Math 151 , Spring 2006, Day 23 Wed. March 29 Hit reload ...After class

Exam 2 this Friday (Day 24).  Covers Normal tables: raw<-->percentiles (Day 13 HW), thru  today's (Day 22) HW. Ch. 13; Probably covers obs. study vs. expt, (retro/prospective),  "Treatment, Factor, Level, Response variable" , "statistical significance",  "Control, Randomize, Replicate." Placebo effect.  Watch this space for any changes. No changes
Alternate exam time:  If you want/need extra time, you may stay late after class.  If that doesn't work for you, you may start early (after 9:30 Fri. ) or take it Fri. afternoon--sign up Wed. in class.  If neither of those work, get in touch with me by email or in person, by Wed. aft.
Sample exam handed out day 21 #7, a, c,d will NOT be covered. (b  may be) Substitute p.259 # 17, b,c,d e: solutions outside my door, + on reserve (soon) Scanned solutions: first attempt, as image files.  Email me if you have trouble with viewing them.  Page1,#1Page2,#2&3Page3,#4,5,&6Page4,#7a,bPage5,#7c,d&8. Page6,#9Page7,#10
How much computational detail from part II?  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 properties pp.121-2.You will need to know, among other things,  how to find b0 and b1 from the means, standard deviations, and r of the x-and y-values,  and to give the formula for the regression line, (like 17, p.154); 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 (negative if the point is below the line), and identify and understand potential influential points.  You should know  that the regression line goes through the point given by the two means, and that the  regression line "rises" r standard deviations in y for each standard deviation increase in x (pp. 137-8); also that the regression line of "weight" on "height" is not the same line as the regression line of "height" on "weight" . You should be able to describe verbally the meaning of R2 in the context of a data set.  "Extrapolation", other details from Ch. 9.
Reading: For Monday's HW: D&V Ch 13: rest of Ch. 13. Review part III p. 262.  AS 13.
Hand in Monday(?) Chapter 13   p257ff.
21 Mozart do b
26 Swimming do d (be clear about what state re depression your subjects should be in to start with)
33 Beetles  (+ make diagram ) 
32 a, b, c  Shingles
On the separate page and keep it:
1,2,4,5,6,10,11,12,17,18 .  Work on the experiment ones now: Do b,c,d,e, g, h, and see if you can pick out which ones are completely randomized (part of f)  We'll finish them when we look at the other designs.
- - - - - - - - - -
Postpone:
Other designs: 
1,2,4,5,6,10,11,12, 17, 18  Finish these for those that are experiments .
32 d Shingles, "better" design 
35 Safety switch
36 Washing clothes

From Review part III, p. 263ff.

26 Laundry
34 Pubs
Read,
  to 
discuss 


Review Part III: 
p. 263 ff: 1 thru 
17 odds, +12, 18 
 

Optional 

Fay's hours: Fay writes: " An emergency has come up and I will have to reschedule myWednesday hours. I will be here from 1 (maybe 1.30) until 3." [SRS says: I can work with you 12:30 on]
Fay's Review Session - a reminder. "There will be a session on Thursday night at 7pm in the Math Clinic. Make sure to go through the practice exam and bring questions."
Homework questions? Day 22
General exam questions?
= = = = = = = = = = = = = = = = = = = = = = = = = =

D&V Ch13  Goal:  show cause-and-effect. Predictor-->Response
Observational study/experiment, Intro to Experiment, Day 22

Experiment: "Experimental Units" = "Subjects" , Treatment,    Factor: Levels
   Response variable(s)

Principles of designing a comparative experiment (p. 243)  Control Randomize, Replicate: (Block--shortly )
Results: 
Measure differences in the response variable for different treatments (e.g. side by side boxplots)

 "Statistically Significant" differences--too big to have plausibly occurred by chance (compare differences to variability within treatment)  We'll quantify later.
Placebo effect.
Exam covers to here.

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 is 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".

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 articles).
        Acupuncture (wrong) vs. Music.
Start here Monday
~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~
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 aimed at cause-effect; rather aimed at describing population.)

~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~
Next--designs other than completely randomized
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.  (Things we can't alter: 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")


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