Math 151 , Spring 2003, Friday Day 21, March 14 After
classHit reload ...
Exam 2 Friday after break (Day 24, April
2. Covers Chapters 2 and 3 (probably all of.) )
Sample exam problems: "Sample
exam 2" given out: Solutions outside my door+ on 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 after
Break:
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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
= = = = = = = = = = = = = =
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?
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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)
= = = = = = = = = = = = =
Hand in Monday??
WednesdayMatched 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.) |
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
= = = = =
= = = = =
(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
= = = = =
= = = = =
p. 203, 3.58 (matched pair)
3.59
|
Homework questions? Are you sure finding
random sample/assigning treatments from Table B is understood?
"Convenience Sample/ Voluntary Response Sample/ Sampling Frame/
Nonresponse bias"--relationships.
Continuing Design of Experiments: Info on Day
20
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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Got to here Friday.
Literary Digest poll,
narrative
= = = = = = = = = = = = = = = = = = =
(if time)Fancier Experimental
designs (not "completely randomized")
Control
extraneous variability by presorting 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.
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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