Math 151 , Spring 2004, Day 20, Wednesday, March 17After classHit reload ...

Exam 2 Friday after break (Day 24, April 2)  Covers Chapters 2 and 3.  Sample exam problems available today.  Extra copies in white folder outside my door. Solutions on reserve, outside my door. 
Placebo effect article is on reserve, 2 copies in folders outside my door.
HW assignment Day 20
Reading: Ch. 3 thru 3.1. (multistage, stratified pp174-5 optional)  Next, section  3.2, to p. 196. (Then Matched pairs&block design.)
   next next: We'll do p. 210, then  4.1, 2, 3.  Skip 4.4 and Skip Ch. 5.
Hand in Friday:
p. 173 3.7 SRS
p. 207, 3.65 SRS
p. 184, 3.26 Random digits
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p. 185 3.30 survey questions
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p. 181  3.16 bigger sample size
p.185 3.31 sampling error for men
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p. 200, 3.46 experiment?
TheseFriday.
Design of experiment: 
p. 187, 3.32 sickle cell
p. 188, 3.34& p. 209 3.70 chemical reaction (randomize order)
    Also: Does this experiment have a Control/Baseline group?
p. 192  3.37  child care, recruitment(randomize)
    Use a diagram like those on pp. 190-1 to show your design.
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Control, randomization, replication 
p. 194  3.38 
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These Monday
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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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)
 Read, to discuss 
 

p.180 3.14 ring-no-answer
3.15 2 campaign questions
 
 

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 Optional :
p.183, 3.24SRS
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 Probability Samples (other): InfoHere
 p. 176 3.11 stratified sample, accounts
3.12 multistage design, schoolkids
p. 184, 3.27,Systematic.
3.28 same chance for each.  SRS?
 
 

 

 
 
 
 

 
Random digits from table B:
25 digits from the random number table: Individual sets of 25 showed much variability.  Pooled  shows more "flatness" --but still much variability.  You would be right to be skeptical when I told you that your "pick-a-number" choices were not random, on the basis of just this class's data.

Homework Questions?
Designing Sample continued Day 19
   Simple Random Sample from Table B.   Sources of bias even if sample designed OK.  Inference to the population.

More kinds of probability samples:
We will focus on the mathematics of the SRS, the most basic.  In practice, more sophisticated sampling methods may be preferred.  The math needed to analyze their effects is beyond our course.
  Optional:  Here are some other ways to design a probability sample.

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Ch. 3.2 Designing Experiments
         Observational Study   vs. Experiment  day 17
                Different jargon; different traditions.

Do something to:
    "Experimental Units" = "Subjects"
Treatment:  Specific experimental condition.
Factor: Explanatory Variable we manipulate.
    Levels: Specific values of a factor that we set.
Response variable(s)

E.g. 2 headache medications, in combination?
A two-factor experiment, each with 3 levels. 9 possible treatments.
    Factor A: Aspirin:  levels None, 500 mg, 1000 mg
    Factor B: Caffeine: levels None, 50 mg, 100 mg
Response variable: reported pain relief



Aspirin


None 500 mg 1000 mg

None Treatment 1 Treatment 2 Treatment 3
Caffeine 50 mg Treatment 4 Treatment 5 Treatment 6

100 mg Treatment 7 Treatment 8 Treatment 9

Lurking variables:  Control--how?  Nothing except experimental treatment should differentially affect response.
    Compare responses under several treatments, look at differences.
Placebo effect: a positive response to a "sham" medical treatment--if you believe it will work, it very likely will. (Tinkerbell?)
    A medical treatment must be shown to be better than a placebo (at least) to be approved by the FDA.
        (Cf. "Claritin," Sunday NYTimes magazine, March 11, '01)
        placebo="I shall please" (Latin)
To control for the placebo effect, All treatments should "look alike".  Treatment 1 above should be a pill with no medicine--a "placebo".  (Some experiments even try to duplicate side effects of actual medication.)

"Control group" Group that gets the "baseline"--"null"-- "none" or "placebo" level of the factor.  Should be "just like" the group(s) that get the "treatment" ("real" levels of the factor).  So Treatment 1 above will go to the "control group", the other 8 will go to "experimental" or "treatment groups."
Murky language here:  "Experimental vs. control" or "Treatment vs. control" is different usage from "Treatments", one of which is the "control"="none"/"placebo".
     *Sometimes the Control  is the current "best practice" treatment, rather than none.
 
How to get groups "just like" one another?  Randomize who goes into which group.  (Usually our batch of  experimental units is not a random sample from the population of all individuals--volunteers, etc.)
Randomized comparative experiment : Diagrams of design, Moore pp. 140-141
Completely randomized: all exp. units allocated at random among the treatments.

E.g. does acupuncture work for PMS?  Response: report of symptoms.
    One factor, 3 Levels:  None (music?), Acupuncture (wrong places), Acupuncture (right places). 3 treatments.
            (control(s)?)
      30 subjects with PMS:  Randomize, 10 each treatment.  Administer treatments.  Compare symptoms. (Do diagram)

Picking groups with random number table:  Pick "sample" of size 10 from the 30 for first treatment.  Pick another "sample" of size 10 for 2nd treatment, from the remainder.  The 10 remaining get the 3rd treatment.

Continue here Friday
Why 10 each, not just 1 each?  Replication of the experimental treatments on many units allows "averaging out" chance variation in the units.  (Don't confuse the replication needed within one experiment, with "replication" of the whole experiment in a different time and place to confirm its results.)

Principles of designing an experiment (p. 143) See above

More problems, cautions:
Placebo and biasing effects can result from expectations of medical staff.  "Blind" means subject doesn't know who's getting "real" treatment.  "Double blind" means neither subject, nor staff administering treatment, nor people recording response variables know who's getting which treatment. (That should really be triple blind?) Most convincing for cause/effect.

Lack of realism Do sociology, psychology experiments generalize to "real life?"  Ethical questions...

Placebo effect article:
Usually an experiment treats the placebo effect as a confounding variable, and is designed so placebo effect will work equally on all groups.  There is no attempt to measure the placebo effect.  ("All" drug studies.)
        PMS/acupuncture:  Acupuncture (wrong) vs. Acupuncture (right).
Sometimes an experiment deliberately tries to measure the placebo effect (as in the article).
        Acupuncture (wrong) vs. Music.

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