Math 151 , Day 18, Friday, March 9, 2001

Ch. 3.1 Designing Samples
Questions on HW:  Day 17
Literary Digest Poll
Probability samples--each member of population has a known chance of being chosen
We can't guarantee the sample is representative, but with a probablility sample we can calculate how often (or seldom) it isn't. (Section 3).
The METHOD is what matters--it will guarantee that most of the time we'll get a representative sample.  (Sometimes we'll do everything right and still have bad luck.  Better than doing it wrong, systematically getting an unrepresentative sample.)

Simple Random Sample (SRS) of size n:  n individuals chosen in such a way that every possible set of n individuals has an equal chance of being chosen.

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.

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 chose 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.

Frito-Lay potato sampling: type(s)?


Return of Exam 1.  Solutions outside my door, and on reserve (afternoon?)  Work on Normal dist., it's coming around again!
10|00
 9|578
 9|3
 8|56789
 8|02
 7|5899
 7|013

HW Day 18 Reread 3.1.  HW is short, please Read 3.2 for next time.
For Wednesday:  Read "Placebo effect" article, one copy on reserve, one outside my door.  I will ask you in class to give an example of the placebo effect, and to explain what the researchers attribute the effect to.
Hand in: 
 p. 176 3.11 stratified sample, accounts
3.12 multistage design, schoolkids
p. 184, 3.27 Systematic.
3.28 same chance for each.  SRS?		 Read, to discuss
 		 Optional

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