Probability Samples
Definition: A sample in which the
probability that any particular member
of the population will be included is
known.
Types of Probability Samples
• Simple Random Sample
– Definition: Every member of the population
has the same probability of inclusion in the
sample
– Examples:
• Names in a hat
• Random Numbers
– Simple Random Sample defines an “unbiased
sample”
Problems with Simple Random
Samples
• Population to be sampled must be
“identified”
– Every member of the population must be
located, labeled, and perhaps numbered
• If population subgroups behave differently,
random chance may create an
unrepresentative sample
– Class in school, race, sex, geographic region,
etc.
Cluster Sampling
• Overcomes the problem of identifying
population
• May greatly reduce cost, especially if
traveling is involved
• Method: define “clusters,” choose a
sample of clusters, then from each cluster
choose a random sample
• May use sub-clusters and so on
Examples of Cluster Sampling
• Telephone survey:
– Pages of telephone book are clusters
– Choose a sample by drawing randomly from a
bucket
– Then choose a sample from each page, say,
by throwing darts
• Geography: McDonald’s, for example
– States are clusters
– Cities are subclusters
– Individual stores are sub-sub-clusters
Stratified Sampling
• Reduces variation if population has
“strata”
• A stratum is a population subgroup that
can be identified by one characteristic and
is expected to behave differently with
respect to some other characteristic
• Examples:
– Men and women differ in voting behavior
– Races differ in unemployment experience
Stratified Sampling, Cont’d.
• Method: Identify strata and from each
stratum select a random sample
• Proportion from each stratum may be
different  sample is biased
– Particularly appropriate if some population
subgroups are very small
• Example: sampling the AEA’s 9,018 males
and 1,623 females
– If each sample is 400, P(S|m) = 400/9018 =
0.045, while P(S|f) = 0.25
Stratified Sampling Cont’d.
• Example: Drawing a sample of ASU
students. We would expect them to differ
systematically by class wrt to trips home
– Suppose we have the following
• Average number of trips home for the
whole student body?
– X-bar = 0.3 X 8 + 0.3 X 6 + 0.2 X 3 + 0.2 X 1
=5
– Note that population proportions are used as
weights
Class
Trips
Home
Number in Proportion
sample
of total
Fresh
8
300
.3
Soph
6
100
.3
Junior
3
100
.2
Senior
1
100
.2
An Important Example: The Current
Population Survey
• Labor force = working + looking for work
– Established by a stratified sample of about 60,000
households each month
– Unemployment rate = (no. looking for work)/(labor
force)
– Sample is stratified with respect to
• Race: white, black, hispanic, asian, etc.
• Sex
• Age
– Overall unemployment rate is a weighted average of
sample values, using population proportions as
weights
Non-Probability Samples
• Examples:
– Truman-Dewey election of 1948: a telephone survey
– Shere Hite: 70% of American wives are having
extramarital affairs (n = 4,500)
• Survey method
• U of Chicago study with probability sample: only 15% of
wives have ever had an affair
– Alfred Kinsey and the famous 10% of homosexuals in
society
• Beware of stepping outside your field of competence
More Examples
• Mail, or any voluntary return, survey
• Call-in votes used by TV stations or
Internet sites
• Nielsen Ratings
• THE ESSENTIAL TASK IN SAMPLING IS
TO AVOID UNKNOWINGLY OVER OR
UNDER REPRESENTING PARTICULAR
ELEMENTS OF THE POPULATION