Math 151 , Spring 2008 Wednesday Day 20, March 12 Hit reload....after Friday class.

HW:  (Re) read pp. 133-136.Ch. 7 (Summary review)  Skip Chapter 6. Read p. 186.  Read for next time: Chapter 8.  Read p. 200 (Other designs) last (optional).  Check p. 206, 8.17-22, 26 at first., then 8.23-25 with Table B.  Ahead, Chapter 9.

Hand in Friday
Residuals plots:  This is the last  SPSS for a while. None required for the next few chapters. These are the Postponed parts from Day 19: 
 p. 129, 5.7 (SPSS) fuel residuals. There is a data file for problem 5.7, and its third column is the residuals.  Do all the parts, and
Also with 5.7, In SPSS, Make a variable containing the residuals (Handout, page 3).  Also middle-bottom of Day 19.)  The values should match the ones in the book/SPSS file.

SPSS Governors' salaries Handout :  You can now finish #12, the last question.  Hand it all  in Next time.

p.133, 5.9 Farm population Do a, b, c (read p. 132 for a good word to use in part c).  Also, make a variable containing the residuals, and plot it against the x (year) values.  Draw (in pencil) a horizontal line at height 0.  What pattern do you see in the residuals?

B.  Use Residuals07.xls or Residuals.xls from the website or the lab to graph these data sets, along with a graph of the residuals.  Print the results, and describe the shape of the residuals (it may help to connect the dots with pencil, to see the pattern.) 
a)  x 1 2 8 4 6 9 
    y 1 3 6 6 7 5 
b) x 1 2 7 4 6 9
   y 7 6 2 4 2 1

p 179 7.28, 29, 30 (SPSS) Soap in the shower.  Also, look carefully at the graph and guess why there is no data after day 21.  (Read p. 132 for the word to describe using the line for day 30, and a discussion of the issue)

p. 136 5.13 hospitals: big = bad?

&Postpone all Ch. 8 Producing Data  & &
p. 192, 8.1, 8.2, 8.3 expt, obsn
p. 207, 8.27 Alcohol & heart attacks

p. 194, 8.4, 5, 6 population/sample
. . . . . .
p. 195, 8.7 Sampling badly on campus
- - - - - - -
p. 199 8.10 Minority Managers Use the Simple Random Sample Applet, and choose a sample of size 6. Give your answer by listing their names. (I believe that everyone will get different samples.) Five of the 28 managers have East Asian surnames:  Huang, Kim, Liao, Shen, Wang.  How many of these are in your sample?  

 Postpone the rest too
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
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p. 205, 8.16, Ask more people
p. 212, 8.50, Polling Hispanics

 Read, to discuss 

p. 136,  5.12 lurking variables

p. 208, 8.29 safety of anesthetics
p. 192 8.3 TV & aggression (lurking)

& &  postpone. . .p.195, 8.8 more Sampling badly on campus
- - - -
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

p. 212, 8.49 Canada healthcare


Optional 
p. 136, 5.11, lurking variables 
- - -
&postpone. .

p. 209, 8.35 Use table B (more practice)

p. 209, 8.34 seat belt use

Pick a digit (from 0, 1, 2, 3, 4, 5, 6, 7, 8, 9).  Write it down.  Write it by your name on the clipboard.
= = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = =
Exam not finished--sorry! Close! Next time for sure.
   Much difficulty with Normal Tables.  They will return!

Finishing Ch. 5:   In HW assigned today:  details on earlier days
Plotting residuals: Day 19
  SPSS makes residuals:   Day 19

Revisit r2:   Day 16 (didn't do this Wed.)
(sum of squared residuals / sum of squared dev's from y-bar) = proportion of variability in y's NOT explained by regression line on x.
 r2 =  1 - (sum of squared residuals / sum of squared dev's from y-bar) = proportion of variability which IS explained by regression line on x.

Cautions: Day 19
     Plot the data:   summary numbers (r, line) not resistant; only measure linear.
      Extrapolation--beware. Relationship may not persist outside range of data.
     "Lurking" variable:  has an important effect, but not one of the variables studied.

Association does not imply causation Day 19

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?)                 

  E.g. Proposed some years ago...
    Partially  hydrogenated oils = "trans fats" --> heart disease? yes.  Homocysteines --> heart disease? unclear.

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Start here Friday

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 the "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):


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: Label everyone in the population.  Use Cards, dice, lotto balls, computer program,
       Simple Random Sample Applet, Enter population size, sample size, hit Reset, then Sample.
OR
Start here after break

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.  (Often a "list" that already exists.) 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?

Suppose we've done it right....
A probability sample (p.200) is from a design where impersonal chance is used to pick the individuals.  SRS is the most straightforward.  More sophisticated methods are often used, but they're optional this term. (More info)
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We want to use the sample to make an inference about the population.  A sample will never exactly represent the population, but larger (RANDOM) samples give more accurate results than smaller random samples.
  (almost always. Quantify "more accurate" and "almost always" in chapter 14.)
(Not in text:  Surprisingly (?), this isn't usually because you have more of the population.  A tablespoon of soup gives a pretty good sample, whether it's from a quart of soup or a 10-gallon vat (as long as it's well-stirred).  A toothpickful does not.

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