Probability Samples

1
Probability Samples

• Definition A sample in which the probability
  that any particular member of the population will
  be included is known.

2
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

3
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.

4
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

5
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 McDonalds, for example
• States are clusters
• Cities are subclusters
• Individual stores are sub-sub-clusters

6
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

7
Stratified Sampling, Contd.

• 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 AEAs 9,018 males and 1,623
  females
• If each sample is 400, P(Sm) 400/9018 0.045,
  while P(Sf) 0.25

8
Stratified Sampling Contd.

• 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

9
Class Trips Home Number in sample Proportion of total
Fresh 8 300 .3
Soph 6 100 .3
Junior 3 100 .2
Senior 1 100 .2
10
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

11
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

12
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