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: McDonald’s, 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, 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

8. 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

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