Practical Aspects of Sampling

An Overview

Why Sample?

Why Sample? Samples are taken to obtain

information about populations.

Sample estimators are computed to estimate parameters of the the population from which the sample was drawn.

Advantages Complete

enumeration of all sample units in the entire universe is often unnecessary to obtain reasonably accurate results.

Advantages An examination of the

entire population is often too costly, too time-consuming, and impractical (….if not impossible).

Advantages In the case of

destructive testing, the sample elements or units must be destroyed or must be consumed to obtain necessary measurements.

Precision The standard error [se] is a measure of

precision. A smaller se, other things remaining the same, means more precision

.....that is, less variance in the sampling.

Sample Sizefor a mean –

n = z2 2 / e2 where:

– e, the sampling error, is the difference between sample mean and population mean

[e is expressed in units]

Sample Sizefor a proportion -

n = [z2 p (1 – p)] / e2 where:

– e, the sampling error, is the difference between sample proportion and population proportion [ e is expressed in percentage points]

Sample Size

Errors

Sampling (internal) Error

The fact that a sample was taken, the sample statistic is expected to deviate

from the population parameter.

Errors Non-Sampling (external) Error

Practical considerations in taking a sample. recording errorscoding errorsprocessing errors

Errors Bias

Most insidious to detect ....poorly defined universeinadequate sampling designimproperly worded questionsdistorted answersconvenience sampling

Errors The sampling error refers to the extent

to which the sample values on some variable of importance to the research differ from those of the population from which it was drawn.

Types of RandomSamples

Simple Random with replacement without replacement

…must be able to identify the target population and ensure each item has an equal likelihood of being selected…

….use table of random numbers …or computer generate a series of random numbers…

Stratified When the population

is heterogeneous overall, but within it there are homogeneous populations (strata) the population is stratified.

Systematic Selecting a random

sample, as opposed to the simple random selection technique.

Select the K-th item. Draw every I-th item.

Cluster Another modified

random sample design -- requires that the sample unites be grouped in clusters in the universe.

Not grouped by homogeneous strata in the population.

Multistage The selection procedure takes place in

a hierarchy of stages. – first primary sample unit– second second sample unit– third tertiary sample unit– . . . . .– last final (or ultimate) sample unit

Multistage - An Example

The president of Supermarkets, Inc. decided to sample purchases at 150 stores in the US.

The first stage is to select, on the basis of clustering (save travel time), 15 of the 150 stores.

Multistage - An Example

The researcher recommends that cash register files be randomly selected at each of the 150 stores. [second stage]

Then select every 20th purchase in a file using a random start. [final stage]

Comparison of Survey Sampling Designs

Simple Random How to Select

– assign numbers to elements using random numbers table

Strengths/Weaknesses

– basic, simple, often costly

– must assign a number to each element in target population

Stratified How to Select

– divide population into groups that are similar within and different between variable of interest

Strengths/Weaknesses– with proper strata, can

produce very accurate estimates.

– less costly than simple random sampling

– must stratify target population correctly

Stratified

One of the main reasons for using a stratified sample is that stratifying has the effect of reducing sampling error for a given sample size to a level lower than that of a simple random sample of the same size.

Stratified This is so because of a very simple

principle: the more homogeneous a population is on the variables being studied, the smaller the sample size needed to represent it accurately.

Stratifying makes each sub-sample more homogeneous by eliminating the variation on the variable that is used for stratifying.

Systematic How to Select

– select every K-th element are from a list after a random start

Strengths/Weaknesses– produces very accurate

estimates when elements in population exhibit order

– used when pop. size not known

– simplifies selection process

Cluster How to Select

– randomly choose clusters and sample all elements within each cluster

Strengths/Weaknesses– with proper clusters,

can produce accurate estimates

– useful when sample frame not available or travel costs high

– must cluster target population correctly

Convenience in Dining Commons at

dinner… in Student Union

between classes… in classes in which you

are enrolled… data available on the

www… friend knows somebody

who...

Mini-Cases

Working as a team…… determine best sampling technique

and explain decision

Scenario 1 You have been hired by the County of

Sacramento to estimate the percentage of registered voters that favor issuing a bond in order to finance the construction of a new bike trail along the Sacramento River. You want no more than a 4 percentage point error margin, at the 95% confidence level. How would you conduct such a survey using a simple random sample?

Scenario 1 (continued)

When going over your sampling design with the county Parks Director, you are asked whether you think a stratified sample would be appropriate? What is your reply? Why?

What about a systematic sample?

Travel Vouchers

Fly the Friendly Skis

Scenario #2

o The State of California has hired you to estimate the number of travel vouchers for legislators that have been filed incorrectly. The vouchers have been filed as they are processed.

o Which sampling technique would you recommend and why?

Light Rail

Scenario #3 Light Rail has hired you to determine

whether passengers like the convenience of using the light rail system.

Which sampling technique would you recommend and why?

Other concerns that might be investigated?

Trucks

Scenario #4

Marketers, Inc., has hired you to determine why so many young drivers, both male and female, prefer owning a pickup truck as compared to an automobile.

Which sampling technique would you recommend and why?

Merit Pay

Scenario #5

You have been hired to determine how faculty at a local university feel about the following statement: “…the union is seeking to obtain a moratorium on merit pay.”

Which sampling technique would you recommend and why?

Questions?

References Levine, David, et al. Statistics for

Managers, Second Edition. Upper Saddle River, NJ: Prentice-Hall, 1999.

Monette, Duane R., et al. Applied Social Research New York: Holt, Rinehart and Winston, 1986.