Math 151, Other Samples, optional

More kinds of probability samples:
We will focus on the mathematics of the Simple Random Sample (SRS), the most basic.  In practice, more sophisticated sampling methods may be preferred.  The math needed to analyze their effects is beyond our course.

Here are some other ways to design a probability sample:


Stratified Random Sample (BPS4e p. 200): population is cut into natural segments ('strata').  A specific number of individuals is chosen from each stratum. (Within each stratum we take a simple random sample).  Advantage: Every stratum is represented with a known proportion of the sample; a simple random sample might under- or over-represent a stratum, by chance. Examples of strata:  Income classes.  Levels of education  (no HS, HS only, Assoc. or Cert., Bachelors,  Masters, etc.).  College year.  M/F.  

Multistage Sample(BPS4e p. 200-1) : Useful when individuals are at the bottom of a sequence of categories: E.g. to choose a sample of college women, first select 10 colleges, at random, then from those colleges select 2 dorms at random, then from each dorm select 10 students to interview.  Total sample = 200.  Advantage: you only have to visit 10 colleges, 2 dorms in each.  An SRS from the whole country, even if you could do it, might mean 200 colleges.  (You can also mix this with stratification, for instance selecting the 10 colleges in a stratified way from large coed, small coed, womens,..., or with the other types of sampling.)

Systematic Random Sample(BPS4e p. 210, #8.44)   Using a list, to pick a sample of 1/20 of the list: First pick a number at random from 1,2,....20.  Suppose you picked 8.  The 8th individual in the list is the first one in the sample.  Then take every 20th individual after that, numbers 28, 48, 68,....   Advantage: Easy to implement, avoids "clumps" that might occur with SRS.

Cluster Sampling (not in this text)  Often used to sample from a geographically large area.  Example, in the news Oct. 06, all of Iraq is divided into a list of roughly equally populated "neighborhoods", and a random sample of neighborhoods is taken.  Then interviewers go into the chosen neighborhoods and interview all the households in the neighborhood to find out how many family members have been killed.  The results are used to estimate the total number of Iraqis killed.  The neighborhoods are the clusters; clusters are chosen randomly, but then all (or sometimes a sample) of the individuals in the cluster are surveyed.  Advantage:  Getting an equal number of individuals chosen at random through a whole country would be prohibitively expensive in time and money, even if it were possible. 


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