Math 151 , Fall 2002, Friday Day 21, Oct. 18 Hit reload to get most current versionAfter class-late, Sorry!

HW assignment Day 21
Reading: ReRead section  3.2, Read Significance, Matched pairs and block design; review ch. 3.
    Next:  4.1, 2, 3.  We'll do  4.1, 2, 3.  Skip 4.4 and Skip Ch. 5.

Hand in:  From Moore Postpone 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 they don't have "charts") = = = = = = = = = = = = = = = =   Significance  p. 195 3.40

Read, to discuss  Matched pairs and blocks  p. 209 3.72 McDonald's vs Wendy's    p. 209 3.71speeding the mail      = = = = = = = = = = p. 209 3.74 Significance

Optional  (more of same)  p. 203, 3.58  3.59

Activstats Chapter 12 "Experience with randomness", pp. 1-2 I prefer to say "chance behavior" because "randomness" carries the flavor of equally likely, which is usually not the case. Anyway , do all 4 activities here.
= = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = =
Continuing Design of Experiments:
HW questions?

Placebo effect article:
a) Give two examples of the placebo effect
b) What do researchers believe causes the placebo effect?

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.

Principles of designing an experiment (p. 143/ACT 11-1)

• 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 below)

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

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 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".)

Not in text:  In practice, the ideal requirements may not be met:  Sometimes the treatment cannot be deliberately  imposed and we must observe it (and the response) when it happens. (Can't force people to smoke.)
"Prospective study--retrospective study."
--Prospective:  You get your subjects before something  (e.g. disease) happens to them, can get information from them.  Then it happens (or doesn't).  E.g. enlist 1000 women, collect info, wait 5 years.  See who gets the disease.  More like an experiment than
--Retrospective:  Ask people with/without disease what they were/are like.  (Problems: Reliability of remembered info,  matching,  sampling)  (My mother's headaches)

Ch. 4, Probability and Sampling Distributions.
Chance  behavior (a random phenomenon): Unpredictable in the short run,  predictable regular pattern in the long run.
  (Random numbers:  equally likely in the long run.  "Random" here is more general--pattern is not necessarily equally likely)
25 digits from the random number table:  More variability, less "flat" than you'd think.  But everyone's variability is different.  Next time: all results pooled.