Math 151 , Fall 2006 Wednesday Day 20, Oct. 11 Hit reload...After class


HW:  (Re) read pp. 133-136.  Skip Chapter 6. Read p. 186.  Read Chapter 8.  Read p. 200 (Other designs) last.  Check p. 206, 8.17-22, 26 at first., then 8.23-25 with Table B.  Ahead, Chapter 9.
Hand in  Friday

p. 136 5.13 hospitals: big = bad?
p. 192, 8.1, 8.2, 8.3 expt, obsn
p. 207, 8.27 Alcohol & heart attacks

p. 198, 8.4, 5, 6 population/sample
p. 195, 8.7 Sampling badly on campus

Postpone the rest:
p. 199 8.9 Apartment living, SRS. Use Table B.
p. 209, 8.36 Area code sample, SRS  Use Table B.
p. 211, 8.45 random digit dialing
p. 210, 8.41 random digit characteristics

p.209-10, 8.38 b only Traffic lights
p. 208, 8.30 movie viewing

Read, to discuss 

p. 136,  5.12 lurking variables
p. 208, 8.29 safety of anesthetics
p. 192 8.3 TV & aggression (lurking)
p.195, 8.8 more Sampling badly on campus
Postpone the rest:
p. 211, 8.47 guns

p. 204, 8.14, 8.15 biases.
p. 208, 8.31 world affairs
p. 211, 8.46 wording survey questions


Optional 
p. 136, 5.11, lurking variables 
Postpone the rest:
p. 209, 8.35 Use table B (more practice)

p. 209, 8.34 seat belt use

Exams not finished.  Friday for sure (?).
= = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = =
If you didn't last Wednesday, Pick a digit (from 0,1,2,3,4,5,6,7,8,9).  Write it down.  Write it to the left of your name on the sign in sheet .

Finishing Ch. 5:
"Lurking" variable:  has an important effect, but not one of the variables studied.
    Meatloaf shrinkage vs. placement in oven?  (cooking thermometer/not had greatest influence)
    Time sequence of observations a common one.  (Learning, tiring, aging)
    The trouble with lurking variables is that by definition you don't know they're there.  Look behind every tree.

Association does not imply causation
Strong association/correlation between A and B could be:
     A causes B/   B causes A/  C causes both A and B (lurking C)/  just Chance that they go together in this data set.    
Direction?  Rooster causes sun to rise by crowing?
Both variables "caused" by a lurking variable?   Lurking variable can be part of the cause
--Women with a history of heavy antibiotic use have higher rates of breast cancer.
--Baby rats whose mothers licked and groomed them more   grew up to be more exploratory, social, less timid.
            Cause? Effect?  How to tell?

Establishing that x "causes" y:  difficult:
    Best: Do an experiment in which we change x, keep lurking variables under control. (E.g.   Rats.  Ch.9)
    Otherwise: Strong association. Consistent over many studies. Higher x-->stronger y.  X precedes y in time.  A plausible mechanism exists (parallel studies?) 
                Generalize rat grooming to humans?

  E.g.Partially  hydrogenated oils = "trans fats" --> heart disease?  Homocysteines --> heart disease?
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Chapters 1 through 5 have covered analyzing data that was given to us--what it said about itself.
    Informally, develop guesses, suspicions, hypotheses about the world the data came from.
From Exploration to Inference p. 186

Ch. 8&9:  Producing Data:  Aim:  create data sets that will allow us to make inferences to a larger world than just the data we have.

  Observational Study:  Observes individuals, measures variables, does not influence the responses. (ch.8) 
                 Sometimes observe individuals who are (more or less) conveniently at hand, or, better,
                  Take Sample from a population, examine it.... (ch.8)
  Experiment: Imposes treatment  on individuals, to see how the treatment influences  the response. (ch.9)  

Confounding:  Two variables (explanatory or lurking) are confounded when you can't sort out their effects on a response variable  (Rats:  Mothers' grooming causes sociability, or inherited sociability from mothers who like to groom?).

Ch. 8 p. 192ff.  Sampling
>>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 design:  Describes exactly how sample is to be chosen from population.

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

Sample survey:  (attempt to) choose a representative sample from a large, varied population. Not Easy!
    Some issues:  What population do we want to understand?  What exactly do we want to measure?

Non-probability samples (sampling badly):

Start here Friday
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.   A probability sample (p.200).
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, p.686)
    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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Some more sources of bias, even in probability samples (p. 201-3):
**Undercoverage:  Some groups in the population are left out, or slighted,  in the process of choosing the sample.
   One possible source of undercoverage: Sampling frame: Moore p. 211 problem 8.45: 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".
**Response bias Lies, bad memory, pleasing interviewer (nutrition surveys) Interview technique
**Wording of questions Confusing? Leading? Limiting choices?


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