Math 151 , Spring 2005, Day 21 Fri. March 18 Hit reload ...After class

Homework questions? Day 20
Chapter 13: (Observational study +) Experiment: Start: Day 20
Principles of designing a comparative experiment (p. 243)

• Control: Control sources of variation other than our factors, by making everthing else exactly the same. Use specific levels of the factor, same within each group. (unfortunately, limits generalizing to other levels not used)
• Randomize the assignment of units to treatments: reduces possibility of confounding some characteristics of exp. units with the treatments.
• Replicate:  In the single experiment:  replicate the treatments on many exp. units:  Reduce the chance of unrepresentative results, assess the variation within a treatment.

   (Replicate the entire experiment in another time, place, setting, on another group.)
• (Block--not required:  Like stratifying--break into like blocks (M/F, age groups), then do above within each block. )

Completely randomized: all experimental units allocated at random among the treatments.

Diagrams p. 248: show sequence: random allocation, groups: counts and labeled treatments, compare results.
  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.
      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.
(Equal numbers to each treatment group is usually desirable, or roughly equal....)

Bias: issues, how to avoid...
--Subjects are not (usually) a random sample from the population; generalize with care. (Most psychology "facts" were based on studies of Ivy League males, before 1970's.)   But random assignment to treatment groups should "equalize" some biases, differences cancel out.
--"Control" treatment is done to "control" group:  baseline or zero-level treatment to compare to.  (Contrast with "control" of extraneous sources of variation.
--Blinding participants to treatment to prevent prejudgments, expectations, subtle changes.  Don't know which treatment.
     +Those who can influence results (subjects, treatment administrators, technicians, nurses, etc.)
     +Those who evaluate  results (judges, physicans, etc.)
   Single blind:  everyone in one category.  Double blind: everyone in both categories.  (Drug:  bottle labeled by number.  Which is which not revealed till the results are in.)
--Placebo effect:  a real improvement in symptoms and/or disease, resulting from a treatment that "should" have no medicinal effect. Placebo ("I shall please") mimicking real treatment is used as control.
--Confounded variables (p.253): are usually either experiment factors, or one(s) we didn't think about or control for (lurking).   If the levels of two variables "travel together" (so we can't sort out which one an effect is due to) they are "confounded".

Start here Monday
Usually an experiment treats the placebo effect as a potentially 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.

Block designs: (not "completely randomized")
Randomized 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.)
(a "parallel" experiment on each block)
    Within each block, randomize the treatments. Compare results  within each block, then summarize all results.
Diagram p. 251: Branch to blocks first, then diagram sub-experiments.

Matched pairs is a special case of block design--each pair is a little "block":
Matched pairs: In experiment, 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 (find difference), then summarize all comparisons.
  Common: Do the control and experiment to same individual (matched with self). (Randomize which is first, L/R...)   Eliminates extraneous variability.
        Are right feet bigger than left feet? (not an experiment)      Sunburn salve experiment?
Matching is also often used in observational studies: try to match individuals differing only on the potential cause-effect variables, so confounding variables will "subtract away".
&&I don't like the way the answer book diagrams Matched pairs.  Inconsistent with rest.

"Two-factor" (p. 252) vs. "one-factor with blocking" (p.251) &&
  A factor is a variable the experimenter can and does manipulate (aspirin dose level); experimental units get assigned factor levels using randomization.
 A blocking variable is one whose values  "come with" the experimental units and can't be changed by the experimenter (M/F, smoker/nonsmoker, age).  The experimenter can require that a certain number of individuals have the blocking variable values desired ("30 M and 30 F were recruited") but can't impose those characteristics on the individuals. (Can't say "You will be M and you will be F")

~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~
Good practice:  Beware confounding; record everything you can in case it turns out to be important; do pilot experiment.

 Recap:  Goal: Show cause-effect by:  eliminating the influence of all variables except the "cause" one(s).  Then the response variable should measure "effect."  (&&Still need--understanding the mechanism cause-->effect.)
Experiment--best for cause-effect.  "Control what you can, randomize the rest."  But limitations on applicability?  Ethical questions, unrealistic levels, applicability to different groups (Treatment group: smoke 2 packs/day? Hamsters-->humans?)
Observation--Prospective better than Retrospective (selection bias, recollecting bias, etc.)
Sample survey--Broader scope of applicability. May show associations but lurking/confounding variables not controllable. (Usually not after cause-effect; rather after describing population.)