Math 151 , Spring 2006, Day 22 Mon. March 26 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. 
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, d will NOT be covered. (b, c 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 tonight's HW, exam: Ch 13: pp. 241-247 (but not Blocks, p.245), Expts& samples p. 249, Control treatments p. 249, Placebo p. 250, Adding more factors p. 252-3.
Hand in Wednesday Chapter 13   p257ff.
1,2,4,5,6,10,11,12,17,18   Do a: Decide if it is an observational study or an experiment.  If it was an observational = "investigative" study answer that b,c,d,e.  (We'll complete the experiment ones later; start the experiment ones on a separate page and keep it, answering the questions you can so far.   1, 6, 17 are (completely randomized) experiments: do b,c,d,e now for these. (answer for 17
25 Wine
24 Full moon
- - - - - - - - - 
Hand in answers to these questions on the "Placebo Effect" articles (outside my door/on reserve) Hand in WEDNESDAY: 
a) Give two examples of the placebo effect (from the article!)
b) What do researchers believe causes the placebo effect? 
c) In the separate article: "Pill will make you feel better...," what country was surveyed?
- - - - - - - - - - -
31 Weekend deaths
21 Mozart do a, read b, do c, d
26 Swimming do a,  b, c

(Check your answers to the first problems: 4,5,10,11,12 are observational.)

x x x x x x x x x x x x x x x

Postpone the rest

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 it when we look at the other designs.
Read,
  to 
discuss 


(review, ch.12) p. 239 #13 Wording
the survey
 

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 21  Circulate your random samples from Old Faithful data?  Lines for n = 20 pretty close to population regression line?  For n = 5 only roughly similar.
Sampling, finished on Friday

Sources of Bias in sampling: any systematic failure of a sample (or its method) to represent its population.  (E.g. sampling frame excludes "different" part of population.)  see Day 21

HW #21: Are we running a risk if we take the same (place) bottle from each case? (Maybe.  Environment effects?  Deliberate "stacking" of bottles?)

Using Random Number Table to sample (p. A-49)      Every digit, every sequence of digits, is equally likely to be "next" in any direction.   see Day 21

= = = = = = = = = = = = = = = = = = = = = = = = = =
D&V Ch13  Goal:  show cause-and-effect. Predictor-->Response
Observational Study:  Observe individuals; don't do anything to them; do not influence the responses.  Can indicate strength of relationship, differences, but not cause and effect.  (Often not with samples, but with selected group(s).)  Lurking variables?!? (Fisher:  Smokers smoke to soothe irritabilities that may cause cancer.)
         Retrospective:  gather data after the fact (observe that x% of men hospitalized with heart disease were/are smokers)
         Prospective:  choose individuals in advance. Measure them; or follow them as events happen.  (Framingham Heart Study: 5,209 (2,873 women and 2,336 men) healthy residents between 30 and 60 years of age.  Followed from 1948 to now. A second-generation cohort recruited 1971, Minority group 1995  http://www.framingham.com/heart/)

Experiment: Impose treatments  on individuals, to see how the treatment influences  the response.
Compare treatments' effects.
Do something to:    "Experimental Units" = "Subjects"
   Treatment:  A Specific experimental condition.
   Factor: = Explanatory (Predictor) Variable that 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

E.g. (Day 14, MRA-95-13 )Corn yield= response variable.  One Factor = Planting rate.  5 Levels=the rates.

Principles of designing a comparative experiment (p. 243)

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:  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.

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

Got to here today (Monday).

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.

Next--designs other than completely randomized

~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~
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.)

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