Math 151 , Spring 2004 Wednesday Day 17, March 10After classHit reload...

In lieu of class, a few paragraphs: (choose One)Hand in separately from HW
B)    A paragraph describing one of the workshops/talks you attended,
  + a paragraph or so on a situation where organized data could be useful to an activist  working for a cause (either data which was cited in a workshop you attended, or a place where you could see that information could help make or strengthen the "case" for a cause, or be useful in improving the activist's skill in some way.)
C)  Find one or more graphs, charts or tables of numbers in the popular press or on the web. Hand in a copy of it/them.  Explain what it's about and what it says, and critique it as to how well it conveys the information.  If you can do it better, redo it.
D)  Research Florence Nightingale, primordial activist and statistician.   Report why/how she fits into this year's theme of "Got Passion", and why I call her a statistician.  (The Biographies link from the link here is excellent. A Yahoo search for "Florence Nightingale" + statistics gives lots more).
E) Nothing.  Counts as a class absence.
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Homework:  Reading:   Sec. 2.4.  Skip 2.5.
Please read ahead: Ch. 3 Intro.  Ch. 3.1, (skip stratified, multistage pp.174-5, on first reading).

Hand in  Monday  Sec. 2.4 p. 132  2.54 Dow average/stocks p. 138 2.63 math&verbal r, states/individuals C.  Look again at p. 122, 2.37(calories).   These values are averaged values, over a bunch of people's guesses.  What would the graph look like if all the individuals' separate guesses had been graphed?  Add points to your graph to give the idea. p. 133  2.55 tv watching & grades   2.56 economists&pay   2.64 herbal tea A.(New problem) Income depends on height?! Read the article and answer this. If your browser doesn't get the link, it's at http://aurora.wells.edu/~srs/Math151-Sp04/tallpeoplewin.htm    a)What is "$789", and what kind of analysis did they do?   b)What does my footnote at the end tell you about the data that the article did not? Postpone ch. 3 Ch.3 Intro:  p. 167, 3.1, 3.2, 3.3 exp, obs = = = = = = = = = = = = Sec.3.1 Sampling  p. 170, 3.4employed women Also: What is the sampling frame? (Def. p. 179, #3.13)  3.6 letters to Congress

Read, to discuss (all Moore)  Sec. 2.4 The Read problems I never asked (C, D) from Day 13 p.136 2.57 firefighters,     2.58 self-esteem p. 138 2.61 shoe size/reading 2.66 Education/income Postpone ch. 3 Ch.3 Intro:  p. 170, 3.5 pop, samp... p.182, 3.17 obsn/exp     3.18 novel--pop, samp.  = = = = = = = = = Sampling  p. 183, 3.22 president 3.23 black police

Optional  Sec. 2.4 p. 137 2.59 size of hospital

= = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = =
Questions on HW: Least squares criterion, residualsDay 16,
Further explanation of r^₂ was expanded before 3:15 Mon.
Income depends on height?!
    What is "$789", and what kind of analysis did they do?

Cautions  Sec. 2.4
Plot the data: Summary formulas and numbers don't tell the whole story.  (Anscombe's quartet, Moore p.127, 2.46-7)

Extrapolation-- extra (outside) polation (putting a point): Using the line to predict outside the range of x's you have data for.

Averaged data will produce a stronger relationship (higher correlation, R²) than the merged raw data from individuals (the averaging hides much variability) Heating-degree days graph (TA 2.1, p. 86, 107:  Each value represents a month's average temperature and average fuel.  If we graphed the daily temperature and fuel use we would see a lot more scatter.

"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
    Manatees:                                         Year
             boat registrations            kills

            If you didn't know boat registrations, would you believe that "year" was the cause of "kills"?
                (Are all boats actually registered?  Possible lurking variable= unregistered boats.)
Direction?  Rooster causes sun to rise by crowing?
Both variables "caused" by a lurking variable?
--Women with a history of heavy antibiotic use have higher rates of breast cancer.
START HERE Monday
--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. (Sec. 3.2)  Rats.
    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. hydrogenated oils --> heart disease?  Homocysteines --> heart disease?
= = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = =
Pick a digit (from 0,1,2,3,4,5,6,7,8,9).  Write it down.
= = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = =
Chapters 1 and 2 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.
Ch. 3:  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. (3.1)
                    Take Sample from a population, examine it,
                           hope it's representative so we can infer population is like sample.
                            (Not very useful for cause-and-effect--see  above)
        Experiment: Imposes treatment  on individuals, to see how the treatment influences  the response. (3.2)
                            Best for cause-and-effect.

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...
Last year: women who ate at least one serving/day of whole grain (cereal, bread) much less likely to have heart attack.
   (Who eats whole grains?  Were those variables taken into account? ?)

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.
How?  Next....