Math 151 , Fall 2002, Wednesday Day 18, Oct. 9Hit reload to get most current versionAfter class

Confounding:  Two variables (explanatory or lurking) are confounded when you can't sort out their effects on a response variable.
--Used to be: coffee drinking and smoking--most people did both, or neither...
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Ch. 3.1 Designing Samples

>>Population: Entire group  that we want information about
>>Sample: The part of the population we actually examine.
      Hope:  Sample will be representative of the population.

(SAMPLING) BIAS:  The design of a study is biased if it systematically favors certain outcomes.
    Check our "sample" of digits

Some refinements:
*Sampling frame: Moore p. 179 problem 3.13: the group from which the sample is actually chosen--as different from the "population"--the group you want information about. The sampling frame is often, unfortunately, smaller than the population.  The sample is (usually much) smaller than the sampling frame.
* "Chosen" sample may not turn out to be actual sample, if some individuals don't respond--"Nonresponse", p. 178.

Non-probability samples:

• Voluntary response sample ( from a general appeal--Ann Landers, Cosmo, Hite Report): biased toward  strong opinions, esp. negative. (Contenteds don't bother.)  www.vote.com
• Convenience sample (whatever/whoever looks good, is handy) Unlikely to be representative.  Digits.

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.
HOW?  A chance mechanism: Cards, dice, computer program, or
Table of random digits (Simulates rolling a die with 0,1,....9, over and over...) (Table B, back flyleaf)
    Every digit, every sequence of digits, is equally likely to be "next" in any direction.
To use:  label everyone in the population with a number.
    Important:  Every labeling number needs the same number of digits.
    To label 9 people, use the labels 1,2,3,....9 (1-digit chunks)
    To label 15 people, use the labels 01, 02, ...10, 11, ...15 (2-digit chunks)
    To label 125 people, use the labels 001, 002, ... 124, 125 (3-digit chunks)
Pick a place (at random) in the table, start reading across in that size chunk.  Get n eligible numbers (discard repeats)
                    Read Row 150:   07511   88915   41267   16853   84569   79367 ..
From 9 people, a sample n = 5:  0, 7, 5, 1, 1, 8, 8, 9, 1, 5, 4,     (sample is individuals 7, 5, 1, 8, 9)
From 15 people, a sample   07, 51, 18, 89, 15, 41, 26, 71, 68, 53, 84, 56, 97, 93, 67.... keep reading,
    go to next line (or back to top line) if you need more.  Individuals 7, 15,...are chosen using this line.
From 125 people, a sample 075, 118, 891, 541, 267, 168, 538, 456, 979, 367...keep reading.  Individuals 75, 118, ...

    Why the same number of digits in each label?  Each individual 3-digit chunk is as likely as any other 3-digit chunk.  But a 1- or 2-digit chunk is more likely than any 3-digit chunk. So 2 will come up more often than 12, but 02 will come up just as often as 12.

    Why across?  For consistency on HW, go the way they say (so you get the answer in the book).  In practice, you can read up, down, backwards, as long as you decide beforehand, and don't change in the middle of choosing the sample.
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Start here Friday
Sources of bias, even in probability samples:

• Undercoverage: some groups left out or slighted in choosing the sample (cf. sampling frame)
• Nonresponse: some individuals chosen 1) can't be contacted 2) refuse to answer

   Census:  2.3 million uncounted in 2000 (3 million in 1990) estimated...
   Mail surveys:
• Response bias Lies, bad memory, pleasing interviewer (nutrition surveys) Interview technique
• Wording of questions Confusing? Leading? Limiting choices?

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.