Math 151 , Fall 2002, Friday Day 19, Oct. 11 Hit reload to get most current versionAfter Class

Multistage Sample: Useful when individuals are at the bottom of a sequence of categories: E.g. to choose a sample of college women, first select 10 colleges, at random, then from those colleges select 2 dorms at random, then from each dorm select 10 students to interview.  Total sample = 200.  Advantage: you only have to visit 10 colleges, 2 dorms in each.  An SRS from the whole country, even if you could do it, might mean 200 colleges.  (You can also mix this with stratification, for instance selecting the 10 colleges in a stratified way from large coed, small coed, womens,...)

Systematic Random Sample (p.184, problem 3.27)  Using a list, to pick a sample of 1/20 of the list: First pick a number at random from 1,2,....20.  Suppose you get 8.  The 8th individual in the list is the first one in the sample.  Then take every 20th individual after that, numbers 28, 48, 68,....   Advantage: Easy to implement, avoids "clumps" that might occur with SRS.

Sources of bias, even in probability samples:

• Undercoverage: some groups left out or slighted in choosing the sample (cf. sampling frame)
• Nonresponse: some individuals chosen 1) can't be contacted 2) refuse to answer

   Census:  2.3 million uncounted in 2000 (3 million in 1990) estimated...
   Mail surveys:
• Response bias Lies, bad memory, pleasing interviewer (nutrition surveys) Interview technique
• Wording of questions Confusing? Leading? Limiting choices?

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 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.

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

• Control effects of lurking and confounding variables, by comparing treatments, where levels of explanatory variables are controlled, and all other conditions are controlled to be the same.
• Randomize the assignment of units to treatments: reduces possibility of confounding characteristics of exp. units with the treatments.
• Replicate the treatments on many exp. units to reduce the chance of unrepresentative results. (see above)

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