and cell phone-users than in samples including landline users alone.

Focal Research

Thinking about ethics Because of the sampling technique employed,

the Pew pollsters never knew the identity of their respondents, so respondent anonymity was never in danger.

Moreover, participation in the survey was voluntary.

Sources of Error Associated with Sampling Types of Survey Error – due to sampling

Coverage Error Nonresponse Error Sampling Error

Sources of Error Associated with Sampling

Coverage Errors Errors that results from differences between the

sampling frame and the target population

Sources of Error Associated with Sampling

Coverage Errors People are typically left out, if samples are drawn from

phone books, car registrations, etc… Unlisted Phone Numbers – one of the greatest potentials for

coverage error Pollsters use random digit dial to avoid unlisted numbers Random-digit dialing

A method for selecting participants in a telephone survey that involves randomly generating telephone numbers

What are potential future problems, with using telephone listings to draw a sample?

Sources of Error Associated with Sampling

Coverage Errors Parameter

A summary of a variable characteristic in a population

Sources of Error Associated with Sampling

Coverage Errors Statistic

A summary of a variable in a sample

Sources of Error Associated with Sampling Nonresponse Error

Errors that result from differences between nonreponders and responders to a survey

Stop and Think

What kinds of people might not be home to pick up the phone in the early evening when most survey organizations make their calls?

What kinds of people might refuse to respond to telephone polls, even if they were contacted?

Sources of Error Associated with Sampling Sampling Error

Any difference between the characteristics of a sample and the characteristics of the population from which the sample is drawn

Sources of Error Associated with Sampling Sampling Error

Sampling Variability The variability in sample statistics that occurs

when different samples are drawn from the same population

Sources of Error Associated with Sampling Margin of error

Suggestion of how far away the actual population parameter is likely to be from the statistic

Types of Probability Sampling

Simple Random Sampling Systematic Sampling Stratified Sampling Cluster Sampling Multistage Sampling

Types of Probability Sampling

Simple Random Sampling A probability sample in which every member of

a study population has been given an equal chance of selection

One way to draw a simple random sample, is to put all possibilities on paper, cut them up, and then draw a sample from a hat

Research Randomizer (http://randomizer.org)

Types of Probability Sampling

Simple Random Sampling Sampling distribution

The distribution of a sample statistic A visual display of the samples

Types of Probability Sampling

Types of Probability Sampling

Systematic Sampling A probability sampling procedure that involves

selecting every kth element from a list of population elements, after the first element has been randomly selected

Example Divide the total number of elements by the number

you want in your sample 24/6 = 4 Randomly select a number between 1 and 4 and

then select every 4th element from that number

Types of Probability Sampling

Systematic Sampling Selection interval

The distance between the elements selected in a sample

Selection Interval (k) = population size

sample size

Types of Probability Sampling

Stratified Sampling A probability sampling procedure that involves

dividing the population in groups or strata defined by the presence of certain characteristics and then random sampling from each stratum

Example If you had a population that was 10% women and

you want a sample that is also 10% women

Types of Probability Sampling

Stratified Sampling Steps to draw a stratified random sample

1. Group the study population into strata or into groups that share a given characteristic

2. Enumerate each group separately

3. Randomly sample within each strata

Types of Probability Sampling

Cluster Sampling A probability sampling procedure that involves

randomly selecting clusters of elements from a population and subsequently selecting every element in each selected cluster for inclusion in the sample

Cluster sampling is an option if data collection involves visits to sites that are far apart

Types of Probability Sampling

Cluster Sampling Example

You are conducting a study of Kentucky high school students

You could obtain a list of all high school students in the state and complete random sampling

A cluster sample would be more practical Obtain a list of all high schools in Kentucky Random sample the high schools from the list Obtain a list of students for each high school

selected and then contact each of those students

Types of Probability Sampling

Multistage Sampling A probability sampling procedure that involves

several stages, such as randomly selecting clusters from a population, then randomly selecting elements from each of the clusters

Types of Probability Sampling

Multistage Sampling Example

Random Digit Dial Stage 1: Areas Codes randomly sampled Stage 2: Three digit local exchanges randomly

sampled Stage 3: Last four digits randomly sampled Stage 4: Asking the person who answer the phone for

the appropriate person you want to interview

Quiz – Question 4

You want to draw a sample of the employees at a large university ensuring that in your sample you have people represented from all personnel categories including administrators, faculty, secretarial staff, cleaning staff, mail room staff, technicians, and students.

What type of probability sample would be best?

Types of Nonprobabilty Sampling

Purposive Sampling Quota Sampling Snowball Sampling Convenience Sampling

Types of Nonprobability Sampling

Purposive Sampling A nonprobability sampling procedure that

involves selecting elements based on a researcher's judgment about which elements will facilitate his or her investigation

Types of Nonprobability Sampling

Quota Sampling A nonprobability sampling procedure that

involves describing the target population in terms of what are thought to be relevant criteria and then selecting sample elements to represent the “relevant” subgroups in proportion to their presence in the target population

Types of Nonprobability Sampling

Snowball Sampling A nonprobability sampling procedure that

involves using members of the group of interest to identify other members of the group

Types of Nonprobability Sampling

Convenience Sampling A nonprobability sampling procedure that

involves selecting elements that are readily accessible to the researcher

Sometimes called an available-subjects sample

Choosing a Sampling Technique

Is it desirable to sample at all or can the whole population be used?

Is it important to generalize to a larger population? Political preference polls

Do you have the access and ability to perform probability sampling?

Major considerations Methods Theory Practicality Ethics

Summary

Sampling is a means to an end. We sample because studying every element

in our population is frequently beyond our means or would jeopardize the quality of our.

On the other hand, we don’t need to sample when studying every member of our population is feasible.