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 X X X 1 = 5 –Note that population proportions are used as weights

ClassTrips Home Number in sample Proportion of total Fresh Soph Junior Senior1100.2

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