MATH 251, Probability and Statistics I, Fall 2007, Mon. Oct. 1, Day 17 Hit reload After class

Reading:   Chapter 3:  Finish 3.2. Then 3.3.  Ahead, 3.4
Hand in:
A.  Read: Placebo effect articles in folder: In 251 box outside my door or on reserve for Math 151.  Write down two examples of the Placebo effect from the articles.  Part of Day 17.

Sec. 3.2 p. 210ff.
3.12 aspirin design, significance
3.19  fabric finishing
3.21 Random allocation with Applet
3.28   Randomness doesn't guarantee alikeness (Applet)
3.18  x% off?   Use the Applet to choose the subjects (everyone's will be different?) 
3.22  x% off Display of 2-factor results.Sec. 3.2, p. 210ff.

3.15 tea and cataracts Use Table B to assign the rats.
3.35 nature of random digits
Fancier:
3.30 forest CO2
3.31 calcium
3.34 ultramarathon and C
3.32 reducing  For part b, there may be different correct ways to do the random assignment.  You want to avoid having all the lowest-excess-in-their-group people getting plan A, for instance.
+ + +Postpone!!the 3.3 problems+ + + + + +
Sec. 3.3, p. 225ff.
3.36 students
3.41 SRS, use Table B
3.55 sampling frame
3.56 online poll
3.59 why biased?
 Read, discuss 
3.14, 3.16
  + + + + 

 3.37, 3.38

 Optional 

 
HW Questions?  Day 16
Pick a digit, from 0,1,2,3,4,5,6,7,8,9.  Write it down.

Data analysis project, See Day 15.  Preliminary report due Friday morning!
Some more on data sources?

Dr. Pericak-Vance, Friday's Science Colloquium: 
--When you find a gene you think is implicated (in a disease), you have to go to a new set of data to confirm it:  Exploratory/Confirmatory.
--When you search a million items for the rarity we say should be "significance" (not likely to have occurred just by chance), ten thousand will be "one in a hundred" rare, just by chance.  What do you do then? (A serious issue for modern science.)

Ch. 3:  Producing Data:  Aim:  create data sets that will allow us to make inferences to a larger world than just the data we have.
Design of experiments Sec 3.2       Day 15

Principles of designing an experiment (p. 203) Control Randomize Repeat
  "Control what you can, Randomize the rest."

Day 16 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.  (Sec. 3.3)
Fancier Experimental designs (not "completely randomized") Matched pairs: Block design: 

= = = = = =Start here Wed: = = = = = = = =
Sampling Design Sec 3.3 (Observational study, usually)  "Sample survey"
>>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) BIAS:  The design of a study is biased if it systematically favors certain outcomes.
    Check our "sample" of digits  Pickadigit

Probability sample: sample chosen by an impersonal chance mechanism
Some refinements:
*Sampling frame: IPS p. 230 problem 3.55: the group from which the sample is actually chosen--as different from the "population"--the group you want information about. The sampling frame is often, unfortunately, smaller than the population.  The sample is (usually much) smaller than the sampling frame.
* "Chosen" sample may not turn out to be actual sample, if some individuals don't respond--"Nonresponse", p. 222.

Non-probability samples:

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. Details Day 16

Sources of bias, even in probability samples:

Next:  some fancier sampling designs:  Systematic, Stratified, Multistage
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