Math 151 , Fall 2004, Ch 3.1 optional

More kinds of probability samples:
We will focus on the mathematics of the 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: 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.

Multistage Sample: 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,...)

Systematic Random Sample (p.184, problem 3.27)  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 get 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.


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