Math 151 , Fall 2007 Monday Day 22, Oct.15 Hit reload....After class.

HW:  Finish Chapter 8.  Optional: p. 200 (Other designs) .  Start Chapter 9, first to p. 224.  Check p. 228: 9.16, 17, 18, 20 (obs/expt, factors:: then 21 (choosing groups), then read p. 224 on, then Check 9.19, 22, 23, 25.
Hand in  Wednesday

p. 205, 8.16, Ask more people
p. 212, 8.50, Polling Hispanics

Chapter 9 ------ ------ -----
p. 229 9.25, 9.26  obsn/expt
p. 215, 9.1, 9.2, 9.3 treatments, factors, response, etc.
p. 216, 9.4 unemployment (confounding)

p. 229 9.27 wine, beer, spirits , diagram design.
p. 230 9.32 a only headache prevention design
p. 231 9.33 fabric finishing, design

Postpone 9.28 and 9.30
p. 230, 9.28 marijuana Use the Simple Random Sample Applet, see below for details, to find who to put in the two groups.  Also: pick just the first 3 people for the "weak" group using Table B at line 131.
p230, 9.30 TV ads  Use the Simple Random Sample Applet, see below for details.

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Hand in Friday: 
Hand in answers to these questions on the "Placebo Effect" articles (outside my door/on reserve): 
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? 
Read, to discuss 

p. 212, 8.49 Canada healthcare

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p. 233, 9.43 quick randomizing 


Optional
 
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Think about this one...
p. 230, 9.29 red wine.  This is a complex experiment with different amounts of polyphenols in different kinds of liquids.
 Doesn't fall neatly into our Factors-value structures?  Think about it a bit...

Exams returned last classSolutions   Solutions also outside my door?. Get yours after class if you weren't here.
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Recap: Sampling  (see days 20, 21)
>>Population: Entire group  that we want information about.
>>Sample: The part of the population we actually examine.
      Hope:  Sample will be representative of the population.
>> Sampling design:  Describes exactly how sample is to be chosen from population.

(SAMPLING) BIAS:  The design of a study is biased if it systematically favors certain outcomes.  
Non-probability samples (sampling badly): Voluntary response sample , Convenience sample

Our main sampling design:
Simple Random Sample
(
SRS) of size n n individuals
chosen in such a way that every possible set of n individuals has an equal chance of being chosen.  See Day 20 for details, table. Simple Random Sample Applet, is easier.  Enter population size, sample size, hit Reset, then Sample.

Some more sources of bias  See Day 21 for details. More discussion.
**Undercoverage:     One possible source of undercoverage: Sampling frame excludes some.
** Nonresponse
**Response bias
**Wording of questions
                         
new today:
 A probability sample (p.200) is from a design where impersonal chance is used to pick the individuals.  SRS is the most straightforward.  More sophisticated methods are often used, but they're optional this term. (More info)
+ + + + + + + +
We want to use the sample to make an inference about the population.  Sample will never exactly represent the population, but larger (RANDOM) samples give more accurate results than smaller random samples.
  (almost always. Quantify "more accurate" and "almost always" in chapter 14.)
(Not in text:  Surprisingly (?), this isn't usually because you have more of the population.  A tablespoon of soup gives a pretty good sample, whether it's from a quart of soup or a 10-gallon vat (as long as it's well-stirred).  A toothpickful does not.

Ch. 9 Designing Experiments
         Observational Study   vs. Experiment  day 20
                Different jargon; different traditions.

Do something to:
    "Experimental Units" = "Subjects" = individuals.
Treatment:  Specific experimental condition we impose on one or more subjects.
Factor: Explanatory Variable we manipulate.
      There will be Specific values of a factor that we set. (Sometimes called "levels")
Response variable(s)  Results that we measure.
    E.g. Corn planting (HW day 14(?), p. 110, 4.28)  1 factor = planting rate.  5 different values (levels). 16 individuals (plots of ground). Response:  yield per acre.

E.g. 2 headache medications, in combination?
A two-factor experiment, each with 3 values (levels). 9 possible treatments.
    Factor A: Aspirin: values: None, 500 mg, 1000 mg
    Factor B: Caffeine: values: 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 differentially 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.
               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" value of the factor.  Should be "just like" the group(s) that get the "treatment" ("real" values 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.

Sometimes (especially in bio, physics, chem experiments)  there is no "control group" --no baseline--just a sequence of different values (like corn planting experiment.)   Moore says "uncontrolled" --which doesn't mean "out of control" :-)
  In these environments also, we make everything else "the same" to try to eliminate confounding/lurking variable effects.

..
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. 218-19: shows where randomizing happens, how many to each treatment, what the treatments are.
Completely randomized: all exp. units allocated at random among the treatments.

E.g. does acupuncture work for Backache??  Response: report of symptoms.
    One factor, 3 values:  None (music??(but might work...!). "Usual treatment"), Acupuncture (wrong places), Acupuncture (right places). 3 treatments.
            (control(s)?)
      30 subjects with Backache:  Randomize, 10 each treatment.  Administer treatments.  Compare symptoms. (Do diagram)
Got to here Monday...
(I'm not making this up.... Backache(1)  (2) )

Picking groups with random number table: Table B. Pick "sample" of size 10 from the 30 for first treatment group.  Pick another "sample" of size 10 for 2nd treatment group, from the remainder.  The 10 remaining get the 3rd treatment. 
Easier with  Simple Random Sample Applet.  Enter total number of subjects in "Population size", enter size of first group in "sample size", hit Reset, then Sample.  Write down the numbers for this sample, it's group 1.  Hit Sample again (DON'T reset) to choose the second group.  Write down the numbers, continue...
Why 10 each, not just 1 each?  Use enough subjects for each treatment so that you can  "average out" (and measure) chance variation in the subjects. 

Principles of designing an experiment (p. 221) See above

More problems, cautions:
Placebo and biasing effects can result from expectations of medical or experimental staff.  "Blind" means subject doesn't know who's getting "real" treatment.  "Double blind" means neither subject, nor staff administering treatment, nor people recording response variables know who's getting which treatment. (Nobody who could influence results in any way.) Most convincing for cause/effect.  (Treatments are coded.  Only people who analyze final results have access to the codes. )

Did you forget to measure something that might be a lurking variable??  Back to the acupuncture/backache experiment.
NY Times Tuesday Science News, p. 10.  "While nearly as many patients receiving a sham form of acupunctur also reported relief, 34% of them needed extra pain pills, compared with just 15% of patients receiving legitimate acupuncture."[and 59% of the control group.]


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