Math 151 , Day 17, Wednesday, March7, 2001

(SAMPLING) BIAS:  The design of a study is biased if it systematically favors certain outcomes.

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.

Some refinements:
*Sampling frame: 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 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.)
• 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...)
    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 ..
For 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)
For 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 first) if you need more.
For 125 people, a sample 075, 118, 891, 541, 267, 168, 538, 456, 979, 367...keep reading

    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- or2-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.

Other probability sampling designs (pp.174-6) next time.

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:
  Mail surveys:
• Response bias Lies, bad memory, pleasing interviewer (nutrition surveys) Interview technique
• Wording of questions Confusing? Leading? Limiting choices?

HW: Read 3.1.  This hw covers all but pp.174-6.

Hand in:  Samples: p. 170, 3.4employed women  Also:What is the sampling frame?   3.6 letters to Congress p. 173 3.7 SRS p. 207, 3.65 SRS p. 184, 3.26 Random digits p. 185 3.30 survey questions p. 181  3.16 bigger sample size p.185 3.31 sampling error for men

Read, to discuss  3.22 president 3.23black police p.180 3.14 ring-no-answer 3.15 2 campaign questions

Optional  p. 3.24SRS Learn how to use SPSS to make an SRS. Ch.3 in the SPSS manual.  Unfortunately you first have to have a variable with a row for each individual in the population (or more properly, the sampling frame).  So it's most useful if you already have a big batch of data and want to look at a sub-sample from it.