Math 151 , Spring '12 Wednesday Day 22, March 14 Hit reload..... After class...

Exam 2 handed back.  Link to statistics, comments, solutions.  A few more comments on content today?
Midterm grades will be posted by Friday afternoon; will be slanted pessimistically at the high end.
Because it's so important to have control of the Normal distribution:
Makeup work to get 90% of the 42 Normal distribution points.  To me by 3:30 pm Day 27 (Monday, April 2; Monday after Monday after Break).  START NOW!  (Print the sheet if you need it.)
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recap: Ch. 8&9:  Producing Data:  Aim:  create data sets that will allow us to make inferences to a larger world than just the data we have.

(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.

 Using Random Number Table. See Day 20 for details. 
      (Simple Random Sample Applet, is easier.  Enter population size, sample size, hit Reset, then Sample.)
See  Day 20 for rest of details on Ch. 8:
Some more sources of bias:  
**Undercoverage:     One possible source of undercoverage: your Sampling frame excludes some individuals.
** Nonresponse
**Response bias
**Wording of questions                         
 A random 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)
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Larger (RANDOM) samples give more accurate results than smaller random samples.
  (but Not because you have more of the population.)

--Pick-a-digit: results from random number table (scroll down)
--p. 209 8.7: Sample of size 6:--East Asian surnames:  14 good answers:  3 people (21%) got 0 names , 7 (50%) got 1, 4 (29%) got 2 names.    In population, 5/28 had E.Asian surname; How many do we expect in sample of 6?  5/28 =x/6:  x = 1.07.  Samples weren't too bad.
Homework Questions Day 21 
 More discussion of terms used in sampling

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Chapter 9, intro
Observational Study:  Observes individuals, measures variables, does not influence the responses. (ch.8) 
                 Sometimes observe individuals who are (more or less) conveniently at hand, or, better,
                  Take Sample from a population, examine it.... (ch.8)
  Experiment: Imposes treatment  on individuals, to see how the treatment influences  the response. (ch.9)   Confounding:  Two variables (explanatory or lurking) are confounded when you can't sort out their effects on a response variable.  (Rats:  Mothers' grooming causes sociability, or inherited sociability from mothers who like to groom? Health: Coffee and cigarettes (till recently)).

Designing Experiments      
                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 ??, p. 116, 4.32)  1 factor = planting rate.  5 different values (levels). 16 individuals ="Experimental Units" (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   caffeine contents
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 treatments 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" treatment ="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.  If there is a sequence of different values we're comparing, (like corn planting experiment?) it is still a comparative experiment.    (Occasionally in "hard" science, there is just one "treatment."  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. 229, 231: shows where randomizing happens, how many to each treatment, what the treatments are.
Completely randomized: all experimental 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 (did) diagram)


Look at example next time: (I'm not making this up.... Backache(1)  (2) Sept. 2007)

"In a study of 1,162 adults with chronic lower back pain, 48 percent of those in a group who underwent between 10 and 15 treatments with traditional Chinese "verum" acupuncture reported at least one-third less pain and an improvement in functional ability, with lasting benefits.  ...
That compared to 27 percent of those reporting relief in the group undergoing drug and exercise therapy.

A third group of patients underwent so-called sham acupuncture, where needles are inserted randomly and less deeply around the painful area while avoiding the medians. Of these, 44 percent reported relief from their back pain -- more patients than conventional therapy and only slightly fewer than traditional acupuncture."

Did picking today (Wed.) 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...

.Continue here Friday..
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.  Corn planting  If we only did one plot at each rate--chance might "show" us a different relationship.

Principles of designing an experiment (p. 233) See above

• Control effects of lurking and confounding variables, by comparing treatments, where values of explanatory variables (=factors) are controlled, and all other conditions are controlled to be the same. ("comparative experiment")
  
• Randomize the assignment of individuals to treatments: reduces possibility of confounding characteristics of individuals with the treatments.
• Use enough subjects  for each treatment to reduce the chance of unrepresentative results. (see above)