Math 151 , Spring 2004, Friday Day 21, Oct. 15After class Hit reload ...

Exam 2 next Friday  (Day 24,  Oct. 22.  Covers Chapters 2 and 3 (except 2.1 )
Sample exam problems: "Sample exam 2" given out: Solutions outside my door+ on reserve + electronic reserve(?).
How much technical detail from sec. 2.2 and 3?  You don't need to know the formula for the correlation coefficient, but you should be able to guess roughly the r from a scatterplot, and know and use the facts pp.99-101.You will need to know, among other things,  how to find a and b from the means, standard deviations, and r of the x-and y-values,  and to give the formula for the regression line, (like 2.47); and to graph the regression line on top of the scatterplot.  Also find by hand the value that the line predicts for a particular x.  You should be able to identify and calculate the residual value for a particular x-y point as its vertical distance from the line (fig. 2.11, p. 108), negative if the point is below the line, and identify potential influential points.  You should know and be able to use the facts on pp. 112-13.

HW assignment Day 21
Reading: ReRead section  3.2 to p. 196, including Significance p. 193.  Read  Matched pairs and block design pp. 196-8; review ch. 3.    Next:  4.1, 2, 3.  We'll do  4.1, 2, 3.  Skip 4.4 and Skip Ch. 5.
Hand in Monday:
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Cautions (blinding, lack of realism) 
p. 196 3.42  pain reliever
p. 202 3.55 placebo effect
p. 208 3.75 reading medical jl
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 Significance 
p. 195 3.40
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Hand in Monday: 
Hand in answers to these questions on the "Placebo Effect" article (outside my door/on reserve): 
a) Give two examples of the placebo effect (from the article!)
b) What do researchers believe causes the placebo effect? 
c) (added after last class:) In the separate article: "Pill will make you feel better...," what country was surveyed?

Hand in Monday:  Wednesday Matched pairs and blocks 
p. 199 3.43 hand strength
3.45 weight loss
3.44 student traders.  The difference in the treatments is whether or not they have software that can make "charts" of past "trends." (If they don't have the software that "highlights trends" they don't have "charts"--they just have lists of numbers giving the price history.)
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Hand in Monday (or Wednesday):
On a separate sheet:   Prep for ch. 4: 
Do p. 216, 4.4 spinning penny  Spin a penny 50 times, keeping track of Heads or Tails.  Bring to class  # of heads , #of spins, proportion that came up heads (# of heads divided by # of spins)

 Read, to discuss 

p. 194 3.39 exercise/heart
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3.41meditation/anxiety
p. 202, 3.52 sickle cell 

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p. 209 3.74 Significance 
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(matched pairs)  p. 209 3.72 McDonald's vs Wendy's

(two-factor) p. 209 3.71speeding the mail
 
 
 

 

 Optional 
(more of same) 

p. 187, 3.33 sealing food
p. 192, 3.36 ditto

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p. 203, 3.58 (matched pair)

3.59
 

 
Homework questions?   Are you sure  finding random sample/assigning treatments from Table B is understood?

Continuing Design of Experiments:  Info on Day 20
Questions?
also

Lack of realism:   Do sociology, psychology experiments generalize to "real life?"
--Subjects are not a random sample from the population. (Most psychology "facts" were based on studies of Ivy League males, before 1970's.)
--Ethical questions...Milgram

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Statistical Significance p.194: An observed effect so large that it would rarely occur by chance (assuming no real difference in treatments) is called "statistically significant".   "So large", "rarely", "by chance" will be defined and quantified in Ch. 6.
Example:  Suppose 95% of the subjects  had their headaches cured by treatment 9 and only 25%  by treatment 1 (placebo).  IF the medicine in fact did "no good" that would be a very unlikely outcome.  So we will say the difference in headache cures between treatment 1 and treatment 9 is "statistically significant" and be inclined to believe the medicine "works".
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Start here Monday
Fancier Experimental designs (not "completely randomized") Control extraneous variability by pre-sorting individuals into  homogeneous groups.
Matched pairs: To compare Control and experimental treatments (i.e. 2 levels)
   Sort experimental units into "matching" pairs.   One member of pair gets control, other gets experimental.
                Randomize which.
        Compare within pair, then summarize all comparisons.
  Common: Do the control and experiment to same individual (matched with self). (Randomize order)
        Are right feet bigger than left feet? (not an experiment)      Sunburn salve experiment?
    Aside:  Sampling data, "longitudinal study" following same people through time.
            Works like matched pair to control variability.
Block design:  Sort experimental units into "Blocks" = groups homogeneous on potentially confounding variables
     e.g. M/F, age, income, weight, fruitflies wild or curly-winged.  (No randomization here.)
    Within each block, randomize the treatments. Compare results  within each block, then summarize all results.
    (Matched pairs is a special case of block design--each pair is a "block".)

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